%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN986+1.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.09s 0.24s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN986+1.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n010.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 17:20:02 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.24 Command-line arguments: --no-flatten-goal
% 0.09/0.24
% 0.09/0.24 % SZS status Theorem
% 0.09/0.24
% 0.09/0.25 % SZS output start Proof
% 0.09/0.25 Axiom 1 (hyp1): r(X, zero, succ(X)) = true.
% 0.09/0.25 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.09/0.25 Axiom 3 (hyp2): ifeq(r(X, Y, Z), true, ifeq(r(W, Y, X), true, r(W, succ(Y), Z), true), true) = true.
% 0.09/0.25
% 0.09/0.25 Goal 1 (ck): tuple(r(zero, X, Y), r(zero, Y, Z), r(zero, zero, X)) = tuple(true, true, true).
% 0.09/0.25 The goal is true when:
% 0.09/0.25 X = succ(zero)
% 0.09/0.25 Y = succ(succ(zero))
% 0.09/0.25 Z = succ(succ(succ(succ(zero))))
% 0.09/0.25
% 0.09/0.25 Proof:
% 0.09/0.25 tuple(r(zero, succ(zero), succ(succ(zero))), r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), r(zero, zero, succ(zero)))
% 0.09/0.25 = { by axiom 2 (ifeq_axiom) R->L }
% 0.09/0.25 tuple(ifeq(true, true, r(zero, succ(zero), succ(succ(zero))), true), r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), r(zero, zero, succ(zero)))
% 0.09/0.25 = { by axiom 1 (hyp1) R->L }
% 0.09/0.25 tuple(ifeq(r(zero, zero, succ(zero)), true, r(zero, succ(zero), succ(succ(zero))), true), r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), r(zero, zero, succ(zero)))
% 0.09/0.25 = { by axiom 2 (ifeq_axiom) R->L }
% 0.09/0.25 tuple(ifeq(true, true, ifeq(r(zero, zero, succ(zero)), true, r(zero, succ(zero), succ(succ(zero))), true), true), r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), r(zero, zero, succ(zero)))
% 0.09/0.25 = { by axiom 1 (hyp1) R->L }
% 0.09/0.25 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, succ(succ(zero)), succ(succ(succ(succ(zero))))), r(zero, zero, succ(zero)))
% 0.09/0.25 = { by axiom 3 (hyp2) }
% 0.09/0.25 tuple(true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), r(zero, zero, succ(zero)))
% 0.09/0.25 = { by axiom 1 (hyp1) }
% 0.09/0.25 tuple(true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true)
% 0.09/0.25 = { by axiom 2 (ifeq_axiom) R->L }
% 0.09/0.25 tuple(true, ifeq(true, true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true)
% 0.09/0.25 = { by axiom 3 (hyp2) R->L }
% 0.09/0.25 tuple(true, ifeq(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), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true)
% 0.09/0.25 = { by axiom 1 (hyp1) }
% 0.09/0.25 tuple(true, ifeq(ifeq(true, true, ifeq(r(zero, zero, succ(zero)), true, r(zero, succ(zero), succ(succ(zero))), true), true), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true)
% 0.09/0.25 = { by axiom 2 (ifeq_axiom) }
% 0.09/0.25 tuple(true, ifeq(ifeq(r(zero, zero, succ(zero)), true, r(zero, succ(zero), succ(succ(zero))), true), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true)
% 0.09/0.25 = { by axiom 1 (hyp1) }
% 0.09/0.25 tuple(true, ifeq(ifeq(true, true, r(zero, succ(zero), succ(succ(zero))), true), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true)
% 0.09/0.25 = { by axiom 2 (ifeq_axiom) }
% 0.09/0.25 tuple(true, ifeq(r(zero, succ(zero), succ(succ(zero))), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true)
% 0.09/0.25 = { by axiom 2 (ifeq_axiom) R->L }
% 0.09/0.25 tuple(true, ifeq(true, true, ifeq(r(zero, succ(zero), succ(succ(zero))), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true), true)
% 0.09/0.25 = { by axiom 3 (hyp2) R->L }
% 0.09/0.25 tuple(true, ifeq(ifeq(r(succ(succ(succ(zero))), zero, succ(succ(succ(succ(zero))))), true, ifeq(r(succ(succ(zero)), zero, succ(succ(succ(zero)))), true, r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero))))), true), true), true, ifeq(r(zero, succ(zero), succ(succ(zero))), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true), true)
% 0.09/0.25 = { by axiom 1 (hyp1) }
% 0.09/0.25 tuple(true, ifeq(ifeq(true, true, ifeq(r(succ(succ(zero)), zero, succ(succ(succ(zero)))), true, r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero))))), true), true), true, ifeq(r(zero, succ(zero), succ(succ(zero))), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true), true)
% 0.09/0.25 = { by axiom 2 (ifeq_axiom) }
% 0.09/0.25 tuple(true, ifeq(ifeq(r(succ(succ(zero)), zero, succ(succ(succ(zero)))), true, r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero))))), true), true, ifeq(r(zero, succ(zero), succ(succ(zero))), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true), true)
% 0.09/0.25 = { by axiom 1 (hyp1) }
% 0.09/0.25 tuple(true, ifeq(ifeq(true, true, r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero))))), true), true, ifeq(r(zero, succ(zero), succ(succ(zero))), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true), true)
% 0.09/0.25 = { by axiom 2 (ifeq_axiom) }
% 0.09/0.25 tuple(true, ifeq(r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero))))), true, ifeq(r(zero, succ(zero), succ(succ(zero))), true, r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))), true), true), true)
% 0.09/0.25 = { by axiom 3 (hyp2) }
% 0.09/0.25 tuple(true, true, true)
% 0.09/0.25 % SZS output end Proof
% 0.09/0.25
% 0.09/0.25 RESULT: Theorem (the conjecture is true).
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