%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN729+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 01:48:20 PM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN729+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n003.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 16:51:27 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.26 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
% 0.07/0.26
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26
% 0.07/0.26 % SZS output start Proof
% 0.07/0.26 Axiom 1 (thm72): p(x) = true.
% 0.07/0.26 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.26 Axiom 3 (thm72_3): ifeq(p(X), true, p(g(X)), true) = true.
% 0.07/0.26 Axiom 4 (thm72_4): ifeq(p(X), true, p(h(X)), true) = true.
% 0.07/0.26 Axiom 5 (thm72_1): ifeq(p(X), true, p(y(X)), true) = true.
% 0.07/0.26 Axiom 6 (thm72_2): ifeq(p(X), true, l(X, g(h(y(X)))), true) = true.
% 0.07/0.26
% 0.07/0.26 Goal 1 (thm72_5): tuple(p(X), l(x, X)) = tuple(true, true).
% 0.07/0.26 The goal is true when:
% 0.07/0.26 X = g(h(y(x)))
% 0.07/0.26
% 0.07/0.26 Proof:
% 0.07/0.26 tuple(p(g(h(y(x)))), l(x, g(h(y(x)))))
% 0.07/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.07/0.26 tuple(ifeq(true, true, p(g(h(y(x)))), true), l(x, g(h(y(x)))))
% 0.07/0.26 = { by axiom 4 (thm72_4) R->L }
% 0.07/0.26 tuple(ifeq(ifeq(p(y(x)), true, p(h(y(x))), true), true, p(g(h(y(x)))), true), l(x, g(h(y(x)))))
% 0.07/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.07/0.26 tuple(ifeq(ifeq(ifeq(true, true, p(y(x)), true), true, p(h(y(x))), true), true, p(g(h(y(x)))), true), l(x, g(h(y(x)))))
% 0.07/0.26 = { by axiom 1 (thm72) R->L }
% 0.07/0.26 tuple(ifeq(ifeq(ifeq(p(x), true, p(y(x)), true), true, p(h(y(x))), true), true, p(g(h(y(x)))), true), l(x, g(h(y(x)))))
% 0.07/0.26 = { by axiom 5 (thm72_1) }
% 0.07/0.26 tuple(ifeq(ifeq(true, true, p(h(y(x))), true), true, p(g(h(y(x)))), true), l(x, g(h(y(x)))))
% 0.07/0.26 = { by axiom 2 (ifeq_axiom) }
% 0.07/0.26 tuple(ifeq(p(h(y(x))), true, p(g(h(y(x)))), true), l(x, g(h(y(x)))))
% 0.07/0.26 = { by axiom 3 (thm72_3) }
% 0.07/0.26 tuple(true, l(x, g(h(y(x)))))
% 0.07/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.07/0.26 tuple(true, ifeq(true, true, l(x, g(h(y(x)))), true))
% 0.07/0.26 = { by axiom 1 (thm72) R->L }
% 0.07/0.26 tuple(true, ifeq(p(x), true, l(x, g(h(y(x)))), true))
% 0.07/0.26 = { by axiom 6 (thm72_2) }
% 0.07/0.26 tuple(true, true)
% 0.07/0.26 % SZS output end Proof
% 0.07/0.26
% 0.07/0.26 RESULT: Theorem (the conjecture is true).
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