%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL069-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 2.12s 0.71s
% Output : Proof 3.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL069-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 15:26:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.12/0.71 Command-line arguments: --no-flatten-goal
% 2.12/0.71
% 2.12/0.71 % SZS status Unsatisfiable
% 2.12/0.71
% 2.93/0.88 % SZS output start Proof
% 2.93/0.88 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.93/0.88 Axiom 2 (cn_19): is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))) = true.
% 2.93/0.88 Axiom 3 (cn_37): is_a_theorem(implies(implies(implies(X, Y), Z), implies(not(X), Z))) = true.
% 2.93/0.88 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.
% 2.93/0.88 Axiom 5 (cn_59): is_a_theorem(implies(implies(not(X), Y), implies(implies(Z, Y), implies(implies(X, Z), Y)))) = true.
% 2.93/0.88
% 2.93/0.88 Goal 1 (prove_cn_3): is_a_theorem(implies(a, implies(not(a), b))) = true.
% 2.93/0.88 Proof:
% 2.93/0.88 is_a_theorem(implies(a, implies(not(a), b)))
% 2.93/0.88 = { by axiom 1 (ifeq_axiom) R->L }
% 2.93/0.88 ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 2.93/0.88 = { by axiom 4 (condensed_detachment) R->L }
% 2.93/0.88 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(not(a), implies(a, implies(not(a), b))))), true, ifeq(is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 2.93/0.88 = { by axiom 3 (cn_37) }
% 2.93/0.88 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 2.93/0.88 = { by axiom 1 (ifeq_axiom) }
% 2.93/0.88 ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 2.93/0.89 = { by axiom 1 (ifeq_axiom) R->L }
% 2.93/0.89 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 2.93/0.89 = { by axiom 4 (condensed_detachment) R->L }
% 2.93/0.89 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 2.93/0.89 = { by axiom 2 (cn_19) }
% 2.93/0.89 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 2.93/0.90 = { by axiom 1 (ifeq_axiom) }
% 2.93/0.90 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 2.93/0.90 = { by axiom 1 (ifeq_axiom) R->L }
% 2.93/0.90 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.90 = { by axiom 5 (cn_59) R->L }
% 3.59/0.90 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.91 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.91 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.91 = { by axiom 4 (condensed_detachment) R->L }
% 3.59/0.91 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.92 = { by axiom 3 (cn_37) }
% 3.59/0.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.92 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.92 = { by axiom 2 (cn_19) }
% 3.59/0.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.92 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(is_a_theorem(implies(not(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(implies(implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.93 = { by axiom 4 (condensed_detachment) }
% 3.59/0.93 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.93 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.93 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.93 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.93 = { by axiom 2 (cn_19) R->L }
% 3.59/0.93 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(X, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.93 = { by axiom 4 (condensed_detachment) }
% 3.59/0.93 ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.93 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.93 ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 3.59/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.93 ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.93 = { by axiom 4 (condensed_detachment) R->L }
% 3.59/0.93 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.93 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.93 = { by axiom 4 (condensed_detachment) R->L }
% 3.59/0.93 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.93 = { by axiom 2 (cn_19) }
% 3.59/0.94 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.94 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.94 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.94 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.95 = { by axiom 5 (cn_59) R->L }
% 3.59/0.95 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.95 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.96 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.96 = { by axiom 4 (condensed_detachment) R->L }
% 3.59/0.96 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.96 = { by axiom 3 (cn_37) }
% 3.59/0.96 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.96 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.97 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.97 = { by axiom 2 (cn_19) }
% 3.59/0.97 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.97 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))))), true, ifeq(is_a_theorem(implies(not(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(implies(implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.97 = { by axiom 4 (condensed_detachment) }
% 3.59/0.97 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.97 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.97 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.98 = { by axiom 2 (cn_19) R->L }
% 3.59/0.98 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))))), true, ifeq(is_a_theorem(implies(implies(implies(W, implies(Z, implies(a, implies(not(a), b)))), implies(a, implies(not(a), b))), implies(implies(Z, implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.98 = { by axiom 4 (condensed_detachment) }
% 3.59/0.98 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.98 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.98 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.98 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.98 = { by axiom 5 (cn_59) R->L }
% 3.59/0.98 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.98 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.98 = { by axiom 4 (condensed_detachment) R->L }
% 3.59/0.98 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), b), implies(a, implies(not(a), b))), implies(not(not(a)), implies(a, implies(not(a), b))))), true, ifeq(is_a_theorem(implies(implies(not(a), b), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.98 = { by axiom 3 (cn_37) }
% 3.59/0.98 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), b), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.99 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.99 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(a), b), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.99 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.99 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), b), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.99 = { by axiom 2 (cn_19) R->L }
% 3.59/0.99 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), b), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.99 = { by axiom 1 (ifeq_axiom) R->L }
% 3.59/0.99 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V, a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), b), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.99 = { by axiom 2 (cn_19) R->L }
% 3.59/0.99 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V, a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), b), implies(a, implies(not(a), b))))), true, ifeq(is_a_theorem(implies(implies(implies(V, a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), b), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.99 = { by axiom 4 (condensed_detachment) }
% 3.59/0.99 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.99 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.99 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.99 = { by axiom 4 (condensed_detachment) }
% 3.59/0.99 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.99 = { by axiom 1 (ifeq_axiom) }
% 3.59/0.99 ifeq(is_a_theorem(implies(implies(not(a), implies(a, implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(is_a_theorem(implies(not(a), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 3.59/0.99 = { by axiom 4 (condensed_detachment) }
% 3.59/0.99 true
% 3.59/0.99 % SZS output end Proof
% 3.59/0.99
% 3.59/0.99 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------