%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL035-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 0.10s 0.45s
% Output : Proof 0.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL035-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 15:18:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 Command-line arguments: --no-flatten-goal
% 0.10/0.45
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45
% 0.17/0.56 % SZS output start Proof
% 0.17/0.56 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.17/0.56 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.
% 0.17/0.57 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.
% 0.17/0.57
% 0.17/0.57 Goal 1 (prove_c0_4): is_a_theorem(implies(falsehood, a)) = true.
% 0.17/0.57 Proof:
% 0.17/0.57 is_a_theorem(implies(falsehood, a))
% 0.17/0.57 = { by axiom 1 (ifeq_axiom) R->L }
% 0.17/0.57 ifeq(true, true, is_a_theorem(implies(falsehood, a)), true)
% 0.17/0.57 = { by axiom 2 (condensed_detachment) R->L }
% 0.17/0.57 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(is_a_theorem(implies(falsehood, implies(X, Y))), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.17/0.57 = { by axiom 1 (ifeq_axiom) R->L }
% 0.17/0.57 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.17/0.57 = { by axiom 2 (condensed_detachment) R->L }
% 0.17/0.57 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V)), implies(U, implies(falsehood, V))), implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V)), implies(U, implies(falsehood, V)))), true, is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.17/0.57 = { by axiom 3 (c0_CAMeredith) }
% 0.17/0.57 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V)), implies(U, implies(falsehood, V)))), true, is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.17/0.58 = { by axiom 1 (ifeq_axiom) }
% 0.17/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V)), implies(U, implies(falsehood, V)))), true, is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.17/0.58 = { by axiom 1 (ifeq_axiom) R->L }
% 0.17/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V)), implies(U, implies(falsehood, V)))), true), true, is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.17/0.58 = { by axiom 3 (c0_CAMeredith) R->L }
% 0.17/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V), implies(X, falsehood)), implies(U, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V)), implies(U, implies(falsehood, V)))), true), true, is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.17/0.58 = { by axiom 1 (ifeq_axiom) R->L }
% 0.17/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V), implies(X, falsehood)), implies(U, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V)), implies(U, implies(falsehood, V)))), true), true), true, is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.17/0.58 = { by axiom 3 (c0_CAMeredith) R->L }
% 0.17/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V), implies(X, falsehood)), implies(U, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood))), implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V)), implies(U, implies(falsehood, V))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V), implies(X, falsehood)), implies(U, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, V)), implies(U, implies(falsehood, V)))), true), true), true, is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.58 = { by axiom 2 (condensed_detachment) }
% 0.99/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.58 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.58 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.58 = { by axiom 2 (condensed_detachment) R->L }
% 0.99/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y)), implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.58 = { by axiom 3 (c0_CAMeredith) }
% 0.99/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.58 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.58 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.58 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 2 (condensed_detachment) R->L }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(implies(implies(X, Y), T), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood))), implies(implies(implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(implies(implies(X, Y), T), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 3 (c0_CAMeredith) }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(implies(implies(X, Y), T), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(implies(implies(X, Y), T), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 3 (c0_CAMeredith) }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 3 (c0_CAMeredith) R->L }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(U, implies(falsehood, V)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(U, implies(falsehood, V)), Y))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 2 (condensed_detachment) }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(falsehood, V)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 2 (condensed_detachment) }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.59 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.59 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.59 = { by axiom 2 (condensed_detachment) R->L }
% 0.99/0.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, a), implies(S, falsehood)), implies(implies(falsehood, implies(Z, W)), falsehood)), X2), implies(implies(X2, falsehood), implies(S, falsehood))), implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(S, falsehood)), implies(implies(falsehood, implies(Z, W)), falsehood)), X2), implies(implies(X2, falsehood), implies(S, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.60 = { by axiom 3 (c0_CAMeredith) }
% 0.99/0.60 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(S, falsehood)), implies(implies(falsehood, implies(Z, W)), falsehood)), X2), implies(implies(X2, falsehood), implies(S, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.60 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(S, falsehood)), implies(implies(falsehood, implies(Z, W)), falsehood)), X2), implies(implies(X2, falsehood), implies(S, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.60 = { by axiom 3 (c0_CAMeredith) }
% 0.99/0.60 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.60 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.60 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.60 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.60 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.60 = { by axiom 2 (condensed_detachment) R->L }
% 0.99/0.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(falsehood, a)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a))), implies(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(falsehood, a)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.60 = { by axiom 3 (c0_CAMeredith) }
% 0.99/0.60 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(falsehood, a)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.60 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(falsehood, a)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.60 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.60 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(falsehood, a)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.60 = { by axiom 3 (c0_CAMeredith) R->L }
% 0.99/0.61 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), falsehood)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(falsehood, a)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.61 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.61 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), falsehood)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(falsehood, a)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.61 = { by axiom 3 (c0_CAMeredith) R->L }
% 0.99/0.61 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, a), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), falsehood)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(falsehood, a)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, a), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), falsehood)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(falsehood, a)), implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.61 = { by axiom 2 (condensed_detachment) }
% 0.99/0.61 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.61 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.61 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, falsehood), implies(S, falsehood)), implies(falsehood, a)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(falsehood, implies(Z, W)), implies(falsehood, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.61 = { by axiom 2 (condensed_detachment) }
% 0.99/0.61 ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.61 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.61 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, is_a_theorem(implies(falsehood, a)), true)
% 0.99/0.61 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.61 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(true, true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.61 = { by axiom 2 (condensed_detachment) R->L }
% 0.99/0.61 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.61 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.61 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.61 = { by axiom 2 (condensed_detachment) R->L }
% 0.99/0.61 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z, W), W2), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.61 = { by axiom 3 (c0_CAMeredith) }
% 0.99/0.61 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.61 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.61 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.61 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.61 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.61 = { by axiom 3 (c0_CAMeredith) R->L }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(implies(implies(Z, W), W2), falsehood)), W), implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(implies(implies(Z, W), W2), falsehood)), W), implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 3 (c0_CAMeredith) R->L }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(implies(implies(Z, W), W2), falsehood)), W), implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood))), implies(implies(implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z, W), W2), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(implies(implies(Z, W), W2), falsehood)), W), implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(implies(Y2, implies(falsehood, Z2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 2 (condensed_detachment) }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 3 (c0_CAMeredith) R->L }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W)), implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z, W), W2), implies(falsehood, falsehood)), W), implies(implies(Y2, implies(falsehood, Z2)), W))), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)), implies(falsehood, implies(Z, W)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 2 (condensed_detachment) }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 2 (condensed_detachment) R->L }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Z2), implies(Z, falsehood)), implies(Y2, falsehood)), W), implies(implies(W, falsehood), implies(Z, falsehood))), implies(implies(implies(implies(W, falsehood), implies(Z, falsehood)), implies(falsehood, Z2)), implies(Y2, implies(falsehood, Z2))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, Z2), implies(Z, falsehood)), implies(Y2, falsehood)), W), implies(implies(W, falsehood), implies(Z, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(Z, falsehood)), implies(falsehood, Z2)), implies(Y2, implies(falsehood, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 3 (c0_CAMeredith) }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, Z2), implies(Z, falsehood)), implies(Y2, falsehood)), W), implies(implies(W, falsehood), implies(Z, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(Z, falsehood)), implies(falsehood, Z2)), implies(Y2, implies(falsehood, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, Z2), implies(Z, falsehood)), implies(Y2, falsehood)), W), implies(implies(W, falsehood), implies(Z, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(Z, falsehood)), implies(falsehood, Z2)), implies(Y2, implies(falsehood, Z2)))), true), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 3 (c0_CAMeredith) }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(Z, falsehood)), implies(falsehood, Z2)), implies(Y2, implies(falsehood, Z2)))), true), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(Z, falsehood)), implies(falsehood, Z2)), implies(Y2, implies(falsehood, Z2)))), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 1 (ifeq_axiom) R->L }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(Z, falsehood)), implies(falsehood, Z2)), implies(Y2, implies(falsehood, Z2)))), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 3 (c0_CAMeredith) R->L }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W, falsehood), implies(Z, falsehood)), implies(falsehood, Z2)), implies(Y2, implies(falsehood, Z2))), implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, falsehood), implies(Z, falsehood)), implies(falsehood, Z2)), implies(Y2, implies(falsehood, Z2)))), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, Z2)), W), implies(Z, W))), true), true), true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 2 (condensed_detachment) }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(Z, W))), true), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 1 (ifeq_axiom) }
% 0.99/0.62 ifeq(is_a_theorem(implies(implies(falsehood, implies(Z, W)), implies(falsehood, a))), true, ifeq(is_a_theorem(implies(falsehood, implies(Z, W))), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.99/0.62 = { by axiom 2 (condensed_detachment) }
% 0.99/0.62 true
% 0.99/0.62 % SZS output end Proof
% 0.99/0.62
% 0.99/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------