%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN057+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 01:46:58 PM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN057+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.16 % Computer : n005.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Mon Sep 28 15:26:46 UTC 2026
% 0.07/0.16 % CPUTime :
% 0.07/0.16 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.23 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.07/0.23
% 0.07/0.23 % SZS status Theorem
% 0.07/0.23
% 0.07/0.24 % SZS output start Proof
% 0.07/0.24 Axiom 1 (pel27_1): big_i(x) = true.
% 0.07/0.24 Axiom 2 (pel27_1): big_f(x2) = true.
% 0.07/0.24 Axiom 3 (pel27): big_j(x) = true.
% 0.07/0.24 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.24 Axiom 5 (pel27_2): ifeq(big_f(X), true, big_h(X), true) = true.
% 0.07/0.24 Axiom 6 (pel27_3): ifeq(big_i(X), true, ifeq(big_j(X), true, big_f(X), true), true) = true.
% 0.07/0.24 Axiom 7 (pel27_4): ifeq(big_i(X), true, ifeq(big_h(X), true, ifeq(big_h(Y), true, big_g(Y), true), true), true) = true.
% 0.07/0.24
% 0.07/0.24 Goal 1 (pel27_1_1): big_g(x2) = true.
% 0.07/0.24 Proof:
% 0.07/0.24 big_g(x2)
% 0.07/0.24 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.24 ifeq(true, true, big_g(x2), true)
% 0.07/0.24 = { by axiom 5 (pel27_2) R->L }
% 0.07/0.24 ifeq(ifeq(big_f(x2), true, big_h(x2), true), true, big_g(x2), true)
% 0.07/0.24 = { by axiom 2 (pel27_1) }
% 0.07/0.24 ifeq(ifeq(true, true, big_h(x2), true), true, big_g(x2), true)
% 0.07/0.24 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.24 ifeq(big_h(x2), true, big_g(x2), true)
% 0.07/0.24 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.24 ifeq(true, true, ifeq(big_h(x2), true, big_g(x2), true), true)
% 0.07/0.24 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.24 ifeq(true, true, ifeq(true, true, ifeq(big_h(x2), true, big_g(x2), true), true), true)
% 0.07/0.24 = { by axiom 1 (pel27_1) R->L }
% 0.07/0.24 ifeq(big_i(x), true, ifeq(true, true, ifeq(big_h(x2), true, big_g(x2), true), true), true)
% 0.07/0.25 = { by axiom 5 (pel27_2) R->L }
% 0.07/0.25 ifeq(big_i(x), true, ifeq(ifeq(big_f(x), true, big_h(x), true), true, ifeq(big_h(x2), true, big_g(x2), true), true), true)
% 0.07/0.25 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.25 ifeq(big_i(x), true, ifeq(ifeq(ifeq(true, true, big_f(x), true), true, big_h(x), true), true, ifeq(big_h(x2), true, big_g(x2), true), true), true)
% 0.07/0.25 = { by axiom 3 (pel27) R->L }
% 0.07/0.25 ifeq(big_i(x), true, ifeq(ifeq(ifeq(big_j(x), true, big_f(x), true), true, big_h(x), true), true, ifeq(big_h(x2), true, big_g(x2), true), true), true)
% 0.07/0.25 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.25 ifeq(big_i(x), true, ifeq(ifeq(ifeq(true, true, ifeq(big_j(x), true, big_f(x), true), true), true, big_h(x), true), true, ifeq(big_h(x2), true, big_g(x2), true), true), true)
% 0.07/0.25 = { by axiom 1 (pel27_1) R->L }
% 0.07/0.25 ifeq(big_i(x), true, ifeq(ifeq(ifeq(big_i(x), true, ifeq(big_j(x), true, big_f(x), true), true), true, big_h(x), true), true, ifeq(big_h(x2), true, big_g(x2), true), true), true)
% 0.07/0.25 = { by axiom 6 (pel27_3) }
% 0.07/0.25 ifeq(big_i(x), true, ifeq(ifeq(true, true, big_h(x), true), true, ifeq(big_h(x2), true, big_g(x2), true), true), true)
% 0.07/0.25 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.25 ifeq(big_i(x), true, ifeq(big_h(x), true, ifeq(big_h(x2), true, big_g(x2), true), true), true)
% 0.07/0.25 = { by axiom 7 (pel27_4) }
% 0.07/0.25 true
% 0.07/0.25 % SZS output end Proof
% 0.07/0.25
% 0.07/0.25 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------