%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : NUM024-1 : 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 12:09:50 PM UTC 2026
% Result : Unsatisfiable 0.69s 0.53s
% Output : Proof 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 18:42:36 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.53 Command-line arguments: --no-flatten-goal
% 0.69/0.53
% 0.69/0.53 % SZS status Unsatisfiable
% 0.69/0.53
% 0.69/0.54 % SZS output start Proof
% 0.69/0.54 Axiom 1 (impossible_a_is_less_than_itself): less(a, a) = true.
% 0.69/0.54 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.69/0.54 Axiom 3 (adding_zero): equalish(add(X, n0), X) = true.
% 0.69/0.54 Axiom 4 (commutativity_of_plus): equalish(add(X, Y), add(Y, X)) = true.
% 0.69/0.54 Axiom 5 (symmetry): ifeq(equalish(X, Y), true, equalish(Y, X), true) = true.
% 0.69/0.54 Axiom 6 (less_lemma): ifeq(less(X, Y), true, equalish(add(successor(predecessor_of_1st_minus_2nd(Y, X)), X), Y), true) = true.
% 0.69/0.54 Axiom 7 (plus_substitution): ifeq(equalish(add(X, Y), add(Z, Y)), true, equalish(X, Z), true) = true.
% 0.69/0.54 Axiom 8 (transitivity): ifeq(equalish(X, Y), true, ifeq(equalish(Z, X), true, equalish(Z, Y), true), true) = true.
% 0.69/0.54
% 0.69/0.54 Goal 1 (prove_a_contradiction): equalish(successor(X), n0) = true.
% 0.69/0.54 The goal is true when:
% 0.69/0.54 X = predecessor_of_1st_minus_2nd(a, a)
% 0.69/0.54
% 0.69/0.54 Proof:
% 0.69/0.54 equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0)
% 0.69/0.54 = { by axiom 2 (ifeq_axiom) R->L }
% 0.69/0.54 ifeq(true, true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 7 (plus_substitution) R->L }
% 0.69/0.54 ifeq(ifeq(equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 2 (ifeq_axiom) R->L }
% 0.69/0.54 ifeq(ifeq(ifeq(true, true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 5 (symmetry) R->L }
% 0.69/0.54 ifeq(ifeq(ifeq(ifeq(equalish(add(successor(predecessor_of_1st_minus_2nd(a, a)), a), a), true, equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 2 (ifeq_axiom) R->L }
% 0.69/0.54 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, equalish(add(successor(predecessor_of_1st_minus_2nd(a, a)), a), a), true), true, equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 1 (impossible_a_is_less_than_itself) R->L }
% 0.69/0.54 ifeq(ifeq(ifeq(ifeq(ifeq(less(a, a), true, equalish(add(successor(predecessor_of_1st_minus_2nd(a, a)), a), a), true), true, equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 6 (less_lemma) }
% 0.69/0.54 ifeq(ifeq(ifeq(ifeq(true, true, equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 2 (ifeq_axiom) }
% 0.69/0.54 ifeq(ifeq(ifeq(equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 2 (ifeq_axiom) R->L }
% 0.69/0.54 ifeq(ifeq(ifeq(equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true, ifeq(true, true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 8 (transitivity) R->L }
% 0.69/0.54 ifeq(ifeq(ifeq(equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true, ifeq(ifeq(equalish(add(a, n0), a), true, ifeq(equalish(add(n0, a), add(a, n0)), true, equalish(add(n0, a), a), true), true), true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 3 (adding_zero) }
% 0.69/0.54 ifeq(ifeq(ifeq(equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true, ifeq(ifeq(true, true, ifeq(equalish(add(n0, a), add(a, n0)), true, equalish(add(n0, a), a), true), true), true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 2 (ifeq_axiom) }
% 0.69/0.54 ifeq(ifeq(ifeq(equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true, ifeq(ifeq(equalish(add(n0, a), add(a, n0)), true, equalish(add(n0, a), a), true), true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 4 (commutativity_of_plus) }
% 0.69/0.54 ifeq(ifeq(ifeq(equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true, ifeq(ifeq(true, true, equalish(add(n0, a), a), true), true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 2 (ifeq_axiom) }
% 0.69/0.54 ifeq(ifeq(ifeq(equalish(a, add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true, ifeq(equalish(add(n0, a), a), true, equalish(add(n0, a), add(successor(predecessor_of_1st_minus_2nd(a, a)), a)), true), true), true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 8 (transitivity) }
% 0.69/0.54 ifeq(ifeq(true, true, equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 2 (ifeq_axiom) }
% 0.69/0.54 ifeq(equalish(n0, successor(predecessor_of_1st_minus_2nd(a, a))), true, equalish(successor(predecessor_of_1st_minus_2nd(a, a)), n0), true)
% 0.69/0.54 = { by axiom 5 (symmetry) }
% 0.69/0.54 true
% 0.69/0.54 % SZS output end Proof
% 0.69/0.54
% 0.69/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------