%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN986+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 01:48:44 PM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22 % Computer : n001.cluster.edu
% 0.07/0.22 % Model : x86_64 x86_64
% 0.07/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.22 % Memory : 8046.5625MB
% 0.07/0.22 % OS : Linux 6.8.0-71-generic
% 0.07/0.22 % CPULimit : 300
% 0.07/0.22 % WCLimit : 300
% 0.07/0.22 % DateTime : Mon Sep 28 17:25:18 UTC 2026
% 0.07/0.22 % CPUTime :
% 0.07/0.22 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.32 Command-line arguments: --no-flatten-goal
% 0.23/0.32
% 0.23/0.32 % SZS status Theorem
% 0.23/0.32
% 0.23/0.33 % SZS output start Proof
% 0.23/0.33 Axiom 1 (hyp1): r(X, zero, succ(X)) = true.
% 0.23/0.33 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.23/0.33 Axiom 3 (hyp2): ifeq(r(X, Y, Z), true, ifeq(r(W, Y, X), true, r(W, succ(Y), Z), true), true) = true.
% 0.23/0.33
% 0.23/0.33 Goal 1 (ck): tuple(r(zero, X, Y), r(zero, zero, X)) = tuple(true, true).
% 0.23/0.33 The goal is true when:
% 0.23/0.33 X = succ(zero)
% 0.23/0.33 Y = succ(succ(zero))
% 0.23/0.33
% 0.23/0.33 Proof:
% 0.23/0.33 tuple(r(zero, succ(zero), succ(succ(zero))), r(zero, zero, succ(zero)))
% 0.23/0.33 = { by axiom 2 (ifeq_axiom) R->L }
% 0.23/0.33 tuple(ifeq(true, true, r(zero, succ(zero), succ(succ(zero))), true), r(zero, zero, succ(zero)))
% 0.23/0.33 = { by axiom 1 (hyp1) R->L }
% 0.23/0.33 tuple(ifeq(r(zero, zero, succ(zero)), true, r(zero, succ(zero), succ(succ(zero))), true), r(zero, zero, succ(zero)))
% 0.23/0.33 = { by axiom 2 (ifeq_axiom) R->L }
% 0.23/0.33 tuple(ifeq(true, true, ifeq(r(zero, zero, succ(zero)), true, r(zero, succ(zero), succ(succ(zero))), true), true), r(zero, zero, succ(zero)))
% 0.23/0.33 = { by axiom 1 (hyp1) R->L }
% 0.23/0.33 tuple(ifeq(r(succ(zero), zero, succ(succ(zero))), true, ifeq(r(zero, zero, succ(zero)), true, r(zero, succ(zero), succ(succ(zero))), true), true), r(zero, zero, succ(zero)))
% 0.23/0.33 = { by axiom 3 (hyp2) }
% 0.23/0.33 tuple(true, r(zero, zero, succ(zero)))
% 0.23/0.33 = { by axiom 1 (hyp1) }
% 0.23/0.33 tuple(true, true)
% 0.23/0.33 % SZS output end Proof
% 0.23/0.33
% 0.23/0.33 RESULT: Theorem (the conjecture is true).
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