%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:09:49 PM UTC 2026
% Result : Unsatisfiable 0.43s 0.52s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 18:42:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.43/0.52 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
% 0.43/0.52
% 0.43/0.52 % SZS status Unsatisfiable
% 0.43/0.52
% 0.43/0.52 % SZS output start Proof
% 0.43/0.52 Axiom 1 (adding_zero): equalish(add(X, n0), X) = true.
% 0.43/0.52 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.43/0.52 Axiom 3 (addition): equalish(add(X, successor(Y)), successor(add(X, Y))) = true.
% 0.43/0.52 Axiom 4 (successor_substitution): ifeq(equalish(X, Y), true, equalish(successor(X), successor(Y)), true) = true.
% 0.43/0.52 Axiom 5 (transitivity): ifeq(equalish(X, Y), true, ifeq(equalish(Z, X), true, equalish(Z, Y), true), true) = true.
% 0.43/0.52
% 0.43/0.52 Goal 1 (deny_addition_lemma): equalish(add(a, successor(n0)), successor(a)) = true.
% 0.43/0.52 Proof:
% 0.43/0.52 equalish(add(a, successor(n0)), successor(a))
% 0.43/0.52 = { by axiom 2 (ifeq_axiom) R->L }
% 0.43/0.52 ifeq(true, true, equalish(add(a, successor(n0)), successor(a)), true)
% 0.43/0.52 = { by axiom 3 (addition) R->L }
% 0.43/0.52 ifeq(equalish(add(a, successor(n0)), successor(add(a, n0))), true, equalish(add(a, successor(n0)), successor(a)), true)
% 0.43/0.52 = { by axiom 2 (ifeq_axiom) R->L }
% 0.43/0.52 ifeq(true, true, ifeq(equalish(add(a, successor(n0)), successor(add(a, n0))), true, equalish(add(a, successor(n0)), successor(a)), true), true)
% 0.43/0.52 = { by axiom 4 (successor_substitution) R->L }
% 0.43/0.52 ifeq(ifeq(equalish(add(a, n0), a), true, equalish(successor(add(a, n0)), successor(a)), true), true, ifeq(equalish(add(a, successor(n0)), successor(add(a, n0))), true, equalish(add(a, successor(n0)), successor(a)), true), true)
% 0.43/0.52 = { by axiom 1 (adding_zero) }
% 0.43/0.52 ifeq(ifeq(true, true, equalish(successor(add(a, n0)), successor(a)), true), true, ifeq(equalish(add(a, successor(n0)), successor(add(a, n0))), true, equalish(add(a, successor(n0)), successor(a)), true), true)
% 0.43/0.52 = { by axiom 2 (ifeq_axiom) }
% 0.43/0.52 ifeq(equalish(successor(add(a, n0)), successor(a)), true, ifeq(equalish(add(a, successor(n0)), successor(add(a, n0))), true, equalish(add(a, successor(n0)), successor(a)), true), true)
% 0.43/0.52 = { by axiom 5 (transitivity) }
% 0.43/0.52 true
% 0.43/0.52 % SZS output end Proof
% 0.43/0.52
% 0.43/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
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