%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : NUM002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:09:48 PM UTC 2026
% Result : Unsatisfiable 16.44s 2.45s
% Output : Proof 16.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sun Sep 27 18:38:49 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.44/2.45 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 16.44/2.45
% 16.44/2.45 % SZS status Unsatisfiable
% 16.44/2.45
% 16.44/2.45 % SZS output start Proof
% 16.44/2.45 Axiom 1 (reflexivity): equalish(X, X) = true.
% 16.44/2.45 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 16.44/2.45 Axiom 3 (addition_inverts_subtraction2): equalish(X, subtract(add(X, Y), Y)) = true.
% 16.44/2.45 Axiom 4 (commutativity_of_addition): equalish(add(X, Y), add(Y, X)) = true.
% 16.44/2.45 Axiom 5 (addition_inverts_subtraction1): equalish(subtract(add(X, Y), Y), X) = true.
% 16.44/2.45 Axiom 6 (associativity_of_addition): equalish(add(X, add(Y, Z)), add(add(X, Y), Z)) = true.
% 16.44/2.45 Axiom 7 (commutativity1): equalish(add(subtract(X, Y), Z), subtract(add(X, Z), Y)) = true.
% 16.44/2.45 Axiom 8 (commutativity2): equalish(subtract(add(X, Y), Z), add(subtract(X, Z), Y)) = true.
% 16.44/2.45 Axiom 9 (transitivity): ifeq(equalish(X, Y), true, ifeq(equalish(Z, X), true, equalish(Z, Y), true), true) = true.
% 16.44/2.45 Axiom 10 (add_substitution1): ifeq(equalish(X, add(Y, Z)), true, ifeq(equalish(Y, W), true, equalish(X, add(W, Z)), true), true) = true.
% 16.44/2.45 Axiom 11 (add_substitution2): ifeq(equalish(X, add(Y, Z)), true, ifeq(equalish(Z, W), true, equalish(X, add(Y, W)), true), true) = true.
% 16.44/2.46
% 16.44/2.46 Goal 1 (prove_equation): equalish(add(subtract(a, b), c), add(a, subtract(c, b))) = true.
% 16.44/2.46 Proof:
% 16.44/2.46 equalish(add(subtract(a, b), c), add(a, subtract(c, b)))
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) R->L }
% 16.44/2.46 ifeq(true, true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 11 (add_substitution2) R->L }
% 16.44/2.46 ifeq(ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), c)), true, ifeq(equalish(c, add(b, subtract(c, b))), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 1 (reflexivity) }
% 16.44/2.46 ifeq(ifeq(true, true, ifeq(equalish(c, add(b, subtract(c, b))), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) }
% 16.44/2.46 ifeq(ifeq(equalish(c, add(b, subtract(c, b))), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) R->L }
% 16.44/2.46 ifeq(ifeq(ifeq(true, true, equalish(c, add(b, subtract(c, b))), true), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 9 (transitivity) R->L }
% 16.44/2.46 ifeq(ifeq(ifeq(ifeq(equalish(subtract(add(c, b), b), add(subtract(c, b), b)), true, ifeq(equalish(c, subtract(add(c, b), b)), true, equalish(c, add(subtract(c, b), b)), true), true), true, equalish(c, add(b, subtract(c, b))), true), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 3 (addition_inverts_subtraction2) }
% 16.44/2.46 ifeq(ifeq(ifeq(ifeq(equalish(subtract(add(c, b), b), add(subtract(c, b), b)), true, ifeq(true, true, equalish(c, add(subtract(c, b), b)), true), true), true, equalish(c, add(b, subtract(c, b))), true), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) }
% 16.44/2.46 ifeq(ifeq(ifeq(ifeq(equalish(subtract(add(c, b), b), add(subtract(c, b), b)), true, equalish(c, add(subtract(c, b), b)), true), true, equalish(c, add(b, subtract(c, b))), true), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 8 (commutativity2) }
% 16.44/2.46 ifeq(ifeq(ifeq(ifeq(true, true, equalish(c, add(subtract(c, b), b)), true), true, equalish(c, add(b, subtract(c, b))), true), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) }
% 16.44/2.46 ifeq(ifeq(ifeq(equalish(c, add(subtract(c, b), b)), true, equalish(c, add(b, subtract(c, b))), true), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) R->L }
% 16.44/2.46 ifeq(ifeq(ifeq(true, true, ifeq(equalish(c, add(subtract(c, b), b)), true, equalish(c, add(b, subtract(c, b))), true), true), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 4 (commutativity_of_addition) R->L }
% 16.44/2.46 ifeq(ifeq(ifeq(equalish(add(subtract(c, b), b), add(b, subtract(c, b))), true, ifeq(equalish(c, add(subtract(c, b), b)), true, equalish(c, add(b, subtract(c, b))), true), true), true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 9 (transitivity) }
% 16.44/2.46 ifeq(ifeq(true, true, equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) }
% 16.44/2.46 ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) R->L }
% 16.44/2.46 ifeq(true, true, ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true), true)
% 16.44/2.46 = { by axiom 10 (add_substitution1) R->L }
% 16.44/2.46 ifeq(ifeq(equalish(add(subtract(a, b), add(b, subtract(c, b))), add(add(subtract(a, b), b), subtract(c, b))), true, ifeq(equalish(add(subtract(a, b), b), a), true, equalish(add(subtract(a, b), add(b, subtract(c, b))), add(a, subtract(c, b))), true), true), true, ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true), true)
% 16.44/2.46 = { by axiom 6 (associativity_of_addition) }
% 16.44/2.46 ifeq(ifeq(true, true, ifeq(equalish(add(subtract(a, b), b), a), true, equalish(add(subtract(a, b), add(b, subtract(c, b))), add(a, subtract(c, b))), true), true), true, ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) }
% 16.44/2.46 ifeq(ifeq(equalish(add(subtract(a, b), b), a), true, equalish(add(subtract(a, b), add(b, subtract(c, b))), add(a, subtract(c, b))), true), true, ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) R->L }
% 16.44/2.46 ifeq(ifeq(ifeq(true, true, equalish(add(subtract(a, b), b), a), true), true, equalish(add(subtract(a, b), add(b, subtract(c, b))), add(a, subtract(c, b))), true), true, ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true), true)
% 16.44/2.46 = { by axiom 7 (commutativity1) R->L }
% 16.44/2.46 ifeq(ifeq(ifeq(equalish(add(subtract(a, b), b), subtract(add(a, b), b)), true, equalish(add(subtract(a, b), b), a), true), true, equalish(add(subtract(a, b), add(b, subtract(c, b))), add(a, subtract(c, b))), true), true, ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) R->L }
% 16.44/2.46 ifeq(ifeq(ifeq(true, true, ifeq(equalish(add(subtract(a, b), b), subtract(add(a, b), b)), true, equalish(add(subtract(a, b), b), a), true), true), true, equalish(add(subtract(a, b), add(b, subtract(c, b))), add(a, subtract(c, b))), true), true, ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true), true)
% 16.44/2.46 = { by axiom 5 (addition_inverts_subtraction1) R->L }
% 16.44/2.46 ifeq(ifeq(ifeq(equalish(subtract(add(a, b), b), a), true, ifeq(equalish(add(subtract(a, b), b), subtract(add(a, b), b)), true, equalish(add(subtract(a, b), b), a), true), true), true, equalish(add(subtract(a, b), add(b, subtract(c, b))), add(a, subtract(c, b))), true), true, ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true), true)
% 16.44/2.46 = { by axiom 9 (transitivity) }
% 16.44/2.46 ifeq(ifeq(true, true, equalish(add(subtract(a, b), add(b, subtract(c, b))), add(a, subtract(c, b))), true), true, ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true), true)
% 16.44/2.46 = { by axiom 2 (ifeq_axiom) }
% 16.44/2.46 ifeq(equalish(add(subtract(a, b), add(b, subtract(c, b))), add(a, subtract(c, b))), true, ifeq(equalish(add(subtract(a, b), c), add(subtract(a, b), add(b, subtract(c, b)))), true, equalish(add(subtract(a, b), c), add(a, subtract(c, b))), true), true)
% 16.44/2.46 = { by axiom 9 (transitivity) }
% 16.44/2.46 true
% 16.44/2.46 % SZS output end Proof
% 16.44/2.46
% 16.44/2.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------