%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL118-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 11:49:05 AM UTC 2026
% Result : Unsatisfiable 0.68s 0.52s
% Output : Proof 1.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL118-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n026.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 27 15:25:41 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.52 Command-line arguments: --no-flatten-goal
% 0.68/0.52
% 0.68/0.52 % SZS status Unsatisfiable
% 0.68/0.52
% 0.68/0.59 % SZS output start Proof
% 0.68/0.59 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.68/0.59 Axiom 2 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 0.68/0.59 Axiom 3 (wo): is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(Y, X)))) = true.
% 0.68/0.59
% 0.68/0.59 Goal 1 (prove_yqm): is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))) = true.
% 0.68/0.59 Proof:
% 0.68/0.59 is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.68/0.59 = { by axiom 1 (ifeq_axiom) R->L }
% 0.68/0.59 ifeq(true, true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.59 = { by axiom 2 (condensed_detachment) R->L }
% 0.68/0.59 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.59 = { by axiom 3 (wo) }
% 0.68/0.59 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.59 = { by axiom 1 (ifeq_axiom) }
% 0.68/0.59 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.59 = { by axiom 1 (ifeq_axiom) R->L }
% 0.68/0.59 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.60 = { by axiom 2 (condensed_detachment) R->L }
% 0.68/0.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.60 = { by axiom 1 (ifeq_axiom) R->L }
% 0.68/0.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.60 = { by axiom 3 (wo) R->L }
% 0.68/0.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(b, equivalent(a, equivalent(c, b)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.60 = { by axiom 1 (ifeq_axiom) R->L }
% 0.68/0.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(b, equivalent(a, equivalent(c, b)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.60 = { by axiom 3 (wo) R->L }
% 0.68/0.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(b, equivalent(a, equivalent(c, b))))), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(b, equivalent(a, equivalent(c, b)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.60 = { by axiom 2 (condensed_detachment) }
% 0.68/0.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.60 = { by axiom 1 (ifeq_axiom) }
% 0.68/0.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.61 = { by axiom 1 (ifeq_axiom) R->L }
% 0.68/0.61 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.61 = { by axiom 2 (condensed_detachment) R->L }
% 0.68/0.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.61 = { by axiom 1 (ifeq_axiom) R->L }
% 0.68/0.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.62 = { by axiom 3 (wo) R->L }
% 0.68/0.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.62 = { by axiom 1 (ifeq_axiom) R->L }
% 0.68/0.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.62 = { by axiom 3 (wo) R->L }
% 0.68/0.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b))))), equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.63 = { by axiom 2 (condensed_detachment) }
% 0.68/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.63 = { by axiom 1 (ifeq_axiom) }
% 0.68/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.63 = { by axiom 3 (wo) }
% 0.68/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.63 = { by axiom 1 (ifeq_axiom) }
% 0.68/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 0.68/0.63 = { by axiom 1 (ifeq_axiom) R->L }
% 1.69/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 1.69/0.64 = { by axiom 3 (wo) R->L }
% 1.69/0.64 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 1.69/0.64 = { by axiom 2 (condensed_detachment) }
% 1.69/0.64 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 1.69/0.64 = { by axiom 1 (ifeq_axiom) }
% 1.69/0.64 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 1.69/0.64 = { by axiom 1 (ifeq_axiom) R->L }
% 1.69/0.64 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 1.69/0.64 = { by axiom 3 (wo) R->L }
% 1.69/0.64 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 1.69/0.64 = { by axiom 2 (condensed_detachment) }
% 1.69/0.64 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 1.69/0.64 = { by axiom 1 (ifeq_axiom) }
% 1.69/0.64 ifeq(is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true)
% 1.69/0.64 = { by axiom 1 (ifeq_axiom) R->L }
% 1.69/0.64 ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true), true)
% 1.69/0.64 = { by axiom 3 (wo) R->L }
% 1.69/0.64 ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))), true, ifeq(is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))), true), true)
% 1.69/0.64 = { by axiom 2 (condensed_detachment) }
% 1.69/0.64 true
% 1.69/0.64 % SZS output end Proof
% 1.69/0.64
% 1.69/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------