%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 11:48:59 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : Proof 1.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:23:23 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 Command-line arguments: --no-flatten-goal
% 0.18/0.48
% 0.18/0.48 % SZS status Unsatisfiable
% 0.18/0.48
% 1.15/0.58 % SZS output start Proof
% 1.15/0.58 Axiom 1 (ic_1): is_a_theorem(implies(X, X)) = true.
% 1.15/0.58 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.15/0.58 Axiom 3 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 1.15/0.58 Axiom 4 (ic_JLukasiewicz): is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X)))) = true.
% 1.15/0.58
% 1.15/0.58 Goal 1 (prove_ic_3): is_a_theorem(implies(implies(implies(a, b), a), a)) = true.
% 1.15/0.58 Proof:
% 1.15/0.58 is_a_theorem(implies(implies(implies(a, b), a), a))
% 1.15/0.59 = { by axiom 2 (ifeq_axiom) R->L }
% 1.15/0.59 ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.60 = { by axiom 3 (condensed_detachment) R->L }
% 1.15/0.60 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.60 = { by axiom 2 (ifeq_axiom) R->L }
% 1.15/0.60 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.60 = { by axiom 4 (ic_JLukasiewicz) R->L }
% 1.15/0.60 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.60 = { by axiom 2 (ifeq_axiom) R->L }
% 1.15/0.60 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.60 = { by axiom 1 (ic_1) R->L }
% 1.15/0.61 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.61 = { by axiom 3 (condensed_detachment) }
% 1.15/0.61 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.61 = { by axiom 2 (ifeq_axiom) }
% 1.15/0.61 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.61 = { by axiom 2 (ifeq_axiom) R->L }
% 1.15/0.61 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.61 = { by axiom 3 (condensed_detachment) R->L }
% 1.15/0.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(is_a_theorem(implies(Y, Y)), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.61 = { by axiom 1 (ic_1) }
% 1.15/0.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.62 = { by axiom 2 (ifeq_axiom) }
% 1.15/0.62 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.62 = { by axiom 2 (ifeq_axiom) R->L }
% 1.15/0.62 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.62 = { by axiom 4 (ic_JLukasiewicz) R->L }
% 1.15/0.62 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.62 = { by axiom 2 (ifeq_axiom) R->L }
% 1.15/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.63 = { by axiom 3 (condensed_detachment) R->L }
% 1.15/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.15/0.64 = { by axiom 4 (ic_JLukasiewicz) }
% 1.15/0.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.65 = { by axiom 2 (ifeq_axiom) }
% 1.67/0.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.65 = { by axiom 2 (ifeq_axiom) R->L }
% 1.67/0.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.66 = { by axiom 3 (condensed_detachment) R->L }
% 1.67/0.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.66 = { by axiom 1 (ic_1) }
% 1.67/0.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.67 = { by axiom 2 (ifeq_axiom) }
% 1.67/0.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.67 = { by axiom 4 (ic_JLukasiewicz) }
% 1.67/0.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.68 = { by axiom 2 (ifeq_axiom) }
% 1.67/0.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.68 = { by axiom 2 (ifeq_axiom) R->L }
% 1.67/0.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.68 = { by axiom 4 (ic_JLukasiewicz) R->L }
% 1.67/0.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Z), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.68 = { by axiom 3 (condensed_detachment) }
% 1.67/0.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.69 = { by axiom 2 (ifeq_axiom) }
% 1.67/0.69 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, Z), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(Y, Y), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.69 = { by axiom 3 (condensed_detachment) }
% 1.67/0.69 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.69 = { by axiom 2 (ifeq_axiom) }
% 1.67/0.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.69 = { by axiom 2 (ifeq_axiom) R->L }
% 1.67/0.69 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.69 = { by axiom 4 (ic_JLukasiewicz) R->L }
% 1.67/0.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(X, X), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.69 = { by axiom 3 (condensed_detachment) }
% 1.67/0.69 ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.69 = { by axiom 2 (ifeq_axiom) }
% 1.67/0.69 ifeq(is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 1.67/0.69 = { by axiom 2 (ifeq_axiom) R->L }
% 1.67/0.69 ifeq(is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 1.67/0.69 = { by axiom 1 (ic_1) R->L }
% 1.67/0.69 ifeq(is_a_theorem(implies(implies(X, X), implies(implies(implies(a, b), a), a))), true, ifeq(is_a_theorem(implies(X, X)), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 1.67/0.69 = { by axiom 3 (condensed_detachment) }
% 1.67/0.69 true
% 1.67/0.69 % SZS output end Proof
% 1.67/0.69
% 1.67/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------