%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL072-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 2.93s 0.94s
% Output : Proof 5.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL072-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n013.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 15:20:06 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.93/0.94 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.93/0.94
% 2.93/0.94 % SZS status Unsatisfiable
% 2.93/0.95
% 2.93/1.12 % SZS output start Proof
% 2.93/1.12 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.93/1.12 Axiom 2 (cn_19): is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))) = true.
% 2.93/1.12 Axiom 3 (cn_37): is_a_theorem(implies(implies(implies(X, Y), Z), implies(not(X), Z))) = true.
% 2.93/1.12 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.
% 4.51/1.13 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.
% 4.51/1.13
% 4.51/1.13 Goal 1 (prove_cn_3): is_a_theorem(implies(a, implies(not(a), b))) = true.
% 4.51/1.13 Proof:
% 4.51/1.13 is_a_theorem(implies(a, implies(not(a), b)))
% 4.51/1.13 = { by axiom 1 (ifeq_axiom) R->L }
% 4.51/1.13 ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 4.51/1.13 = { by axiom 1 (ifeq_axiom) R->L }
% 4.51/1.13 ifeq(true, true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.13 = { by axiom 4 (condensed_detachment) R->L }
% 4.51/1.13 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.13 = { by axiom 1 (ifeq_axiom) R->L }
% 4.51/1.13 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.13 = { by axiom 4 (condensed_detachment) R->L }
% 4.51/1.14 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.14 = { by axiom 1 (ifeq_axiom) R->L }
% 4.51/1.14 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.14 = { by axiom 4 (condensed_detachment) R->L }
% 4.51/1.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(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(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.15 = { by axiom 3 (cn_37) }
% 4.51/1.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(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(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.15 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(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(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.15 = { by axiom 1 (ifeq_axiom) R->L }
% 4.51/1.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(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(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.16 = { by axiom 2 (cn_19) R->L }
% 4.51/1.16 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W, 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(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.16 = { by axiom 1 (ifeq_axiom) R->L }
% 4.51/1.16 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W, 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(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.16 = { by axiom 2 (cn_19) R->L }
% 4.51/1.16 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, 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(W, 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(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.17 = { by axiom 4 (condensed_detachment) }
% 4.51/1.17 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.17 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.17 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.17 = { by axiom 1 (ifeq_axiom) R->L }
% 4.51/1.17 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.17 = { by axiom 4 (condensed_detachment) R->L }
% 4.51/1.18 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V, implies(Y, implies(Z, Y))), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(Y, implies(Z, Y))), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))))), true, is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.18 = { by axiom 2 (cn_19) }
% 4.51/1.18 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), 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, implies(Y, implies(Z, Y))), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))))), true, is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.18 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.18 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, implies(Y, implies(Z, Y))), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))))), true, is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))))), true), true, ifeq(is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.18 = { by axiom 2 (cn_19) }
% 4.51/1.19 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))))), true), true, ifeq(is_a_theorem(implies(not(not(a)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.19 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.19 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(a, implies(not(a), b))), implies(implies(Y, implies(Z, Y)), implies(not(not(a)), 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(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.19 = { by axiom 4 (condensed_detachment) }
% 4.51/1.19 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.19 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.19 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(not(not(a)), implies(a, implies(not(a), b)))), implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.19 = { by axiom 5 (cn_60) }
% 4.51/1.19 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 1 (ifeq_axiom) R->L }
% 4.51/1.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 4 (condensed_detachment) R->L }
% 4.51/1.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, Z), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, ifeq(is_a_theorem(implies(implies(implies(U, Z), Y), implies(Z, Y))), true, is_a_theorem(implies(Y, implies(Z, Y))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 2 (cn_19) }
% 4.51/1.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U, Z), Y), implies(Z, Y))), true, is_a_theorem(implies(Y, implies(Z, Y))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(U, Z), Y), implies(Z, Y))), true, is_a_theorem(implies(Y, implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 2 (cn_19) }
% 4.51/1.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(Y, implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))))), true, ifeq(is_a_theorem(implies(Y, implies(Z, Y))), true, is_a_theorem(implies(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b))), implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 4 (condensed_detachment) }
% 4.51/1.20 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.20 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, X), a), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 2 (cn_19) }
% 4.51/1.20 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.20 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.20 = { by axiom 4 (condensed_detachment) R->L }
% 4.51/1.20 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))), implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))))), true, ifeq(is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.21 = { by axiom 3 (cn_37) }
% 4.51/1.21 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.21 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.21 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.21 = { by axiom 1 (ifeq_axiom) R->L }
% 4.51/1.21 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.21 = { by axiom 4 (condensed_detachment) R->L }
% 4.51/1.21 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.21 = { by axiom 1 (ifeq_axiom) R->L }
% 4.51/1.21 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.21 = { by axiom 4 (condensed_detachment) R->L }
% 4.51/1.21 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, X), b), implies(not(a), b)), implies(not(implies(a, X)), implies(not(a), b)))), true, ifeq(is_a_theorem(implies(implies(implies(a, X), b), implies(not(a), b))), true, is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.21 = { by axiom 3 (cn_37) }
% 4.51/1.21 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, X), b), implies(not(a), b)), implies(not(implies(a, X)), implies(not(a), b)))), true, ifeq(true, true, is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.22 = { by axiom 1 (ifeq_axiom) }
% 4.51/1.22 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, X), b), implies(not(a), b)), implies(not(implies(a, X)), implies(not(a), b)))), true, is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.22 = { by axiom 3 (cn_37) }
% 4.51/1.22 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 4.51/1.22 = { by axiom 1 (ifeq_axiom) }
% 5.40/1.22 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.22 = { by axiom 1 (ifeq_axiom) R->L }
% 5.40/1.22 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.22 = { by axiom 4 (condensed_detachment) R->L }
% 5.40/1.23 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X2, implies(T, implies(S, T))), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), implies(implies(not(implies(a, X)), implies(not(a), b)), implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(X2, implies(T, implies(S, T))), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))))), true, is_a_theorem(implies(implies(not(implies(a, X)), implies(not(a), b)), implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))))), true), true), true, ifeq(is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.23 = { by axiom 2 (cn_19) }
% 5.40/1.23 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X2, implies(T, implies(S, T))), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))))), true, is_a_theorem(implies(implies(not(implies(a, X)), implies(not(a), b)), implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))))), true), true), true, ifeq(is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.23 = { by axiom 1 (ifeq_axiom) }
% 5.40/1.23 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X2, implies(T, implies(S, T))), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))))), true, is_a_theorem(implies(implies(not(implies(a, X)), implies(not(a), b)), implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.23 = { by axiom 2 (cn_19) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(a, X)), implies(not(a), b)), implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))))), true), true, ifeq(is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 1 (ifeq_axiom) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, X)), implies(not(a), b)), implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))))), true, ifeq(is_a_theorem(implies(not(implies(a, X)), implies(not(a), b))), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b)))), true), true), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 4 (condensed_detachment) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 1 (ifeq_axiom) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, implies(S, T)), implies(not(implies(a, X)), implies(not(a), b))), implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))))), true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 5 (cn_60) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 1 (ifeq_axiom) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 1 (ifeq_axiom) R->L }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 4 (condensed_detachment) R->L }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, S), T), implies(S, T)), implies(T, implies(S, T)))), true, ifeq(is_a_theorem(implies(implies(implies(Y2, S), T), implies(S, T))), true, is_a_theorem(implies(T, implies(S, T))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 2 (cn_19) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y2, S), T), implies(S, T))), true, is_a_theorem(implies(T, implies(S, T))), true), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 1 (ifeq_axiom) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, S), T), implies(S, T))), true, is_a_theorem(implies(T, implies(S, T))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 2 (cn_19) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(T, implies(S, T))), true), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 1 (ifeq_axiom) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(T, implies(S, T)), implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b))))), true, ifeq(is_a_theorem(implies(T, implies(S, T))), true, is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 4 (condensed_detachment) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 1 (ifeq_axiom) }
% 5.40/1.24 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b))), implies(a, implies(not(a), b)))), true, ifeq(is_a_theorem(implies(not(a), implies(implies(implies(a, X), a), implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 5.40/1.24 = { by axiom 4 (condensed_detachment) }
% 5.40/1.24 true
% 5.40/1.24 % SZS output end Proof
% 5.40/1.24
% 5.40/1.24 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------