%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN333+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 01:47:34 PM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN333+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 15:48:18 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.26 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
% 0.08/0.26
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26
% 0.08/0.26 % SZS output start Proof
% 0.08/0.26 Axiom 1 (church_46_14_5): big_f(X, Y) = true.
% 0.08/0.26 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.08/0.26 Axiom 3 (church_46_14_5_2): ifeq(big_f(z(X, Y), z(X, Y)), true, ifeq(big_f(Y, z(X, Y)), true, big_g(X, Y), true), true) = true.
% 0.08/0.26
% 0.08/0.26 Goal 1 (church_46_14_5_3): tuple(big_f(X, z(Y, X)), big_f(z(Y, X), z(Y, X)), big_g(Y, z(Y, X)), big_g(z(Y, X), z(Y, X))) = tuple(true, true, true, true).
% 0.08/0.26 The goal is true when:
% 0.08/0.26 X = Y
% 0.08/0.26 Y = X
% 0.08/0.26
% 0.08/0.26 Proof:
% 0.08/0.26 tuple(big_f(Y, z(X, Y)), big_f(z(X, Y), z(X, Y)), big_g(X, z(X, Y)), big_g(z(X, Y), z(X, Y)))
% 0.08/0.26 = { by axiom 1 (church_46_14_5) }
% 0.08/0.26 tuple(true, big_f(z(X, Y), z(X, Y)), big_g(X, z(X, Y)), big_g(z(X, Y), z(X, Y)))
% 0.08/0.26 = { by axiom 1 (church_46_14_5) }
% 0.08/0.26 tuple(true, true, big_g(X, z(X, Y)), big_g(z(X, Y), z(X, Y)))
% 0.08/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.26 tuple(true, true, ifeq(true, true, big_g(X, z(X, Y)), true), big_g(z(X, Y), z(X, Y)))
% 0.08/0.26 = { by axiom 1 (church_46_14_5) R->L }
% 0.08/0.26 tuple(true, true, ifeq(big_f(z(X, Y), z(X, z(X, Y))), true, big_g(X, z(X, Y)), true), big_g(z(X, Y), z(X, Y)))
% 0.08/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.26 tuple(true, true, ifeq(true, true, ifeq(big_f(z(X, Y), z(X, z(X, Y))), true, big_g(X, z(X, Y)), true), true), big_g(z(X, Y), z(X, Y)))
% 0.08/0.26 = { by axiom 1 (church_46_14_5) R->L }
% 0.08/0.26 tuple(true, true, ifeq(big_f(z(X, z(X, Y)), z(X, z(X, Y))), true, ifeq(big_f(z(X, Y), z(X, z(X, Y))), true, big_g(X, z(X, Y)), true), true), big_g(z(X, Y), z(X, Y)))
% 0.08/0.26 = { by axiom 3 (church_46_14_5_2) }
% 0.08/0.26 tuple(true, true, true, big_g(z(X, Y), z(X, Y)))
% 0.08/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.26 tuple(true, true, true, ifeq(true, true, big_g(z(X, Y), z(X, Y)), true))
% 0.08/0.26 = { by axiom 1 (church_46_14_5) R->L }
% 0.08/0.26 tuple(true, true, true, ifeq(big_f(z(X, Y), z(z(X, Y), z(X, Y))), true, big_g(z(X, Y), z(X, Y)), true))
% 0.08/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.26 tuple(true, true, true, ifeq(true, true, ifeq(big_f(z(X, Y), z(z(X, Y), z(X, Y))), true, big_g(z(X, Y), z(X, Y)), true), true))
% 0.08/0.26 = { by axiom 1 (church_46_14_5) R->L }
% 0.08/0.26 tuple(true, true, true, ifeq(big_f(z(z(X, Y), z(X, Y)), z(z(X, Y), z(X, Y))), true, ifeq(big_f(z(X, Y), z(z(X, Y), z(X, Y))), true, big_g(z(X, Y), z(X, Y)), true), true))
% 0.08/0.26 = { by axiom 3 (church_46_14_5_2) }
% 0.08/0.26 tuple(true, true, true, true)
% 0.08/0.26 % SZS output end Proof
% 0.08/0.26
% 0.08/0.26 RESULT: Theorem (the conjecture is true).
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