%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 11:49:48 AM UTC 2026
% Result : Theorem 0.02s 0.44s
% Output : Proof 0.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.35 % Computer : n020.cluster.edu
% 0.02/0.35 % Model : x86_64 x86_64
% 0.02/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.35 % Memory : 8046.5625MB
% 0.02/0.35 % OS : Linux 6.8.0-71-generic
% 0.02/0.35 % CPULimit : 300
% 0.02/0.35 % WCLimit : 300
% 0.02/0.35 % DateTime : Sun Sep 27 15:41:34 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.44 Command-line arguments: --no-flatten-goal
% 0.02/0.44
% 0.02/0.44 % SZS status Theorem
% 0.02/0.44
% 0.02/0.44 % SZS output start Proof
% 0.02/0.44 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.02/0.44 Axiom 2 (thm147): a_truth(implies(X, implies(Y, X))) = true.
% 0.02/0.44 Axiom 3 (thm147_3): ifeq(a_truth(implies(X, Y)), true, ifeq(a_truth(X), true, a_truth(Y), true), true) = true.
% 0.02/0.44 Axiom 4 (thm147_1): a_truth(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 0.02/0.44
% 0.02/0.44 Goal 1 (thm147_4): a_truth(implies(a, a)) = true.
% 0.02/0.45 Proof:
% 0.02/0.45 a_truth(implies(a, a))
% 0.02/0.45 = { by axiom 1 (ifeq_axiom) R->L }
% 0.02/0.45 ifeq(true, true, a_truth(implies(a, a)), true)
% 0.02/0.45 = { by axiom 3 (thm147_3) R->L }
% 0.02/0.45 ifeq(ifeq(a_truth(implies(implies(a, implies(implies(X, a), a)), implies(implies(a, implies(X, a)), implies(a, a)))), true, ifeq(a_truth(implies(a, implies(implies(X, a), a))), true, a_truth(implies(implies(a, implies(X, a)), implies(a, a))), true), true), true, a_truth(implies(a, a)), true)
% 0.02/0.45 = { by axiom 2 (thm147) }
% 0.02/0.45 ifeq(ifeq(a_truth(implies(implies(a, implies(implies(X, a), a)), implies(implies(a, implies(X, a)), implies(a, a)))), true, ifeq(true, true, a_truth(implies(implies(a, implies(X, a)), implies(a, a))), true), true), true, a_truth(implies(a, a)), true)
% 0.02/0.45 = { by axiom 1 (ifeq_axiom) }
% 0.02/0.45 ifeq(ifeq(a_truth(implies(implies(a, implies(implies(X, a), a)), implies(implies(a, implies(X, a)), implies(a, a)))), true, a_truth(implies(implies(a, implies(X, a)), implies(a, a))), true), true, a_truth(implies(a, a)), true)
% 0.02/0.45 = { by axiom 4 (thm147_1) }
% 0.02/0.45 ifeq(ifeq(true, true, a_truth(implies(implies(a, implies(X, a)), implies(a, a))), true), true, a_truth(implies(a, a)), true)
% 0.02/0.45 = { by axiom 1 (ifeq_axiom) }
% 0.02/0.45 ifeq(a_truth(implies(implies(a, implies(X, a)), implies(a, a))), true, a_truth(implies(a, a)), true)
% 0.02/0.45 = { by axiom 1 (ifeq_axiom) R->L }
% 0.02/0.45 ifeq(a_truth(implies(implies(a, implies(X, a)), implies(a, a))), true, ifeq(true, true, a_truth(implies(a, a)), true), true)
% 0.02/0.45 = { by axiom 2 (thm147) R->L }
% 0.02/0.45 ifeq(a_truth(implies(implies(a, implies(X, a)), implies(a, a))), true, ifeq(a_truth(implies(a, implies(X, a))), true, a_truth(implies(a, a)), true), true)
% 0.02/0.45 = { by axiom 3 (thm147_3) }
% 0.02/0.45 true
% 0.02/0.45 % SZS output end Proof
% 0.02/0.45
% 0.02/0.45 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------