%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ROB021-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:36:12 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB021-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 23:27:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.45 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 0.14/0.45
% 0.14/0.45 % SZS status Unsatisfiable
% 0.14/0.45
% 0.14/0.45 % SZS output start Proof
% 0.14/0.45 Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.14/0.45 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.14/0.45 Axiom 3 (negative_equality_implies_positive_equality): ifeq(negate(X), negate(Y), X, Y) = Y.
% 0.14/0.45 Axiom 4 (robbins_axiom): negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X.
% 0.14/0.45
% 0.14/0.45 Goal 1 (prove_huntingtons_axiom): add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = b.
% 0.14/0.45 Proof:
% 0.14/0.45 add(negate(add(a, negate(b))), negate(add(negate(a), negate(b))))
% 0.14/0.45 = { by axiom 3 (negative_equality_implies_positive_equality) R->L }
% 0.14/0.45 ifeq(negate(b), negate(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b))))), b, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))
% 0.14/0.45 = { by axiom 1 (commutativity_of_add) R->L }
% 0.14/0.45 ifeq(negate(b), negate(add(negate(add(a, negate(b))), negate(add(negate(b), negate(a))))), b, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))
% 0.14/0.45 = { by axiom 1 (commutativity_of_add) }
% 0.14/0.45 ifeq(negate(b), negate(add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))), b, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))
% 0.14/0.45 = { by axiom 4 (robbins_axiom) }
% 0.14/0.45 ifeq(negate(b), negate(b), b, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))
% 0.14/0.45 = { by axiom 2 (ifeq_axiom) }
% 0.14/0.45 b
% 0.14/0.45 % SZS output end Proof
% 0.14/0.45
% 0.14/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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