%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN919+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 01:48:37 PM UTC 2026
% Result : Theorem 0.08s 0.14s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN919+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/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 17:12:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.14 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
% 0.08/0.14
% 0.08/0.14 % SZS status Theorem
% 0.08/0.14
% 0.08/0.14 % SZS output start Proof
% 0.08/0.14 Axiom 1 (prove_this): r(x, y) = true.
% 0.08/0.14 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.08/0.14 Axiom 3 (prove_this_1): ifeq(r(X, Y), true, r(Y, X), true) = true.
% 0.08/0.14 Axiom 4 (prove_this_2): ifeq(r(X, Y), true, ifeq(r(Z, X), true, r(Z, Y), true), true) = true.
% 0.08/0.14
% 0.08/0.14 Goal 1 (prove_this_3): r(x, x) = true.
% 0.08/0.14 Proof:
% 0.08/0.14 r(x, x)
% 0.08/0.14 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.14 ifeq(true, true, r(x, x), true)
% 0.08/0.14 = { by axiom 3 (prove_this_1) R->L }
% 0.08/0.14 ifeq(ifeq(r(x, y), true, r(y, x), true), true, r(x, x), true)
% 0.08/0.14 = { by axiom 1 (prove_this) }
% 0.08/0.14 ifeq(ifeq(true, true, r(y, x), true), true, r(x, x), true)
% 0.08/0.14 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.14 ifeq(r(y, x), true, r(x, x), true)
% 0.08/0.14 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.14 ifeq(r(y, x), true, ifeq(true, true, r(x, x), true), true)
% 0.08/0.14 = { by axiom 1 (prove_this) R->L }
% 0.08/0.14 ifeq(r(y, x), true, ifeq(r(x, y), true, r(x, x), true), true)
% 0.08/0.14 = { by axiom 4 (prove_this_2) }
% 0.08/0.14 true
% 0.08/0.14 % SZS output end Proof
% 0.08/0.14
% 0.08/0.14 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------