%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL033-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:48:52 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.50s
% Output : Proof 1.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL033-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 15:20:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.50 Command-line arguments: --no-flatten-goal
% 0.23/0.50
% 0.23/0.50 % SZS status Unsatisfiable
% 0.23/0.50
% 1.18/0.66 % SZS output start Proof
% 1.18/0.66 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.18/0.66 Axiom 2 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 1.18/0.66 Axiom 3 (c0_CAMeredith): is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X)))) = true.
% 1.18/0.66
% 1.18/0.66 Goal 1 (prove_c0_2): is_a_theorem(implies(a, implies(b, a))) = true.
% 1.18/0.66 Proof:
% 1.18/0.66 is_a_theorem(implies(a, implies(b, a)))
% 1.18/0.66 = { by axiom 1 (ifeq_axiom) R->L }
% 1.18/0.66 ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.18/0.66 = { by axiom 2 (condensed_detachment) R->L }
% 1.18/0.66 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.18/0.66 = { by axiom 1 (ifeq_axiom) R->L }
% 1.18/0.67 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.67 = { by axiom 2 (condensed_detachment) R->L }
% 1.32/0.67 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood))), implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.67 = { by axiom 3 (c0_CAMeredith) }
% 1.32/0.67 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.67 = { by axiom 1 (ifeq_axiom) }
% 1.32/0.67 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.67 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.67 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.67 = { by axiom 2 (condensed_detachment) R->L }
% 1.32/0.67 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(b, a), W), falsehood)), implies(implies(a, Z), falsehood)), implies(a, falsehood)), implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)), implies(falsehood, falsehood)), implies(implies(a, Z), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(b, a), W), falsehood)), implies(implies(a, Z), falsehood)), implies(a, falsehood)), implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)), implies(falsehood, falsehood)), implies(implies(a, Z), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.67 = { by axiom 3 (c0_CAMeredith) }
% 1.32/0.67 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(b, a), W), falsehood)), implies(implies(a, Z), falsehood)), implies(a, falsehood)), implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)), implies(falsehood, falsehood)), implies(implies(a, Z), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.67 = { by axiom 1 (ifeq_axiom) }
% 1.32/0.67 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(b, a), W), falsehood)), implies(implies(a, Z), falsehood)), implies(a, falsehood)), implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)), implies(falsehood, falsehood)), implies(implies(a, Z), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 3 (c0_CAMeredith) }
% 1.32/0.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)), implies(falsehood, falsehood)), implies(implies(a, Z), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 1 (ifeq_axiom) }
% 1.32/0.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)), implies(falsehood, falsehood)), implies(implies(a, Z), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)), implies(falsehood, falsehood)), implies(implies(a, Z), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 3 (c0_CAMeredith) R->L }
% 1.32/0.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)), implies(falsehood, falsehood)), implies(implies(a, Z), implies(falsehood, falsehood))), implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(implies(b, a), W), falsehood)), implies(falsehood, falsehood)), implies(implies(a, Z), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(falsehood, falsehood)), implies(a, falsehood)), implies(implies(implies(b, a), W), implies(a, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 2 (condensed_detachment) }
% 1.32/0.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 1 (ifeq_axiom) }
% 1.32/0.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 3 (c0_CAMeredith) R->L }
% 1.32/0.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a)), implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), W), implies(a, falsehood)), a), implies(falsehood, a))), true, is_a_theorem(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 2 (condensed_detachment) }
% 1.32/0.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 1 (ifeq_axiom) }
% 1.32/0.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.68 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 3 (c0_CAMeredith) R->L }
% 1.32/0.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), implies(b, falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(falsehood, a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.68 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), implies(b, falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(falsehood, a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.68 = { by axiom 3 (c0_CAMeredith) R->L }
% 1.32/0.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(b, a)), implies(b, falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(falsehood, a), implies(b, a))), implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), implies(b, falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(falsehood, a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.69 = { by axiom 2 (condensed_detachment) }
% 1.32/0.69 ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.69 = { by axiom 1 (ifeq_axiom) }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, is_a_theorem(implies(a, implies(b, a))), true)
% 1.32/0.69 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.69 = { by axiom 2 (condensed_detachment) R->L }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.69 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.69 = { by axiom 2 (condensed_detachment) R->L }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true), true), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.69 = { by axiom 3 (c0_CAMeredith) }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true), true), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.69 = { by axiom 1 (ifeq_axiom) }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.69 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.69 = { by axiom 3 (c0_CAMeredith) R->L }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(implies(implies(X, Y), T), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.69 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(implies(implies(X, Y), T), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.69 = { by axiom 3 (c0_CAMeredith) R->L }
% 1.32/0.69 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(implies(implies(X, Y), T), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood))), implies(implies(implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(implies(implies(X, Y), T), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(V, implies(falsehood, U)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), T), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.69 = { by axiom 2 (condensed_detachment) }
% 1.32/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.70 = { by axiom 1 (ifeq_axiom) }
% 1.32/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.70 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.70 = { by axiom 3 (c0_CAMeredith) R->L }
% 1.32/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y)), implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), T), implies(falsehood, falsehood)), Y), implies(implies(V, implies(falsehood, U)), Y))), true, is_a_theorem(implies(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.70 = { by axiom 2 (condensed_detachment) }
% 1.32/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.70 = { by axiom 1 (ifeq_axiom) }
% 1.32/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.70 = { by axiom 1 (ifeq_axiom) R->L }
% 1.32/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.70 = { by axiom 2 (condensed_detachment) R->L }
% 1.32/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, U), implies(X, falsehood)), implies(V, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood))), implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, U)), implies(V, implies(falsehood, U))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, U), implies(X, falsehood)), implies(V, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, U)), implies(V, implies(falsehood, U)))), true), true), true, is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.70 = { by axiom 3 (c0_CAMeredith) }
% 1.32/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, U), implies(X, falsehood)), implies(V, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, U)), implies(V, implies(falsehood, U)))), true), true), true, is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.70 = { by axiom 1 (ifeq_axiom) }
% 1.32/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, U), implies(X, falsehood)), implies(V, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, U)), implies(V, implies(falsehood, U)))), true), true, is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.32/0.70 = { by axiom 3 (c0_CAMeredith) }
% 1.29/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, U)), implies(V, implies(falsehood, U)))), true), true, is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.29/0.70 = { by axiom 1 (ifeq_axiom) }
% 1.29/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, U)), implies(V, implies(falsehood, U)))), true, is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.29/0.70 = { by axiom 1 (ifeq_axiom) R->L }
% 1.29/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, U)), implies(V, implies(falsehood, U)))), true, is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.29/0.70 = { by axiom 3 (c0_CAMeredith) R->L }
% 1.29/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, U)), implies(V, implies(falsehood, U))), implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, U)), implies(V, implies(falsehood, U)))), true, is_a_theorem(implies(implies(implies(V, implies(falsehood, U)), Y), implies(X, Y))), true), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.29/0.70 = { by axiom 2 (condensed_detachment) }
% 1.29/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.29/0.70 = { by axiom 1 (ifeq_axiom) }
% 1.29/0.70 ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(a, implies(b, a)))), true, ifeq(is_a_theorem(implies(falsehood, implies(X, Y))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 1.29/0.70 = { by axiom 2 (condensed_detachment) }
% 1.29/0.70 true
% 1.29/0.70 % SZS output end Proof
% 1.29/0.71
% 1.29/0.71 RESULT: Unsatisfiable (the axioms are contradictory).
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