%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN365+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 01:47:39 PM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN365+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 15:48:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.15 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
% 0.08/0.15
% 0.08/0.15 % SZS status Theorem
% 0.08/0.15
% 0.08/0.15 % SZS output start Proof
% 0.08/0.15 Axiom 1 (x2116): big_p(x) = true.
% 0.08/0.15 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.08/0.15 Axiom 3 (x2116_3): ifeq(big_p(X), true, big_p(g(X)), true) = true.
% 0.08/0.15 Axiom 4 (x2116_4): ifeq(big_p(X), true, big_p(h(X)), true) = true.
% 0.08/0.15 Axiom 5 (x2116_1): ifeq(big_p(X), true, big_p(y(X)), true) = true.
% 0.08/0.15 Axiom 6 (x2116_2): ifeq(big_p(X), true, big_r(X, g(h(y(X)))), true) = true.
% 0.08/0.15
% 0.08/0.15 Goal 1 (x2116_5): tuple(big_p(X), big_r(x, X)) = tuple(true, true).
% 0.08/0.15 The goal is true when:
% 0.08/0.15 X = g(h(y(x)))
% 0.08/0.15
% 0.08/0.15 Proof:
% 0.08/0.15 tuple(big_p(g(h(y(x)))), big_r(x, g(h(y(x)))))
% 0.08/0.15 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.15 tuple(ifeq(true, true, big_p(g(h(y(x)))), true), big_r(x, g(h(y(x)))))
% 0.08/0.15 = { by axiom 4 (x2116_4) R->L }
% 0.08/0.15 tuple(ifeq(ifeq(big_p(y(x)), true, big_p(h(y(x))), true), true, big_p(g(h(y(x)))), true), big_r(x, g(h(y(x)))))
% 0.08/0.15 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.15 tuple(ifeq(ifeq(ifeq(true, true, big_p(y(x)), true), true, big_p(h(y(x))), true), true, big_p(g(h(y(x)))), true), big_r(x, g(h(y(x)))))
% 0.08/0.15 = { by axiom 1 (x2116) R->L }
% 0.08/0.15 tuple(ifeq(ifeq(ifeq(big_p(x), true, big_p(y(x)), true), true, big_p(h(y(x))), true), true, big_p(g(h(y(x)))), true), big_r(x, g(h(y(x)))))
% 0.08/0.15 = { by axiom 5 (x2116_1) }
% 0.08/0.16 tuple(ifeq(ifeq(true, true, big_p(h(y(x))), true), true, big_p(g(h(y(x)))), true), big_r(x, g(h(y(x)))))
% 0.08/0.16 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.16 tuple(ifeq(big_p(h(y(x))), true, big_p(g(h(y(x)))), true), big_r(x, g(h(y(x)))))
% 0.08/0.16 = { by axiom 3 (x2116_3) }
% 0.08/0.16 tuple(true, big_r(x, g(h(y(x)))))
% 0.08/0.16 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.16 tuple(true, ifeq(true, true, big_r(x, g(h(y(x)))), true))
% 0.08/0.16 = { by axiom 1 (x2116) R->L }
% 0.08/0.16 tuple(true, ifeq(big_p(x), true, big_r(x, g(h(y(x)))), true))
% 0.08/0.16 = { by axiom 6 (x2116_2) }
% 0.08/0.16 tuple(true, true)
% 0.08/0.16 % SZS output end Proof
% 0.08/0.16
% 0.08/0.16 RESULT: Theorem (the conjecture is true).
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