%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL070-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 11:48:57 AM UTC 2026
% Result : Unsatisfiable 13.77s 2.25s
% Output : Proof 19.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL070-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:20:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.77/2.25 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 13.77/2.25
% 13.77/2.25 % SZS status Unsatisfiable
% 13.77/2.25
% 17.74/2.71 % SZS output start Proof
% 17.74/2.71 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 17.74/2.71 Axiom 2 (cn_19): is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))) = true.
% 17.74/2.71 Axiom 3 (cn_37): is_a_theorem(implies(implies(implies(X, Y), Z), implies(not(X), Z))) = true.
% 17.74/2.71 Axiom 4 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 17.74/2.73 Axiom 5 (cn_60): is_a_theorem(implies(implies(X, implies(not(Y), Z)), implies(X, implies(implies(W, Z), implies(implies(Y, W), Z))))) = true.
% 17.74/2.73
% 17.74/2.73 Goal 1 (prove_cn_1): is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))) = true.
% 17.74/2.73 Proof:
% 17.74/2.73 is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 17.74/2.73 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.73 ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 17.74/2.73 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.73 ifeq(true, true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.73 = { by axiom 4 (condensed_detachment) R->L }
% 17.74/2.73 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.73 = { by axiom 2 (cn_19) }
% 17.74/2.73 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.73 = { by axiom 1 (ifeq_axiom) }
% 17.74/2.73 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.73 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.73 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.73 = { by axiom 4 (condensed_detachment) R->L }
% 17.74/2.73 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.73 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.73 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.74 = { by axiom 2 (cn_19) R->L }
% 17.74/2.74 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W, implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(not(a), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.74 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.74 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W, implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(not(a), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.74 = { by axiom 2 (cn_19) R->L }
% 17.74/2.74 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(not(a), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(W, implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(not(a), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.74 = { by axiom 4 (condensed_detachment) }
% 17.74/2.74 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.74 = { by axiom 1 (ifeq_axiom) }
% 17.74/2.74 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.74 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.74 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.74 = { by axiom 4 (condensed_detachment) R->L }
% 17.74/2.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c))), implies(implies(a, c), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.75 = { by axiom 2 (cn_19) }
% 17.74/2.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.75 = { by axiom 1 (ifeq_axiom) }
% 17.74/2.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.75 = { by axiom 2 (cn_19) }
% 17.74/2.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.75 = { by axiom 1 (ifeq_axiom) }
% 17.74/2.75 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.76 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 3 (cn_37) R->L }
% 17.74/2.76 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, c), implies(implies(b, c), implies(a, c))), implies(not(a), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 4 (condensed_detachment) }
% 17.74/2.76 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 1 (ifeq_axiom) }
% 17.74/2.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.76 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 5 (cn_60) R->L }
% 17.74/2.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(not(a), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 4 (condensed_detachment) }
% 17.74/2.76 ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 1 (ifeq_axiom) }
% 17.74/2.76 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 4 (condensed_detachment) R->L }
% 17.74/2.76 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.76 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.76 = { by axiom 4 (condensed_detachment) R->L }
% 17.74/2.76 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(U, T), S), implies(T, S))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.77 = { by axiom 2 (cn_19) }
% 17.74/2.77 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.77 = { by axiom 1 (ifeq_axiom) }
% 17.74/2.77 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.77 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.77 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.77 = { by axiom 4 (condensed_detachment) R->L }
% 17.74/2.77 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.77 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.78 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.78 = { by axiom 2 (cn_19) R->L }
% 17.74/2.79 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X2, implies(implies(implies(U, T), S), implies(T, S))), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.79 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.79 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X2, implies(implies(implies(U, T), S), implies(T, S))), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.79 = { by axiom 2 (cn_19) R->L }
% 17.74/2.79 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X2, implies(implies(implies(U, T), S), implies(T, S))), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), implies(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(X2, implies(implies(implies(U, T), S), implies(T, S))), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.79 = { by axiom 4 (condensed_detachment) }
% 17.74/2.79 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.79 = { by axiom 1 (ifeq_axiom) }
% 17.74/2.80 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 17.74/2.80 = { by axiom 1 (ifeq_axiom) R->L }
% 17.74/2.80 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.80 = { by axiom 4 (condensed_detachment) R->L }
% 18.49/2.80 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y2, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.80 = { by axiom 2 (cn_19) }
% 18.49/2.80 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y2, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.80 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.81 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.81 = { by axiom 2 (cn_19) }
% 18.49/2.81 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.81 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.81 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.81 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.81 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.81 = { by axiom 3 (cn_37) R->L }
% 18.49/2.81 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c)))), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.82 = { by axiom 4 (condensed_detachment) }
% 18.49/2.82 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.82 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.82 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.82 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.82 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.82 = { by axiom 5 (cn_60) R->L }
% 18.49/2.82 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(T, S)), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.82 = { by axiom 4 (condensed_detachment) }
% 18.49/2.82 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.82 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.83 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.83 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.83 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.83 = { by axiom 2 (cn_19) R->L }
% 18.49/2.83 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.83 = { by axiom 4 (condensed_detachment) }
% 18.49/2.83 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.83 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.83 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.83 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.83 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.83 = { by axiom 4 (condensed_detachment) R->L }
% 18.49/2.83 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.83 = { by axiom 2 (cn_19) }
% 18.49/2.83 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.83 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.83 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.83 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.83 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.83 = { by axiom 4 (condensed_detachment) R->L }
% 18.49/2.84 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z2, implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z2, implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.84 = { by axiom 2 (cn_19) }
% 18.49/2.84 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z2, implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.84 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.84 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z2, implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.84 = { by axiom 2 (cn_19) }
% 18.49/2.84 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.84 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.84 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.84 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.84 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.84 = { by axiom 2 (cn_19) R->L }
% 18.49/2.84 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.84 = { by axiom 4 (condensed_detachment) }
% 18.49/2.84 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.84 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.84 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.84 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.84 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.85 = { by axiom 4 (condensed_detachment) R->L }
% 18.49/2.85 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.85 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.85 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.85 = { by axiom 5 (cn_60) R->L }
% 18.49/2.86 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.86 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.86 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.86 = { by axiom 3 (cn_37) R->L }
% 18.49/2.87 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.87 = { by axiom 4 (condensed_detachment) }
% 18.49/2.87 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.87 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.87 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.87 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.87 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.87 = { by axiom 4 (condensed_detachment) R->L }
% 18.49/2.87 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.87 = { by axiom 5 (cn_60) }
% 18.49/2.88 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.88 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.88 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.89 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.89 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.89 = { by axiom 4 (condensed_detachment) R->L }
% 18.49/2.89 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, c), implies(implies(b, c), implies(a, c))), implies(not(a), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.89 = { by axiom 3 (cn_37) }
% 18.49/2.89 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.89 = { by axiom 1 (ifeq_axiom) }
% 18.49/2.89 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.89 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.90 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.90 = { by axiom 2 (cn_19) R->L }
% 18.49/2.90 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T2, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.90 = { by axiom 1 (ifeq_axiom) R->L }
% 18.49/2.90 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T2, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 18.49/2.90 = { by axiom 2 (cn_19) R->L }
% 19.27/2.90 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T2, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c))), implies(implies(a, c), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(implies(T2, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.90 = { by axiom 4 (condensed_detachment) }
% 19.27/2.90 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.91 = { by axiom 1 (ifeq_axiom) }
% 19.27/2.91 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.91 = { by axiom 1 (ifeq_axiom) R->L }
% 19.27/2.91 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.91 = { by axiom 4 (condensed_detachment) R->L }
% 19.27/2.91 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S2, implies(implies(implies(W2, V2), U2), implies(V2, U2))), implies(not(a), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(S2, implies(implies(implies(W2, V2), U2), implies(V2, U2))), implies(not(a), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.91 = { by axiom 2 (cn_19) }
% 19.27/2.92 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S2, implies(implies(implies(W2, V2), U2), implies(V2, U2))), implies(not(a), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.92 = { by axiom 1 (ifeq_axiom) }
% 19.27/2.92 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, implies(implies(implies(W2, V2), U2), implies(V2, U2))), implies(not(a), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.92 = { by axiom 2 (cn_19) }
% 19.27/2.92 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.92 = { by axiom 1 (ifeq_axiom) }
% 19.27/2.92 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(not(a), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.92 = { by axiom 4 (condensed_detachment) }
% 19.27/2.92 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.93 = { by axiom 1 (ifeq_axiom) }
% 19.27/2.93 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.93 = { by axiom 1 (ifeq_axiom) R->L }
% 19.27/2.93 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.93 = { by axiom 2 (cn_19) R->L }
% 19.27/2.93 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(V2, U2)), implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), U2), implies(V2, U2))), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.93 = { by axiom 4 (condensed_detachment) }
% 19.27/2.93 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.93 = { by axiom 1 (ifeq_axiom) }
% 19.27/2.93 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.93 = { by axiom 4 (condensed_detachment) }
% 19.27/2.93 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.93 = { by axiom 1 (ifeq_axiom) }
% 19.27/2.93 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(b, implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 19.27/2.93 = { by axiom 4 (condensed_detachment) }
% 19.27/2.93 true
% 19.27/2.93 % SZS output end Proof
% 19.27/2.93
% 19.27/2.93 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------