%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL036-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:48:52 AM UTC 2026
% Result : Unsatisfiable 1.60s 0.64s
% Output : Proof 118.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL036-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n026.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sun Sep 27 15:21:11 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.60/0.64 Command-line arguments: --no-flatten-goal
% 1.60/0.64
% 1.60/0.64 % SZS status Unsatisfiable
% 1.60/0.64
% 100.34/14.08 % SZS output start Proof
% 100.34/14.08 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 100.34/14.08 Axiom 2 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 101.03/14.29 Axiom 3 (c0_CAMeredith): is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X)))) = true.
% 101.03/14.29
% 101.03/14.29 Goal 1 (prove_c0_5): is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)) = true.
% 101.03/14.29 Proof:
% 101.03/14.29 is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a))
% 101.03/14.29 = { by axiom 1 (ifeq_axiom) R->L }
% 101.03/14.29 ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.03/14.29 = { by axiom 2 (condensed_detachment) R->L }
% 101.03/14.29 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.03/14.29 = { by axiom 1 (ifeq_axiom) R->L }
% 101.03/14.29 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.03/14.29 = { by axiom 2 (condensed_detachment) R->L }
% 101.03/14.29 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.03/14.29 = { by axiom 3 (c0_CAMeredith) }
% 101.03/14.29 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.03/14.30 = { by axiom 1 (ifeq_axiom) }
% 101.03/14.30 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.03/14.30 = { by axiom 1 (ifeq_axiom) R->L }
% 101.03/14.30 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.30 = { by axiom 2 (condensed_detachment) R->L }
% 101.44/14.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(falsehood, implies(W, V))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.30 = { by axiom 1 (ifeq_axiom) R->L }
% 101.44/14.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(W, V))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.31 = { by axiom 2 (condensed_detachment) R->L }
% 101.44/14.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, falsehood), implies(W, falsehood)), implies(falsehood, U)), implies(T, implies(falsehood, U))), implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(W, falsehood)), implies(falsehood, U)), implies(T, implies(falsehood, U)))), true, is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true), true), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.31 = { by axiom 3 (c0_CAMeredith) }
% 101.44/14.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(W, falsehood)), implies(falsehood, U)), implies(T, implies(falsehood, U)))), true, is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true), true), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.31 = { by axiom 1 (ifeq_axiom) }
% 101.44/14.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(W, falsehood)), implies(falsehood, U)), implies(T, implies(falsehood, U)))), true, is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.32 = { by axiom 1 (ifeq_axiom) R->L }
% 101.44/14.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(W, falsehood)), implies(falsehood, U)), implies(T, implies(falsehood, U)))), true), true, is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.32 = { by axiom 3 (c0_CAMeredith) R->L }
% 101.44/14.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, U), implies(W, falsehood)), implies(T, falsehood)), V), implies(implies(V, falsehood), implies(W, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(W, falsehood)), implies(falsehood, U)), implies(T, implies(falsehood, U)))), true), true, is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.32 = { by axiom 1 (ifeq_axiom) R->L }
% 101.44/14.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, U), implies(W, falsehood)), implies(T, falsehood)), V), implies(implies(V, falsehood), implies(W, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(W, falsehood)), implies(falsehood, U)), implies(T, implies(falsehood, U)))), true), true), true, is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.33 = { by axiom 3 (c0_CAMeredith) R->L }
% 101.44/14.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, U), implies(W, falsehood)), implies(T, falsehood)), V), implies(implies(V, falsehood), implies(W, falsehood))), implies(implies(implies(implies(V, falsehood), implies(W, falsehood)), implies(falsehood, U)), implies(T, implies(falsehood, U))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, U), implies(W, falsehood)), implies(T, falsehood)), V), implies(implies(V, falsehood), implies(W, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(W, falsehood)), implies(falsehood, U)), implies(T, implies(falsehood, U)))), true), true), true, is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.33 = { by axiom 2 (condensed_detachment) }
% 101.44/14.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.33 = { by axiom 1 (ifeq_axiom) }
% 101.44/14.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.34 = { by axiom 1 (ifeq_axiom) R->L }
% 101.44/14.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.34 = { by axiom 2 (condensed_detachment) R->L }
% 101.44/14.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V)), implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.34 = { by axiom 3 (c0_CAMeredith) }
% 101.44/14.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.35 = { by axiom 1 (ifeq_axiom) }
% 101.44/14.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.35 = { by axiom 1 (ifeq_axiom) R->L }
% 101.44/14.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.36 = { by axiom 2 (condensed_detachment) R->L }
% 101.44/14.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(implies(implies(W, V), S), falsehood)), V), implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood))), implies(implies(implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(W, V), S), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(implies(implies(W, V), S), falsehood)), V), implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(W, V), S), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.38 = { by axiom 3 (c0_CAMeredith) }
% 101.44/14.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(implies(implies(W, V), S), falsehood)), V), implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(W, V), S), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.39 = { by axiom 1 (ifeq_axiom) }
% 101.44/14.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(implies(implies(W, V), S), falsehood)), V), implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(W, V), S), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.39 = { by axiom 3 (c0_CAMeredith) }
% 101.44/14.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(W, V), S), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.39 = { by axiom 1 (ifeq_axiom) }
% 101.44/14.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(W, V), S), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.44/14.40 = { by axiom 1 (ifeq_axiom) R->L }
% 101.84/14.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(W, V), S), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.40 = { by axiom 3 (c0_CAMeredith) R->L }
% 101.84/14.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(W, V), S), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V, falsehood), implies(implies(T, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(W, V), S), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(W, V), S), implies(falsehood, falsehood)), V), implies(implies(T, implies(falsehood, U)), V))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.41 = { by axiom 2 (condensed_detachment) }
% 101.84/14.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.41 = { by axiom 1 (ifeq_axiom) }
% 101.84/14.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V)), implies(falsehood, implies(W, V)))), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(falsehood, U)), V), implies(W, V))), true, is_a_theorem(implies(falsehood, implies(W, V))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.41 = { by axiom 2 (condensed_detachment) }
% 101.84/14.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.42 = { by axiom 1 (ifeq_axiom) }
% 101.84/14.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.42 = { by axiom 1 (ifeq_axiom) R->L }
% 101.84/14.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.43 = { by axiom 2 (condensed_detachment) R->L }
% 101.84/14.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), falsehood)), implies(implies(falsehood, implies(W, V)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), falsehood)), implies(implies(falsehood, implies(W, V)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.43 = { by axiom 3 (c0_CAMeredith) }
% 101.84/14.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), falsehood)), implies(implies(falsehood, implies(W, V)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.44 = { by axiom 1 (ifeq_axiom) }
% 101.84/14.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), falsehood)), implies(implies(falsehood, implies(W, V)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.45 = { by axiom 3 (c0_CAMeredith) }
% 101.84/14.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.45 = { by axiom 1 (ifeq_axiom) }
% 101.84/14.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.46 = { by axiom 1 (ifeq_axiom) R->L }
% 101.84/14.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.47 = { by axiom 2 (condensed_detachment) R->L }
% 101.84/14.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.48 = { by axiom 3 (c0_CAMeredith) }
% 101.84/14.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.49 = { by axiom 1 (ifeq_axiom) }
% 101.84/14.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 101.84/14.50 = { by axiom 1 (ifeq_axiom) R->L }
% 102.24/14.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.24/14.51 = { by axiom 2 (condensed_detachment) R->L }
% 102.24/14.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.24/14.52 = { by axiom 3 (c0_CAMeredith) }
% 102.24/14.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.24/14.53 = { by axiom 1 (ifeq_axiom) }
% 102.24/14.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.24/14.54 = { by axiom 1 (ifeq_axiom) R->L }
% 102.24/14.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.24/14.56 = { by axiom 3 (c0_CAMeredith) R->L }
% 102.24/14.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.24/14.57 = { by axiom 1 (ifeq_axiom) R->L }
% 102.24/14.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.24/14.58 = { by axiom 3 (c0_CAMeredith) R->L }
% 102.24/14.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.24/14.59 = { by axiom 2 (condensed_detachment) }
% 102.24/14.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.60 = { by axiom 1 (ifeq_axiom) }
% 102.65/14.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.61 = { by axiom 1 (ifeq_axiom) R->L }
% 102.65/14.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.62 = { by axiom 3 (c0_CAMeredith) R->L }
% 102.65/14.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), Y2), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), X2), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.62 = { by axiom 2 (condensed_detachment) }
% 102.65/14.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.63 = { by axiom 1 (ifeq_axiom) }
% 102.65/14.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(falsehood, implies(W, V)), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.63 = { by axiom 2 (condensed_detachment) }
% 102.65/14.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.63 = { by axiom 1 (ifeq_axiom) }
% 102.65/14.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.63 = { by axiom 1 (ifeq_axiom) R->L }
% 102.65/14.64 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.64 = { by axiom 3 (c0_CAMeredith) R->L }
% 102.65/14.64 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), Z), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), a), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.64 = { by axiom 2 (condensed_detachment) }
% 102.65/14.64 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.64 = { by axiom 1 (ifeq_axiom) }
% 102.65/14.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.64 = { by axiom 1 (ifeq_axiom) R->L }
% 102.65/14.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.64 = { by axiom 2 (condensed_detachment) R->L }
% 102.65/14.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(is_a_theorem(implies(falsehood, implies(Z2, W2))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.65 = { by axiom 1 (ifeq_axiom) R->L }
% 102.65/14.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.65 = { by axiom 2 (condensed_detachment) R->L }
% 102.65/14.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W2, falsehood), implies(Z2, falsehood)), implies(falsehood, V2)), implies(U2, implies(falsehood, V2))), implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(Z2, falsehood)), implies(falsehood, V2)), implies(U2, implies(falsehood, V2)))), true, is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true), true), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.65 = { by axiom 3 (c0_CAMeredith) }
% 102.65/14.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(Z2, falsehood)), implies(falsehood, V2)), implies(U2, implies(falsehood, V2)))), true, is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true), true), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.65 = { by axiom 1 (ifeq_axiom) }
% 102.65/14.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(Z2, falsehood)), implies(falsehood, V2)), implies(U2, implies(falsehood, V2)))), true, is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.66 = { by axiom 1 (ifeq_axiom) R->L }
% 102.65/14.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(Z2, falsehood)), implies(falsehood, V2)), implies(U2, implies(falsehood, V2)))), true), true, is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.66 = { by axiom 3 (c0_CAMeredith) R->L }
% 102.65/14.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V2), implies(Z2, falsehood)), implies(U2, falsehood)), W2), implies(implies(W2, falsehood), implies(Z2, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(Z2, falsehood)), implies(falsehood, V2)), implies(U2, implies(falsehood, V2)))), true), true, is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.66 = { by axiom 1 (ifeq_axiom) R->L }
% 102.65/14.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V2), implies(Z2, falsehood)), implies(U2, falsehood)), W2), implies(implies(W2, falsehood), implies(Z2, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(Z2, falsehood)), implies(falsehood, V2)), implies(U2, implies(falsehood, V2)))), true), true), true, is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.66 = { by axiom 3 (c0_CAMeredith) R->L }
% 102.65/14.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V2), implies(Z2, falsehood)), implies(U2, falsehood)), W2), implies(implies(W2, falsehood), implies(Z2, falsehood))), implies(implies(implies(implies(W2, falsehood), implies(Z2, falsehood)), implies(falsehood, V2)), implies(U2, implies(falsehood, V2))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V2), implies(Z2, falsehood)), implies(U2, falsehood)), W2), implies(implies(W2, falsehood), implies(Z2, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(Z2, falsehood)), implies(falsehood, V2)), implies(U2, implies(falsehood, V2)))), true), true), true, is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.67 = { by axiom 2 (condensed_detachment) }
% 102.65/14.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.67 = { by axiom 1 (ifeq_axiom) }
% 102.65/14.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.67 = { by axiom 1 (ifeq_axiom) R->L }
% 102.65/14.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.67 = { by axiom 2 (condensed_detachment) R->L }
% 102.65/14.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2)), implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.68 = { by axiom 3 (c0_CAMeredith) }
% 102.65/14.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.68 = { by axiom 1 (ifeq_axiom) }
% 102.65/14.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.68 = { by axiom 1 (ifeq_axiom) R->L }
% 102.65/14.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.69 = { by axiom 2 (condensed_detachment) R->L }
% 102.65/14.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(implies(implies(Z2, W2), T2), falsehood)), W2), implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood))), implies(implies(implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(implies(implies(Z2, W2), T2), falsehood)), W2), implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.69 = { by axiom 3 (c0_CAMeredith) }
% 102.65/14.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(implies(implies(Z2, W2), T2), falsehood)), W2), implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.70 = { by axiom 1 (ifeq_axiom) }
% 102.65/14.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(implies(implies(Z2, W2), T2), falsehood)), W2), implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 102.65/14.70 = { by axiom 3 (c0_CAMeredith) }
% 103.05/14.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.70 = { by axiom 1 (ifeq_axiom) }
% 103.05/14.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.70 = { by axiom 1 (ifeq_axiom) R->L }
% 103.05/14.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.71 = { by axiom 3 (c0_CAMeredith) R->L }
% 103.05/14.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, falsehood), implies(implies(U2, implies(falsehood, V2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z2, W2), T2), implies(falsehood, falsehood)), W2), implies(implies(U2, implies(falsehood, V2)), W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.71 = { by axiom 2 (condensed_detachment) }
% 103.05/14.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.71 = { by axiom 1 (ifeq_axiom) }
% 103.05/14.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2)), implies(falsehood, implies(Z2, W2)))), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(falsehood, V2)), W2), implies(Z2, W2))), true, is_a_theorem(implies(falsehood, implies(Z2, W2))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.72 = { by axiom 2 (condensed_detachment) }
% 103.05/14.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.72 = { by axiom 1 (ifeq_axiom) }
% 103.05/14.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.72 = { by axiom 1 (ifeq_axiom) R->L }
% 103.05/14.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.72 = { by axiom 2 (condensed_detachment) R->L }
% 103.05/14.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(falsehood, implies(Z2, W2)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(falsehood, implies(Z2, W2)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.73 = { by axiom 3 (c0_CAMeredith) }
% 103.05/14.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(falsehood, implies(Z2, W2)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.73 = { by axiom 1 (ifeq_axiom) }
% 103.05/14.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(falsehood, implies(Z2, W2)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.73 = { by axiom 3 (c0_CAMeredith) }
% 103.05/14.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.74 = { by axiom 1 (ifeq_axiom) }
% 103.05/14.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.74 = { by axiom 1 (ifeq_axiom) R->L }
% 103.05/14.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.75 = { by axiom 2 (condensed_detachment) R->L }
% 103.05/14.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.75 = { by axiom 3 (c0_CAMeredith) }
% 103.05/14.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.76 = { by axiom 1 (ifeq_axiom) }
% 103.05/14.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.76 = { by axiom 1 (ifeq_axiom) R->L }
% 103.05/14.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.77 = { by axiom 2 (condensed_detachment) R->L }
% 103.05/14.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.77 = { by axiom 3 (c0_CAMeredith) }
% 103.05/14.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.78 = { by axiom 1 (ifeq_axiom) }
% 103.05/14.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.79 = { by axiom 1 (ifeq_axiom) R->L }
% 103.05/14.79 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.05/14.79 = { by axiom 3 (c0_CAMeredith) R->L }
% 103.05/14.80 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.80 = { by axiom 1 (ifeq_axiom) R->L }
% 103.47/14.80 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.81 = { by axiom 3 (c0_CAMeredith) R->L }
% 103.47/14.81 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood), falsehood), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.81 = { by axiom 2 (condensed_detachment) }
% 103.47/14.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.82 = { by axiom 1 (ifeq_axiom) }
% 103.47/14.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.82 = { by axiom 1 (ifeq_axiom) R->L }
% 103.47/14.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.83 = { by axiom 3 (c0_CAMeredith) R->L }
% 103.47/14.83 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), X3), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)), S2), implies(implies(implies(implies(a, falsehood), falsehood), a), falsehood)), implies(implies(implies(a, falsehood), falsehood), a)), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.83 = { by axiom 2 (condensed_detachment) }
% 103.47/14.83 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.83 = { by axiom 1 (ifeq_axiom) }
% 103.47/14.83 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, is_a_theorem(implies(implies(falsehood, implies(Z2, W2)), implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.83 = { by axiom 2 (condensed_detachment) }
% 103.47/14.83 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.83 = { by axiom 1 (ifeq_axiom) }
% 103.47/14.83 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true, is_a_theorem(implies(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.83 = { by axiom 2 (condensed_detachment) }
% 103.47/14.83 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.84 = { by axiom 1 (ifeq_axiom) }
% 103.47/14.84 ifeq(ifeq(is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.84 = { by axiom 1 (ifeq_axiom) R->L }
% 103.47/14.84 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.84 = { by axiom 2 (condensed_detachment) R->L }
% 103.47/14.84 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.84 = { by axiom 3 (c0_CAMeredith) }
% 103.47/14.84 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.84 = { by axiom 1 (ifeq_axiom) }
% 103.47/14.84 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.84 = { by axiom 1 (ifeq_axiom) R->L }
% 103.47/14.84 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.84 = { by axiom 2 (condensed_detachment) R->L }
% 103.47/14.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.84 = { by axiom 3 (c0_CAMeredith) }
% 103.47/14.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.85 = { by axiom 1 (ifeq_axiom) }
% 103.47/14.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.85 = { by axiom 1 (ifeq_axiom) R->L }
% 103.47/14.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.85 = { by axiom 2 (condensed_detachment) R->L }
% 103.47/14.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.86 = { by axiom 3 (c0_CAMeredith) }
% 103.47/14.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.86 = { by axiom 1 (ifeq_axiom) }
% 103.47/14.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.87 = { by axiom 1 (ifeq_axiom) R->L }
% 103.47/14.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.87 = { by axiom 2 (condensed_detachment) R->L }
% 103.47/14.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(falsehood, implies(U3, T3))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.88 = { by axiom 1 (ifeq_axiom) R->L }
% 103.47/14.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.88 = { by axiom 2 (condensed_detachment) R->L }
% 103.47/14.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T3, falsehood), implies(U3, falsehood)), implies(falsehood, S3)), implies(X4, implies(falsehood, S3))), implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(U3, falsehood)), implies(falsehood, S3)), implies(X4, implies(falsehood, S3)))), true, is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true), true), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.89 = { by axiom 3 (c0_CAMeredith) }
% 103.47/14.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(U3, falsehood)), implies(falsehood, S3)), implies(X4, implies(falsehood, S3)))), true, is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true), true), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.47/14.90 = { by axiom 1 (ifeq_axiom) }
% 103.88/14.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(U3, falsehood)), implies(falsehood, S3)), implies(X4, implies(falsehood, S3)))), true, is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.90 = { by axiom 1 (ifeq_axiom) R->L }
% 103.88/14.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(U3, falsehood)), implies(falsehood, S3)), implies(X4, implies(falsehood, S3)))), true), true, is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.91 = { by axiom 3 (c0_CAMeredith) R->L }
% 103.88/14.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S3), implies(U3, falsehood)), implies(X4, falsehood)), T3), implies(implies(T3, falsehood), implies(U3, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(U3, falsehood)), implies(falsehood, S3)), implies(X4, implies(falsehood, S3)))), true), true, is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.92 = { by axiom 1 (ifeq_axiom) R->L }
% 103.88/14.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S3), implies(U3, falsehood)), implies(X4, falsehood)), T3), implies(implies(T3, falsehood), implies(U3, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(U3, falsehood)), implies(falsehood, S3)), implies(X4, implies(falsehood, S3)))), true), true), true, is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.92 = { by axiom 3 (c0_CAMeredith) R->L }
% 103.88/14.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, S3), implies(U3, falsehood)), implies(X4, falsehood)), T3), implies(implies(T3, falsehood), implies(U3, falsehood))), implies(implies(implies(implies(T3, falsehood), implies(U3, falsehood)), implies(falsehood, S3)), implies(X4, implies(falsehood, S3))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S3), implies(U3, falsehood)), implies(X4, falsehood)), T3), implies(implies(T3, falsehood), implies(U3, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(U3, falsehood)), implies(falsehood, S3)), implies(X4, implies(falsehood, S3)))), true), true), true, is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.93 = { by axiom 2 (condensed_detachment) }
% 103.88/14.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.94 = { by axiom 1 (ifeq_axiom) }
% 103.88/14.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.95 = { by axiom 1 (ifeq_axiom) R->L }
% 103.88/14.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.95 = { by axiom 2 (condensed_detachment) R->L }
% 103.88/14.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3)), implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.96 = { by axiom 3 (c0_CAMeredith) }
% 103.88/14.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.97 = { by axiom 1 (ifeq_axiom) }
% 103.88/14.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.97 = { by axiom 1 (ifeq_axiom) R->L }
% 103.88/14.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.98 = { by axiom 2 (condensed_detachment) R->L }
% 103.88/14.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(implies(implies(U3, T3), Y4), falsehood)), T3), implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood))), implies(implies(implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(implies(implies(U3, T3), Y4), falsehood)), T3), implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/14.99 = { by axiom 3 (c0_CAMeredith) }
% 103.88/15.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(implies(implies(U3, T3), Y4), falsehood)), T3), implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/15.00 = { by axiom 1 (ifeq_axiom) }
% 103.88/15.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(implies(implies(U3, T3), Y4), falsehood)), T3), implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/15.01 = { by axiom 3 (c0_CAMeredith) }
% 103.88/15.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/15.01 = { by axiom 1 (ifeq_axiom) }
% 103.88/15.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/15.02 = { by axiom 1 (ifeq_axiom) R->L }
% 103.88/15.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 103.88/15.03 = { by axiom 3 (c0_CAMeredith) R->L }
% 104.41/15.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, falsehood), implies(implies(X4, implies(falsehood, S3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(U3, T3), Y4), implies(falsehood, falsehood)), T3), implies(implies(X4, implies(falsehood, S3)), T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.41/15.03 = { by axiom 2 (condensed_detachment) }
% 104.41/15.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.41/15.04 = { by axiom 1 (ifeq_axiom) }
% 104.41/15.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3)), implies(falsehood, implies(U3, T3)))), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(falsehood, S3)), T3), implies(U3, T3))), true, is_a_theorem(implies(falsehood, implies(U3, T3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.41/15.05 = { by axiom 2 (condensed_detachment) }
% 104.41/15.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.41/15.06 = { by axiom 1 (ifeq_axiom) }
% 104.41/15.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.41/15.07 = { by axiom 1 (ifeq_axiom) R->L }
% 104.41/15.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.41/15.08 = { by axiom 2 (condensed_detachment) R->L }
% 104.41/15.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), falsehood)), implies(implies(falsehood, implies(U3, T3)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), falsehood)), implies(implies(falsehood, implies(U3, T3)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.41/15.09 = { by axiom 3 (c0_CAMeredith) }
% 104.41/15.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), falsehood)), implies(implies(falsehood, implies(U3, T3)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.41/15.10 = { by axiom 1 (ifeq_axiom) }
% 104.41/15.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), falsehood)), implies(implies(falsehood, implies(U3, T3)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.41/15.12 = { by axiom 3 (c0_CAMeredith) }
% 104.41/15.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.83/15.13 = { by axiom 1 (ifeq_axiom) }
% 104.83/15.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.83/15.15 = { by axiom 1 (ifeq_axiom) R->L }
% 104.83/15.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.83/15.16 = { by axiom 2 (condensed_detachment) R->L }
% 104.83/15.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 104.83/15.19 = { by axiom 3 (c0_CAMeredith) }
% 104.83/15.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.11/15.21 = { by axiom 1 (ifeq_axiom) }
% 105.11/15.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.11/15.23 = { by axiom 1 (ifeq_axiom) R->L }
% 105.11/15.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.11/15.25 = { by axiom 2 (condensed_detachment) R->L }
% 105.11/15.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.11/15.28 = { by axiom 3 (c0_CAMeredith) }
% 105.11/15.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.51/15.30 = { by axiom 1 (ifeq_axiom) }
% 105.51/15.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.51/15.33 = { by axiom 1 (ifeq_axiom) R->L }
% 105.51/15.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.51/15.36 = { by axiom 3 (c0_CAMeredith) R->L }
% 105.51/15.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.51/15.39 = { by axiom 1 (ifeq_axiom) R->L }
% 105.51/15.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.91/15.41 = { by axiom 3 (c0_CAMeredith) R->L }
% 105.91/15.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.91/15.43 = { by axiom 2 (condensed_detachment) }
% 105.91/15.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.91/15.45 = { by axiom 1 (ifeq_axiom) }
% 105.91/15.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.91/15.47 = { by axiom 1 (ifeq_axiom) R->L }
% 105.91/15.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 105.91/15.50 = { by axiom 3 (c0_CAMeredith) R->L }
% 106.32/15.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), W4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), Z4), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.51 = { by axiom 2 (condensed_detachment) }
% 106.32/15.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.52 = { by axiom 1 (ifeq_axiom) }
% 106.32/15.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(falsehood, implies(U3, T3)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.53 = { by axiom 2 (condensed_detachment) }
% 106.32/15.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.53 = { by axiom 1 (ifeq_axiom) }
% 106.32/15.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.54 = { by axiom 1 (ifeq_axiom) R->L }
% 106.32/15.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.54 = { by axiom 3 (c0_CAMeredith) R->L }
% 106.32/15.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood), implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), V3), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.55 = { by axiom 2 (condensed_detachment) }
% 106.32/15.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.55 = { by axiom 1 (ifeq_axiom) }
% 106.32/15.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.55 = { by axiom 1 (ifeq_axiom) R->L }
% 106.32/15.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.56 = { by axiom 2 (condensed_detachment) R->L }
% 106.32/15.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3)), implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.56 = { by axiom 3 (c0_CAMeredith) }
% 106.32/15.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.56 = { by axiom 1 (ifeq_axiom) }
% 106.32/15.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.57 = { by axiom 1 (ifeq_axiom) R->L }
% 106.32/15.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.57 = { by axiom 2 (condensed_detachment) R->L }
% 106.32/15.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(falsehood, falsehood)), implies(implies(Z3, U4), implies(falsehood, falsehood))), implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(falsehood, falsehood)), implies(implies(Z3, U4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.58 = { by axiom 3 (c0_CAMeredith) }
% 106.32/15.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(falsehood, falsehood)), implies(implies(Z3, U4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.58 = { by axiom 1 (ifeq_axiom) }
% 106.32/15.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(falsehood, falsehood)), implies(implies(Z3, U4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.59 = { by axiom 1 (ifeq_axiom) R->L }
% 106.32/15.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(falsehood, falsehood)), implies(implies(Z3, U4), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.59 = { by axiom 3 (c0_CAMeredith) R->L }
% 106.32/15.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(implies(Z3, U4), falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(falsehood, falsehood)), implies(implies(Z3, U4), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.32/15.60 = { by axiom 1 (ifeq_axiom) R->L }
% 106.32/15.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(implies(Z3, U4), falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(falsehood, falsehood)), implies(implies(Z3, U4), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.60 = { by axiom 3 (c0_CAMeredith) R->L }
% 106.73/15.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(implies(Z3, U4), falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(falsehood, falsehood)), implies(implies(Z3, U4), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(implies(Z3, U4), falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), falsehood)), implies(falsehood, falsehood)), implies(implies(Z3, U4), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.61 = { by axiom 2 (condensed_detachment) }
% 106.73/15.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.61 = { by axiom 1 (ifeq_axiom) }
% 106.73/15.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.61 = { by axiom 1 (ifeq_axiom) R->L }
% 106.73/15.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.62 = { by axiom 3 (c0_CAMeredith) R->L }
% 106.73/15.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, U4), implies(falsehood, falsehood)), implies(implies(falsehood, W3), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), V4), implies(implies(falsehood, W3), falsehood)), Z3), implies(falsehood, Z3))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.62 = { by axiom 2 (condensed_detachment) }
% 106.73/15.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.62 = { by axiom 1 (ifeq_axiom) }
% 106.73/15.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, Z3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), falsehood)), implies(implies(falsehood, Z3), falsehood)), implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.62 = { by axiom 2 (condensed_detachment) }
% 106.73/15.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.63 = { by axiom 1 (ifeq_axiom) }
% 106.73/15.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.63 = { by axiom 1 (ifeq_axiom) R->L }
% 106.73/15.63 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.63 = { by axiom 3 (c0_CAMeredith) R->L }
% 106.73/15.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W3), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), Y3), implies(implies(a, falsehood), falsehood)), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.63 = { by axiom 2 (condensed_detachment) }
% 106.73/15.63 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.63 = { by axiom 1 (ifeq_axiom) }
% 106.73/15.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.63 = { by axiom 1 (ifeq_axiom) R->L }
% 106.73/15.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(true, true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.63 = { by axiom 2 (condensed_detachment) R->L }
% 106.73/15.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(is_a_theorem(implies(falsehood, implies(T4, S4))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.63 = { by axiom 1 (ifeq_axiom) R->L }
% 106.73/15.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.64 = { by axiom 2 (condensed_detachment) R->L }
% 106.73/15.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S4, falsehood), implies(T4, falsehood)), implies(falsehood, X5)), implies(Y5, implies(falsehood, X5))), implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(T4, falsehood)), implies(falsehood, X5)), implies(Y5, implies(falsehood, X5)))), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true), true), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.64 = { by axiom 3 (c0_CAMeredith) }
% 106.73/15.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(T4, falsehood)), implies(falsehood, X5)), implies(Y5, implies(falsehood, X5)))), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true), true), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.65 = { by axiom 1 (ifeq_axiom) }
% 106.73/15.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(T4, falsehood)), implies(falsehood, X5)), implies(Y5, implies(falsehood, X5)))), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.65 = { by axiom 1 (ifeq_axiom) R->L }
% 106.73/15.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(T4, falsehood)), implies(falsehood, X5)), implies(Y5, implies(falsehood, X5)))), true), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.65 = { by axiom 3 (c0_CAMeredith) R->L }
% 106.73/15.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, X5), implies(T4, falsehood)), implies(Y5, falsehood)), S4), implies(implies(S4, falsehood), implies(T4, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(T4, falsehood)), implies(falsehood, X5)), implies(Y5, implies(falsehood, X5)))), true), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.66 = { by axiom 1 (ifeq_axiom) R->L }
% 106.73/15.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, X5), implies(T4, falsehood)), implies(Y5, falsehood)), S4), implies(implies(S4, falsehood), implies(T4, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(T4, falsehood)), implies(falsehood, X5)), implies(Y5, implies(falsehood, X5)))), true), true), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.66 = { by axiom 3 (c0_CAMeredith) R->L }
% 106.73/15.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, X5), implies(T4, falsehood)), implies(Y5, falsehood)), S4), implies(implies(S4, falsehood), implies(T4, falsehood))), implies(implies(implies(implies(S4, falsehood), implies(T4, falsehood)), implies(falsehood, X5)), implies(Y5, implies(falsehood, X5))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, X5), implies(T4, falsehood)), implies(Y5, falsehood)), S4), implies(implies(S4, falsehood), implies(T4, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(T4, falsehood)), implies(falsehood, X5)), implies(Y5, implies(falsehood, X5)))), true), true), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.66 = { by axiom 2 (condensed_detachment) }
% 106.73/15.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.67 = { by axiom 1 (ifeq_axiom) }
% 106.73/15.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.67 = { by axiom 1 (ifeq_axiom) R->L }
% 106.73/15.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.67 = { by axiom 2 (condensed_detachment) R->L }
% 106.73/15.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4)), implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.68 = { by axiom 3 (c0_CAMeredith) }
% 106.73/15.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.68 = { by axiom 1 (ifeq_axiom) }
% 106.73/15.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.69 = { by axiom 1 (ifeq_axiom) R->L }
% 106.73/15.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.69 = { by axiom 2 (condensed_detachment) R->L }
% 106.73/15.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(implies(implies(T4, S4), Z5), falsehood)), S4), implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood))), implies(implies(implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(implies(implies(T4, S4), Z5), falsehood)), S4), implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 106.73/15.70 = { by axiom 3 (c0_CAMeredith) }
% 107.14/15.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(implies(implies(T4, S4), Z5), falsehood)), S4), implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.70 = { by axiom 1 (ifeq_axiom) }
% 107.14/15.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(implies(implies(T4, S4), Z5), falsehood)), S4), implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.71 = { by axiom 3 (c0_CAMeredith) }
% 107.14/15.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.71 = { by axiom 1 (ifeq_axiom) }
% 107.14/15.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.72 = { by axiom 1 (ifeq_axiom) R->L }
% 107.14/15.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.72 = { by axiom 3 (c0_CAMeredith) R->L }
% 107.14/15.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S4, falsehood), implies(implies(Y5, implies(falsehood, X5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(T4, S4), Z5), implies(falsehood, falsehood)), S4), implies(implies(Y5, implies(falsehood, X5)), S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.72 = { by axiom 2 (condensed_detachment) }
% 107.14/15.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.73 = { by axiom 1 (ifeq_axiom) }
% 107.14/15.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4)), implies(falsehood, implies(T4, S4)))), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, X5)), S4), implies(T4, S4))), true, is_a_theorem(implies(falsehood, implies(T4, S4))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.73 = { by axiom 2 (condensed_detachment) }
% 107.14/15.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.73 = { by axiom 1 (ifeq_axiom) }
% 107.14/15.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.74 = { by axiom 1 (ifeq_axiom) R->L }
% 107.14/15.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.74 = { by axiom 2 (condensed_detachment) R->L }
% 107.14/15.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.75 = { by axiom 1 (ifeq_axiom) R->L }
% 107.14/15.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.76 = { by axiom 2 (condensed_detachment) R->L }
% 107.14/15.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.77 = { by axiom 3 (c0_CAMeredith) }
% 107.14/15.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.78 = { by axiom 1 (ifeq_axiom) }
% 107.14/15.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.79 = { by axiom 1 (ifeq_axiom) R->L }
% 107.14/15.79 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.14/15.79 = { by axiom 2 (condensed_detachment) R->L }
% 107.55/15.80 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(implies(W5, V5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(falsehood, falsehood)), implies(implies(W5, V5), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(implies(W5, V5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(falsehood, falsehood)), implies(implies(W5, V5), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.80 = { by axiom 3 (c0_CAMeredith) }
% 107.55/15.81 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(implies(W5, V5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(falsehood, falsehood)), implies(implies(W5, V5), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.81 = { by axiom 1 (ifeq_axiom) }
% 107.55/15.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(implies(W5, V5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(falsehood, falsehood)), implies(implies(W5, V5), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.83 = { by axiom 3 (c0_CAMeredith) }
% 107.55/15.83 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(falsehood, falsehood)), implies(implies(W5, V5), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.83 = { by axiom 1 (ifeq_axiom) }
% 107.55/15.84 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(falsehood, falsehood)), implies(implies(W5, V5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.84 = { by axiom 1 (ifeq_axiom) R->L }
% 107.55/15.84 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(falsehood, falsehood)), implies(implies(W5, V5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.85 = { by axiom 3 (c0_CAMeredith) R->L }
% 107.55/15.85 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(falsehood, falsehood)), implies(implies(W5, V5), implies(falsehood, falsehood))), implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), falsehood)), implies(falsehood, falsehood)), implies(implies(W5, V5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W5, V5), implies(falsehood, falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.86 = { by axiom 2 (condensed_detachment) }
% 107.55/15.86 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.86 = { by axiom 1 (ifeq_axiom) }
% 107.55/15.87 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.87 = { by axiom 1 (ifeq_axiom) R->L }
% 107.55/15.87 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.88 = { by axiom 3 (c0_CAMeredith) R->L }
% 107.55/15.88 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5)), implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), U5), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), falsehood)), W5), implies(falsehood, W5))), true, is_a_theorem(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.88 = { by axiom 2 (condensed_detachment) }
% 107.55/15.88 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.89 = { by axiom 1 (ifeq_axiom) }
% 107.55/15.89 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.55/15.90 = { by axiom 1 (ifeq_axiom) R->L }
% 107.55/15.90 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.95/15.90 = { by axiom 2 (condensed_detachment) R->L }
% 107.95/15.91 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.95/15.91 = { by axiom 3 (c0_CAMeredith) }
% 107.95/15.92 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.95/15.93 = { by axiom 1 (ifeq_axiom) }
% 107.95/15.93 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.95/15.95 = { by axiom 1 (ifeq_axiom) R->L }
% 107.95/15.96 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.95/15.98 = { by axiom 2 (condensed_detachment) R->L }
% 107.95/15.99 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.95/16.00 = { by axiom 1 (ifeq_axiom) R->L }
% 107.95/16.01 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 107.95/16.03 = { by axiom 2 (condensed_detachment) R->L }
% 108.49/16.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 108.49/16.08 = { by axiom 3 (c0_CAMeredith) }
% 108.49/16.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 108.49/16.13 = { by axiom 1 (ifeq_axiom) }
% 108.90/16.14 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 108.90/16.17 = { by axiom 1 (ifeq_axiom) R->L }
% 108.90/16.18 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.16/16.20 = { by axiom 2 (condensed_detachment) R->L }
% 109.16/16.23 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.16/16.25 = { by axiom 3 (c0_CAMeredith) }
% 109.16/16.27 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.16/16.29 = { by axiom 1 (ifeq_axiom) }
% 109.57/16.31 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.57/16.34 = { by axiom 3 (c0_CAMeredith) }
% 109.57/16.35 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.57/16.37 = { by axiom 1 (ifeq_axiom) }
% 109.57/16.38 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.57/16.39 = { by axiom 1 (ifeq_axiom) R->L }
% 109.57/16.40 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.97/16.41 = { by axiom 3 (c0_CAMeredith) R->L }
% 109.97/16.42 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), Y6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.97/16.43 = { by axiom 2 (condensed_detachment) }
% 109.97/16.43 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.97/16.44 = { by axiom 1 (ifeq_axiom) }
% 109.97/16.45 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.97/16.46 = { by axiom 1 (ifeq_axiom) R->L }
% 109.97/16.46 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.97/16.47 = { by axiom 3 (c0_CAMeredith) R->L }
% 109.97/16.48 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), Z6), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.97/16.48 = { by axiom 2 (condensed_detachment) }
% 109.97/16.49 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 109.97/16.49 = { by axiom 1 (ifeq_axiom) }
% 109.97/16.50 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.50 = { by axiom 1 (ifeq_axiom) R->L }
% 110.36/16.51 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.51 = { by axiom 3 (c0_CAMeredith) R->L }
% 110.36/16.52 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), falsehood)), implies(implies(falsehood, implies(S5, X6)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.52 = { by axiom 1 (ifeq_axiom) R->L }
% 110.36/16.53 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), falsehood)), implies(implies(falsehood, implies(S5, X6)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.53 = { by axiom 3 (c0_CAMeredith) R->L }
% 110.36/16.54 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), falsehood)), implies(implies(falsehood, implies(S5, X6)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), falsehood)), implies(implies(falsehood, implies(S5, X6)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.54 = { by axiom 2 (condensed_detachment) }
% 110.36/16.55 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.55 = { by axiom 1 (ifeq_axiom) }
% 110.36/16.55 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.56 = { by axiom 1 (ifeq_axiom) R->L }
% 110.36/16.56 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.57 = { by axiom 2 (condensed_detachment) R->L }
% 110.36/16.57 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.57 = { by axiom 1 (ifeq_axiom) R->L }
% 110.36/16.58 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.58 = { by axiom 2 (condensed_detachment) R->L }
% 110.36/16.58 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.59 = { by axiom 3 (c0_CAMeredith) }
% 110.36/16.59 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.36/16.60 = { by axiom 1 (ifeq_axiom) }
% 110.77/16.60 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.60 = { by axiom 1 (ifeq_axiom) R->L }
% 110.77/16.61 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.61 = { by axiom 3 (c0_CAMeredith) R->L }
% 110.77/16.62 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(implies(implies(S5, X6), U6), falsehood)), X6), implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.62 = { by axiom 1 (ifeq_axiom) R->L }
% 110.77/16.62 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(implies(implies(S5, X6), U6), falsehood)), X6), implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.63 = { by axiom 3 (c0_CAMeredith) R->L }
% 110.77/16.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(implies(implies(S5, X6), U6), falsehood)), X6), implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood))), implies(implies(implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(implies(implies(S5, X6), U6), falsehood)), X6), implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(implies(W6, implies(falsehood, V6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.64 = { by axiom 2 (condensed_detachment) }
% 110.77/16.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.64 = { by axiom 1 (ifeq_axiom) }
% 110.77/16.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.65 = { by axiom 1 (ifeq_axiom) R->L }
% 110.77/16.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.66 = { by axiom 3 (c0_CAMeredith) R->L }
% 110.77/16.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6)), implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(S5, X6), U6), implies(falsehood, falsehood)), X6), implies(implies(W6, implies(falsehood, V6)), X6))), true, is_a_theorem(implies(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)), implies(falsehood, implies(S5, X6)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.66 = { by axiom 2 (condensed_detachment) }
% 110.77/16.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.67 = { by axiom 1 (ifeq_axiom) }
% 110.77/16.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.68 = { by axiom 1 (ifeq_axiom) R->L }
% 110.77/16.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 110.77/16.69 = { by axiom 2 (condensed_detachment) R->L }
% 110.77/16.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V6), implies(S5, falsehood)), implies(W6, falsehood)), X6), implies(implies(X6, falsehood), implies(S5, falsehood))), implies(implies(implies(implies(X6, falsehood), implies(S5, falsehood)), implies(falsehood, V6)), implies(W6, implies(falsehood, V6))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V6), implies(S5, falsehood)), implies(W6, falsehood)), X6), implies(implies(X6, falsehood), implies(S5, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(S5, falsehood)), implies(falsehood, V6)), implies(W6, implies(falsehood, V6)))), true), true), true, is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.71 = { by axiom 3 (c0_CAMeredith) }
% 111.18/16.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V6), implies(S5, falsehood)), implies(W6, falsehood)), X6), implies(implies(X6, falsehood), implies(S5, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(S5, falsehood)), implies(falsehood, V6)), implies(W6, implies(falsehood, V6)))), true), true), true, is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.71 = { by axiom 1 (ifeq_axiom) }
% 111.18/16.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V6), implies(S5, falsehood)), implies(W6, falsehood)), X6), implies(implies(X6, falsehood), implies(S5, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(S5, falsehood)), implies(falsehood, V6)), implies(W6, implies(falsehood, V6)))), true), true, is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.72 = { by axiom 3 (c0_CAMeredith) }
% 111.18/16.72 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(S5, falsehood)), implies(falsehood, V6)), implies(W6, implies(falsehood, V6)))), true), true, is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.73 = { by axiom 1 (ifeq_axiom) }
% 111.18/16.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(S5, falsehood)), implies(falsehood, V6)), implies(W6, implies(falsehood, V6)))), true, is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.73 = { by axiom 1 (ifeq_axiom) R->L }
% 111.18/16.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(S5, falsehood)), implies(falsehood, V6)), implies(W6, implies(falsehood, V6)))), true, is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true), true), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.74 = { by axiom 3 (c0_CAMeredith) R->L }
% 111.18/16.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X6, falsehood), implies(S5, falsehood)), implies(falsehood, V6)), implies(W6, implies(falsehood, V6))), implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X6, falsehood), implies(S5, falsehood)), implies(falsehood, V6)), implies(W6, implies(falsehood, V6)))), true, is_a_theorem(implies(implies(implies(W6, implies(falsehood, V6)), X6), implies(S5, X6))), true), true), true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.74 = { by axiom 2 (condensed_detachment) }
% 111.18/16.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(S5, X6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.75 = { by axiom 1 (ifeq_axiom) }
% 111.18/16.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(S5, X6)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(falsehood, implies(S5, X6))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.75 = { by axiom 2 (condensed_detachment) }
% 111.18/16.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.75 = { by axiom 1 (ifeq_axiom) }
% 111.18/16.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.75 = { by axiom 1 (ifeq_axiom) R->L }
% 111.18/16.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.76 = { by axiom 3 (c0_CAMeredith) R->L }
% 111.18/16.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), T5), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), falsehood)), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, W5), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.76 = { by axiom 2 (condensed_detachment) }
% 111.18/16.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.76 = { by axiom 1 (ifeq_axiom) }
% 111.18/16.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.76 = { by axiom 1 (ifeq_axiom) R->L }
% 111.18/16.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.77 = { by axiom 2 (condensed_detachment) R->L }
% 111.18/16.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.77 = { by axiom 3 (c0_CAMeredith) }
% 111.18/16.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.77 = { by axiom 1 (ifeq_axiom) }
% 111.18/16.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.78 = { by axiom 1 (ifeq_axiom) R->L }
% 111.18/16.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.78 = { by axiom 2 (condensed_detachment) R->L }
% 111.18/16.79 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.79 = { by axiom 3 (c0_CAMeredith) }
% 111.18/16.79 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.18/16.80 = { by axiom 1 (ifeq_axiom) }
% 111.18/16.80 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.59/16.80 = { by axiom 1 (ifeq_axiom) R->L }
% 111.59/16.81 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.59/16.81 = { by axiom 2 (condensed_detachment) R->L }
% 111.59/16.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.59/16.82 = { by axiom 1 (ifeq_axiom) R->L }
% 111.59/16.83 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.59/16.84 = { by axiom 2 (condensed_detachment) R->L }
% 111.59/16.84 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.59/16.85 = { by axiom 3 (c0_CAMeredith) }
% 111.59/16.85 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.59/16.86 = { by axiom 1 (ifeq_axiom) }
% 111.59/16.87 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.59/16.88 = { by axiom 1 (ifeq_axiom) R->L }
% 111.59/16.88 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 111.59/16.89 = { by axiom 2 (condensed_detachment) R->L }
% 111.59/16.90 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(implies(X7, Y7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(falsehood, falsehood)), implies(implies(X7, Y7), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(implies(X7, Y7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(falsehood, falsehood)), implies(implies(X7, Y7), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/16.90 = { by axiom 3 (c0_CAMeredith) }
% 112.00/16.91 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(implies(X7, Y7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(falsehood, falsehood)), implies(implies(X7, Y7), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/16.92 = { by axiom 1 (ifeq_axiom) }
% 112.00/16.92 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(implies(X7, Y7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(falsehood, falsehood)), implies(implies(X7, Y7), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/16.93 = { by axiom 3 (c0_CAMeredith) }
% 112.00/16.94 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(falsehood, falsehood)), implies(implies(X7, Y7), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/16.94 = { by axiom 1 (ifeq_axiom) }
% 112.00/16.95 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(falsehood, falsehood)), implies(implies(X7, Y7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/16.96 = { by axiom 1 (ifeq_axiom) R->L }
% 112.00/16.96 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(falsehood, falsehood)), implies(implies(X7, Y7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/16.97 = { by axiom 3 (c0_CAMeredith) R->L }
% 112.00/16.98 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(falsehood, falsehood)), implies(implies(X7, Y7), implies(falsehood, falsehood))), implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), falsehood)), implies(falsehood, falsehood)), implies(implies(X7, Y7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/16.98 = { by axiom 2 (condensed_detachment) }
% 112.00/16.99 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/16.99 = { by axiom 1 (ifeq_axiom) }
% 112.00/17.00 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/17.00 = { by axiom 1 (ifeq_axiom) R->L }
% 112.00/17.01 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/17.01 = { by axiom 3 (c0_CAMeredith) R->L }
% 112.00/17.02 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7)), implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), Z7), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), falsehood)), X7), implies(falsehood, X7))), true, is_a_theorem(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.00/17.02 = { by axiom 2 (condensed_detachment) }
% 112.00/17.03 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.53/17.04 = { by axiom 1 (ifeq_axiom) }
% 112.53/17.04 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.53/17.05 = { by axiom 1 (ifeq_axiom) R->L }
% 112.53/17.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.53/17.06 = { by axiom 2 (condensed_detachment) R->L }
% 112.53/17.06 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.53/17.07 = { by axiom 3 (c0_CAMeredith) }
% 112.53/17.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.53/17.10 = { by axiom 1 (ifeq_axiom) }
% 112.53/17.10 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.93/17.13 = { by axiom 1 (ifeq_axiom) R->L }
% 112.93/17.14 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 112.93/17.17 = { by axiom 2 (condensed_detachment) R->L }
% 112.93/17.19 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 113.22/17.22 = { by axiom 1 (ifeq_axiom) R->L }
% 113.22/17.23 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 113.22/17.26 = { by axiom 2 (condensed_detachment) R->L }
% 113.22/17.28 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 113.63/17.32 = { by axiom 3 (c0_CAMeredith) }
% 113.63/17.34 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 113.63/17.38 = { by axiom 1 (ifeq_axiom) }
% 114.05/17.42 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 114.05/17.46 = { by axiom 1 (ifeq_axiom) R->L }
% 114.05/17.47 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 114.36/17.51 = { by axiom 2 (condensed_detachment) R->L }
% 114.36/17.54 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 114.36/17.57 = { by axiom 3 (c0_CAMeredith) }
% 114.36/17.59 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 114.66/17.63 = { by axiom 1 (ifeq_axiom) }
% 114.66/17.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 114.66/17.68 = { by axiom 3 (c0_CAMeredith) }
% 114.66/17.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 114.96/17.74 = { by axiom 1 (ifeq_axiom) }
% 114.96/17.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 114.96/17.78 = { by axiom 1 (ifeq_axiom) R->L }
% 114.96/17.80 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 115.26/17.82 = { by axiom 3 (c0_CAMeredith) R->L }
% 115.26/17.85 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), T7), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 115.26/17.88 = { by axiom 2 (condensed_detachment) }
% 115.26/17.89 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 115.55/17.92 = { by axiom 1 (ifeq_axiom) }
% 115.55/17.93 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 115.55/17.95 = { by axiom 1 (ifeq_axiom) R->L }
% 115.55/17.96 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 115.55/17.98 = { by axiom 3 (c0_CAMeredith) R->L }
% 115.55/17.99 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), S7), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 115.55/18.01 = { by axiom 2 (condensed_detachment) }
% 115.55/18.02 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 115.95/18.04 = { by axiom 1 (ifeq_axiom) }
% 115.95/18.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 115.95/18.07 = { by axiom 1 (ifeq_axiom) R->L }
% 115.95/18.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 115.95/18.09 = { by axiom 3 (c0_CAMeredith) R->L }
% 115.95/18.11 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), falsehood)), implies(implies(falsehood, implies(V7, U7)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 115.95/18.12 = { by axiom 1 (ifeq_axiom) R->L }
% 115.95/18.13 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), falsehood)), implies(implies(falsehood, implies(V7, U7)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.26/18.14 = { by axiom 3 (c0_CAMeredith) R->L }
% 116.26/18.16 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), falsehood)), implies(implies(falsehood, implies(V7, U7)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), falsehood)), implies(implies(falsehood, implies(V7, U7)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.26/18.16 = { by axiom 2 (condensed_detachment) }
% 116.26/18.17 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.26/18.18 = { by axiom 1 (ifeq_axiom) }
% 116.26/18.19 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.26/18.20 = { by axiom 1 (ifeq_axiom) R->L }
% 116.47/18.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.47/18.21 = { by axiom 2 (condensed_detachment) R->L }
% 116.47/18.22 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.47/18.23 = { by axiom 1 (ifeq_axiom) R->L }
% 116.47/18.24 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.47/18.25 = { by axiom 2 (condensed_detachment) R->L }
% 116.47/18.26 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.47/18.27 = { by axiom 3 (c0_CAMeredith) }
% 116.47/18.27 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.47/18.28 = { by axiom 1 (ifeq_axiom) }
% 116.47/18.29 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.78/18.30 = { by axiom 1 (ifeq_axiom) R->L }
% 116.78/18.31 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.78/18.32 = { by axiom 3 (c0_CAMeredith) R->L }
% 116.78/18.33 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(implies(implies(V7, U7), Z8), falsehood)), U7), implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.78/18.34 = { by axiom 1 (ifeq_axiom) R->L }
% 116.78/18.34 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(implies(implies(V7, U7), Z8), falsehood)), U7), implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.78/18.35 = { by axiom 3 (c0_CAMeredith) R->L }
% 116.78/18.36 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(implies(implies(V7, U7), Z8), falsehood)), U7), implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood))), implies(implies(implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(implies(implies(V7, U7), Z8), falsehood)), U7), implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(implies(X8, implies(falsehood, Y8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.78/18.37 = { by axiom 2 (condensed_detachment) }
% 116.78/18.38 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 116.78/18.39 = { by axiom 1 (ifeq_axiom) }
% 116.78/18.40 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.08/18.41 = { by axiom 1 (ifeq_axiom) R->L }
% 117.08/18.41 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.08/18.43 = { by axiom 3 (c0_CAMeredith) R->L }
% 117.08/18.44 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7)), implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V7, U7), Z8), implies(falsehood, falsehood)), U7), implies(implies(X8, implies(falsehood, Y8)), U7))), true, is_a_theorem(implies(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)), implies(falsehood, implies(V7, U7)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.08/18.45 = { by axiom 2 (condensed_detachment) }
% 117.08/18.46 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.08/18.47 = { by axiom 1 (ifeq_axiom) }
% 117.08/18.47 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.08/18.48 = { by axiom 1 (ifeq_axiom) R->L }
% 117.08/18.49 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.39/18.50 = { by axiom 2 (condensed_detachment) R->L }
% 117.39/18.51 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y8), implies(V7, falsehood)), implies(X8, falsehood)), U7), implies(implies(U7, falsehood), implies(V7, falsehood))), implies(implies(implies(implies(U7, falsehood), implies(V7, falsehood)), implies(falsehood, Y8)), implies(X8, implies(falsehood, Y8))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, Y8), implies(V7, falsehood)), implies(X8, falsehood)), U7), implies(implies(U7, falsehood), implies(V7, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(V7, falsehood)), implies(falsehood, Y8)), implies(X8, implies(falsehood, Y8)))), true), true), true, is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.39/18.52 = { by axiom 3 (c0_CAMeredith) }
% 117.39/18.53 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, Y8), implies(V7, falsehood)), implies(X8, falsehood)), U7), implies(implies(U7, falsehood), implies(V7, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(V7, falsehood)), implies(falsehood, Y8)), implies(X8, implies(falsehood, Y8)))), true), true), true, is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.39/18.54 = { by axiom 1 (ifeq_axiom) }
% 117.39/18.54 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, Y8), implies(V7, falsehood)), implies(X8, falsehood)), U7), implies(implies(U7, falsehood), implies(V7, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(V7, falsehood)), implies(falsehood, Y8)), implies(X8, implies(falsehood, Y8)))), true), true, is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.39/18.55 = { by axiom 3 (c0_CAMeredith) }
% 117.39/18.56 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(V7, falsehood)), implies(falsehood, Y8)), implies(X8, implies(falsehood, Y8)))), true), true, is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.39/18.57 = { by axiom 1 (ifeq_axiom) }
% 117.39/18.58 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(V7, falsehood)), implies(falsehood, Y8)), implies(X8, implies(falsehood, Y8)))), true, is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.39/18.58 = { by axiom 1 (ifeq_axiom) R->L }
% 117.39/18.59 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(V7, falsehood)), implies(falsehood, Y8)), implies(X8, implies(falsehood, Y8)))), true, is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true), true), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.39/18.60 = { by axiom 3 (c0_CAMeredith) R->L }
% 117.70/18.61 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U7, falsehood), implies(V7, falsehood)), implies(falsehood, Y8)), implies(X8, implies(falsehood, Y8))), implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, falsehood), implies(V7, falsehood)), implies(falsehood, Y8)), implies(X8, implies(falsehood, Y8)))), true, is_a_theorem(implies(implies(implies(X8, implies(falsehood, Y8)), U7), implies(V7, U7))), true), true), true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.61 = { by axiom 2 (condensed_detachment) }
% 117.70/18.62 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(V7, U7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.63 = { by axiom 1 (ifeq_axiom) }
% 117.70/18.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(V7, U7)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(falsehood, implies(V7, U7))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.64 = { by axiom 2 (condensed_detachment) }
% 117.70/18.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.65 = { by axiom 1 (ifeq_axiom) }
% 117.70/18.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.66 = { by axiom 1 (ifeq_axiom) R->L }
% 117.70/18.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.66 = { by axiom 3 (c0_CAMeredith) R->L }
% 117.70/18.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), W7), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, X7), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.67 = { by axiom 2 (condensed_detachment) }
% 117.70/18.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.68 = { by axiom 1 (ifeq_axiom) }
% 117.70/18.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.68 = { by axiom 1 (ifeq_axiom) R->L }
% 117.70/18.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.69 = { by axiom 3 (c0_CAMeredith) R->L }
% 117.70/18.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood), implies(implies(implies(implies(falsehood, W5), falsehood), S6), falsehood)), implies(implies(falsehood, X7), falsehood)), implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(T4, S4)), falsehood), T6), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.69 = { by axiom 2 (condensed_detachment) }
% 117.70/18.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 117.70/18.70 = { by axiom 1 (ifeq_axiom) }
% 117.70/18.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 118.00/18.70 = { by axiom 1 (ifeq_axiom) R->L }
% 118.00/18.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 118.00/18.70 = { by axiom 3 (c0_CAMeredith) R->L }
% 118.00/18.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W5), falsehood), S6), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood)), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), falsehood), implies(implies(falsehood, implies(T4, S4)), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 118.00/18.70 = { by axiom 2 (condensed_detachment) }
% 118.00/18.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 118.00/18.71 = { by axiom 1 (ifeq_axiom) }
% 118.00/18.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(falsehood, W5), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, is_a_theorem(implies(implies(falsehood, implies(T4, S4)), implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 118.00/18.71 = { by axiom 2 (condensed_detachment) }
% 118.00/18.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 118.00/18.71 = { by axiom 1 (ifeq_axiom) }
% 118.00/18.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true, is_a_theorem(implies(implies(a, falsehood), implies(implies(implies(a, falsehood), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 118.00/18.71 = { by axiom 2 (condensed_detachment) }
% 118.00/18.71 ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 118.00/18.71 = { by axiom 1 (ifeq_axiom) }
% 118.00/18.71 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true)
% 118.00/18.71 = { by axiom 1 (ifeq_axiom) R->L }
% 118.00/18.71 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.71 = { by axiom 2 (condensed_detachment) R->L }
% 118.00/18.71 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.71 = { by axiom 1 (ifeq_axiom) R->L }
% 118.00/18.71 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.71 = { by axiom 2 (condensed_detachment) R->L }
% 118.00/18.71 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), U8), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true), true), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.71 = { by axiom 3 (c0_CAMeredith) }
% 118.00/18.71 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true), true), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.71 = { by axiom 1 (ifeq_axiom) }
% 118.00/18.71 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.71 = { by axiom 1 (ifeq_axiom) R->L }
% 118.00/18.71 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 3 (c0_CAMeredith) R->L }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(implies(implies(X, Y), U8), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 1 (ifeq_axiom) R->L }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(implies(implies(X, Y), U8), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 3 (c0_CAMeredith) R->L }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(implies(implies(X, Y), U8), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood))), implies(implies(implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), U8), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(implies(implies(X, Y), U8), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(W8, implies(falsehood, V8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 2 (condensed_detachment) }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 1 (ifeq_axiom) }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 1 (ifeq_axiom) R->L }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 3 (c0_CAMeredith) R->L }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y)), implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), U8), implies(falsehood, falsehood)), Y), implies(implies(W8, implies(falsehood, V8)), Y))), true, is_a_theorem(implies(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 2 (condensed_detachment) }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 1 (ifeq_axiom) }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 1 (ifeq_axiom) R->L }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 2 (condensed_detachment) R->L }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V8), implies(X, falsehood)), implies(W8, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood))), implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V8)), implies(W8, implies(falsehood, V8))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V8), implies(X, falsehood)), implies(W8, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V8)), implies(W8, implies(falsehood, V8)))), true), true), true, is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 3 (c0_CAMeredith) }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V8), implies(X, falsehood)), implies(W8, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V8)), implies(W8, implies(falsehood, V8)))), true), true), true, is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.72 = { by axiom 1 (ifeq_axiom) }
% 118.00/18.72 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V8), implies(X, falsehood)), implies(W8, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V8)), implies(W8, implies(falsehood, V8)))), true), true, is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.73 = { by axiom 3 (c0_CAMeredith) }
% 118.00/18.73 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V8)), implies(W8, implies(falsehood, V8)))), true), true, is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.73 = { by axiom 1 (ifeq_axiom) }
% 118.00/18.73 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V8)), implies(W8, implies(falsehood, V8)))), true, is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.73 = { by axiom 1 (ifeq_axiom) R->L }
% 118.00/18.73 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V8)), implies(W8, implies(falsehood, V8)))), true, is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.73 = { by axiom 3 (c0_CAMeredith) R->L }
% 118.00/18.73 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V8)), implies(W8, implies(falsehood, V8))), implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V8)), implies(W8, implies(falsehood, V8)))), true, is_a_theorem(implies(implies(implies(W8, implies(falsehood, V8)), Y), implies(X, Y))), true), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.73 = { by axiom 2 (condensed_detachment) }
% 118.00/18.73 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.73 = { by axiom 1 (ifeq_axiom) }
% 118.00/18.73 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, falsehood), falsehood), a))), true, ifeq(is_a_theorem(implies(falsehood, implies(X, Y))), true, is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true), true)
% 118.00/18.73 = { by axiom 2 (condensed_detachment) }
% 118.00/18.73 true
% 118.00/18.73 % SZS output end Proof
% 118.00/18.73
% 118.00/18.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------