%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN068+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 01:47:01 PM UTC 2026
% Result : Theorem 0.06s 0.24s
% Output : Proof 0.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN068+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.16 % Computer : n014.cluster.edu
% 0.06/0.16 % Model : x86_64 x86_64
% 0.06/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.16 % Memory : 8046.5625MB
% 0.06/0.16 % OS : Linux 6.8.0-71-generic
% 0.06/0.16 % CPULimit : 300
% 0.06/0.16 % WCLimit : 300
% 0.06/0.16 % DateTime : Mon Sep 28 15:28:30 UTC 2026
% 0.06/0.16 % CPUTime :
% 0.06/0.16 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.24 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 0.06/0.24
% 0.06/0.24 % SZS status Theorem
% 0.06/0.24
% 0.06/0.24 % SZS output start Proof
% 0.06/0.24 Axiom 1 (pel44_2): big_j(x) = true.
% 0.06/0.24 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.06/0.24 Axiom 3 (pel44): ifeq(big_j(X), true, big_f(X), true) = true.
% 0.06/0.24 Axiom 4 (pel44_1_1): ifeq(big_f(X), true, big_g(y1(X)), true) = true.
% 0.06/0.24 Axiom 5 (pel44_2_1): ifeq(big_g(X), true, big_h(x, X), true) = true.
% 0.06/0.24
% 0.06/0.24 Goal 1 (pel44_1_3): tuple(big_f(X), big_h(X, y1(X))) = tuple(true, true).
% 0.06/0.24 The goal is true when:
% 0.06/0.24 X = x
% 0.06/0.24
% 0.06/0.24 Proof:
% 0.06/0.24 tuple(big_f(x), big_h(x, y1(x)))
% 0.06/0.24 = { by axiom 2 (ifeq_axiom) R->L }
% 0.06/0.24 tuple(big_f(x), ifeq(true, true, big_h(x, y1(x)), true))
% 0.06/0.24 = { by axiom 4 (pel44_1_1) R->L }
% 0.06/0.24 tuple(big_f(x), ifeq(ifeq(big_f(x), true, big_g(y1(x)), true), true, big_h(x, y1(x)), true))
% 0.06/0.24 = { by axiom 2 (ifeq_axiom) R->L }
% 0.06/0.24 tuple(big_f(x), ifeq(ifeq(ifeq(true, true, big_f(x), true), true, big_g(y1(x)), true), true, big_h(x, y1(x)), true))
% 0.06/0.24 = { by axiom 1 (pel44_2) R->L }
% 0.06/0.24 tuple(big_f(x), ifeq(ifeq(ifeq(big_j(x), true, big_f(x), true), true, big_g(y1(x)), true), true, big_h(x, y1(x)), true))
% 0.06/0.24 = { by axiom 3 (pel44) }
% 0.06/0.24 tuple(big_f(x), ifeq(ifeq(true, true, big_g(y1(x)), true), true, big_h(x, y1(x)), true))
% 0.06/0.24 = { by axiom 2 (ifeq_axiom) }
% 0.06/0.24 tuple(big_f(x), ifeq(big_g(y1(x)), true, big_h(x, y1(x)), true))
% 0.06/0.24 = { by axiom 5 (pel44_2_1) }
% 0.06/0.24 tuple(big_f(x), true)
% 0.06/0.24 = { by axiom 2 (ifeq_axiom) R->L }
% 0.06/0.24 tuple(ifeq(true, true, big_f(x), true), true)
% 0.06/0.24 = { by axiom 1 (pel44_2) R->L }
% 0.06/0.24 tuple(ifeq(big_j(x), true, big_f(x), true), true)
% 0.06/0.24 = { by axiom 3 (pel44) }
% 0.06/0.24 tuple(true, true)
% 0.06/0.24 % SZS output end Proof
% 0.06/0.24
% 0.06/0.24 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------