%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP069-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 10:09:12 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.46s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP069-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n007.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 09:15:54 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.46 Command-line arguments: --no-flatten-goal
% 0.08/0.46
% 0.08/0.46 % SZS status Unsatisfiable
% 0.08/0.46
% 0.08/0.46 % SZS output start Proof
% 0.08/0.46 Axiom 1 (identity): identity = divide(X, X).
% 0.08/0.46 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.18/0.46 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.18/0.46 Axiom 4 (single_axiom): divide(X, divide(divide(divide(divide(X, X), Y), Z), divide(divide(identity, X), Z))) = Y.
% 0.18/0.46
% 0.18/0.46 Lemma 5: divide(X, inverse(Y)) = multiply(X, Y).
% 0.18/0.46 Proof:
% 0.18/0.46 divide(X, inverse(Y))
% 0.18/0.46 = { by axiom 2 (inverse) }
% 0.18/0.46 divide(X, divide(identity, Y))
% 0.18/0.46 = { by axiom 3 (multiply) R->L }
% 0.18/0.46 multiply(X, Y)
% 0.18/0.46
% 0.18/0.46 Lemma 6: divide(X, divide(divide(inverse(Y), Z), divide(inverse(X), Z))) = Y.
% 0.18/0.46 Proof:
% 0.18/0.46 divide(X, divide(divide(inverse(Y), Z), divide(inverse(X), Z)))
% 0.18/0.46 = { by axiom 2 (inverse) }
% 0.18/0.46 divide(X, divide(divide(inverse(Y), Z), divide(divide(identity, X), Z)))
% 0.18/0.46 = { by axiom 2 (inverse) }
% 0.18/0.46 divide(X, divide(divide(divide(identity, Y), Z), divide(divide(identity, X), Z)))
% 0.18/0.46 = { by axiom 1 (identity) }
% 0.18/0.46 divide(X, divide(divide(divide(divide(X, X), Y), Z), divide(divide(identity, X), Z)))
% 0.18/0.46 = { by axiom 4 (single_axiom) }
% 0.18/0.46 Y
% 0.18/0.46
% 0.18/0.46 Lemma 7: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.18/0.46 Proof:
% 0.18/0.46 multiply(X, multiply(inverse(X), Y))
% 0.18/0.46 = { by lemma 5 R->L }
% 0.18/0.46 multiply(X, divide(inverse(X), inverse(Y)))
% 0.18/0.46 = { by lemma 5 R->L }
% 0.18/0.46 divide(X, inverse(divide(inverse(X), inverse(Y))))
% 0.18/0.46 = { by axiom 2 (inverse) }
% 0.18/0.46 divide(X, divide(identity, divide(inverse(X), inverse(Y))))
% 0.18/0.46 = { by axiom 1 (identity) }
% 0.18/0.46 divide(X, divide(divide(inverse(Y), inverse(Y)), divide(inverse(X), inverse(Y))))
% 0.18/0.46 = { by lemma 6 }
% 0.18/0.46 Y
% 0.18/0.46
% 0.18/0.46 Lemma 8: divide(X, identity) = X.
% 0.18/0.46 Proof:
% 0.18/0.46 divide(X, identity)
% 0.18/0.46 = { by axiom 1 (identity) }
% 0.18/0.46 divide(X, divide(divide(inverse(X), Y), divide(inverse(X), Y)))
% 0.18/0.46 = { by lemma 6 }
% 0.18/0.46 X
% 0.18/0.46
% 0.18/0.46 Lemma 9: multiply(X, identity) = X.
% 0.18/0.46 Proof:
% 0.18/0.46 multiply(X, identity)
% 0.18/0.46 = { by lemma 5 R->L }
% 0.18/0.46 divide(X, inverse(identity))
% 0.18/0.46 = { by axiom 2 (inverse) }
% 0.18/0.46 divide(X, divide(identity, identity))
% 0.18/0.46 = { by axiom 1 (identity) R->L }
% 0.18/0.46 divide(X, identity)
% 0.18/0.46 = { by lemma 8 }
% 0.18/0.46 X
% 0.18/0.46
% 0.18/0.46 Lemma 10: inverse(inverse(X)) = X.
% 0.18/0.46 Proof:
% 0.18/0.46 inverse(inverse(X))
% 0.18/0.46 = { by lemma 7 R->L }
% 0.18/0.46 multiply(X, multiply(inverse(X), inverse(inverse(X))))
% 0.18/0.46 = { by lemma 9 R->L }
% 0.18/0.46 multiply(X, multiply(inverse(X), multiply(inverse(inverse(X)), identity)))
% 0.18/0.46 = { by lemma 7 }
% 0.18/0.46 multiply(X, identity)
% 0.18/0.46 = { by lemma 9 }
% 0.18/0.46 X
% 0.18/0.46
% 0.18/0.46 Lemma 11: divide(X, Y) = multiply(X, inverse(Y)).
% 0.18/0.46 Proof:
% 0.18/0.46 divide(X, Y)
% 0.18/0.46 = { by lemma 10 R->L }
% 0.18/0.46 divide(X, inverse(inverse(Y)))
% 0.18/0.46 = { by lemma 5 }
% 0.18/0.46 multiply(X, inverse(Y))
% 0.18/0.46
% 0.18/0.46 Lemma 12: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 0.18/0.46 Proof:
% 0.18/0.46 multiply(X, inverse(multiply(Y, X)))
% 0.18/0.46 = { by lemma 11 R->L }
% 0.18/0.46 divide(X, multiply(Y, X))
% 0.18/0.46 = { by lemma 10 R->L }
% 0.18/0.46 divide(X, multiply(inverse(inverse(Y)), X))
% 0.18/0.46 = { by lemma 5 R->L }
% 0.18/0.46 divide(X, divide(inverse(inverse(Y)), inverse(X)))
% 0.18/0.46 = { by lemma 8 R->L }
% 0.18/0.46 divide(X, divide(inverse(inverse(Y)), divide(inverse(X), identity)))
% 0.18/0.46 = { by lemma 8 R->L }
% 0.18/0.46 divide(X, divide(divide(inverse(inverse(Y)), identity), divide(inverse(X), identity)))
% 0.18/0.46 = { by lemma 6 }
% 0.18/0.46 inverse(Y)
% 0.18/0.46
% 0.18/0.46 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3)) = tuple(identity, a2, multiply(a3, multiply(b3, c3))).
% 0.18/0.46 Proof:
% 0.18/0.46 tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3))
% 0.18/0.46 = { by lemma 5 R->L }
% 0.18/0.46 tuple(multiply(inverse(a1), a1), divide(identity, inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.18/0.46 = { by axiom 2 (inverse) R->L }
% 0.18/0.46 tuple(multiply(inverse(a1), a1), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.18/0.46 = { by lemma 5 R->L }
% 0.18/0.46 tuple(divide(inverse(a1), inverse(a1)), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.18/0.46 = { by axiom 1 (identity) R->L }
% 0.18/0.46 tuple(identity, inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.18/0.46 = { by lemma 10 }
% 0.18/0.46 tuple(identity, a2, multiply(multiply(a3, b3), c3))
% 0.18/0.46 = { by lemma 7 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(multiply(a3, b3), multiply(inverse(b3), multiply(inverse(inverse(b3)), c3))))
% 0.18/0.46 = { by lemma 10 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), b3), multiply(inverse(b3), multiply(inverse(inverse(b3)), c3))))
% 0.18/0.46 = { by lemma 7 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), b3), multiply(inverse(b3), multiply(inverse(inverse(b3)), c3))))))
% 0.18/0.46 = { by lemma 10 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), b3), multiply(inverse(b3), inverse(inverse(multiply(inverse(inverse(b3)), c3))))))))
% 0.18/0.46 = { by lemma 12 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), b3), multiply(inverse(b3), multiply(b3, inverse(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3))))))))
% 0.18/0.46 = { by lemma 10 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), b3), multiply(inverse(b3), multiply(inverse(inverse(b3)), inverse(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3))))))))
% 0.18/0.46 = { by lemma 7 }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), b3), inverse(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3))))))
% 0.18/0.46 = { by lemma 5 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(divide(inverse(inverse(a3)), inverse(b3)), inverse(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3))))))
% 0.18/0.46 = { by lemma 12 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(divide(inverse(inverse(a3)), inverse(b3)), multiply(inverse(divide(inverse(inverse(a3)), inverse(b3))), inverse(multiply(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3), inverse(divide(inverse(inverse(a3)), inverse(b3))))))))))
% 0.18/0.46 = { by lemma 7 }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(inverse(a3), inverse(multiply(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3), inverse(divide(inverse(inverse(a3)), inverse(b3))))))))
% 0.18/0.46 = { by lemma 11 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(inverse(a3), inverse(divide(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3), divide(inverse(inverse(a3)), inverse(b3)))))))
% 0.18/0.46 = { by lemma 11 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(a3, divide(inverse(a3), divide(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3), divide(inverse(inverse(a3)), inverse(b3))))))
% 0.18/0.46 = { by lemma 5 R->L }
% 0.18/0.46 tuple(identity, a2, multiply(a3, divide(inverse(a3), divide(divide(inverse(multiply(inverse(inverse(b3)), c3)), inverse(b3)), divide(inverse(inverse(a3)), inverse(b3))))))
% 0.18/0.46 = { by lemma 6 }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(inverse(inverse(b3)), c3)))
% 0.18/0.46 = { by lemma 10 }
% 0.18/0.46 tuple(identity, a2, multiply(a3, multiply(b3, c3)))
% 0.18/0.46 % SZS output end Proof
% 0.18/0.46
% 0.18/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------