%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP065-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 10:09:11 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.46s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP065-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:20:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.46 Command-line arguments: --no-flatten-goal
% 0.09/0.46
% 0.09/0.46 % SZS status Unsatisfiable
% 0.09/0.46
% 0.50/0.49 % SZS output start Proof
% 0.50/0.49 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.50/0.49 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.50/0.49 Axiom 3 (single_axiom): divide(divide(divide(X, X), divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z) = Y.
% 0.50/0.49
% 0.50/0.49 Lemma 4: divide(X, inverse(Y)) = multiply(X, Y).
% 0.50/0.49 Proof:
% 0.50/0.49 divide(X, inverse(Y))
% 0.50/0.49 = { by axiom 1 (inverse) }
% 0.50/0.49 divide(X, divide(divide(Z, Z), Y))
% 0.50/0.49 = { by axiom 2 (multiply) R->L }
% 0.50/0.49 multiply(X, Y)
% 0.50/0.49
% 0.50/0.49 Lemma 5: multiply(divide(X, X), Y) = inverse(inverse(Y)).
% 0.50/0.49 Proof:
% 0.50/0.49 multiply(divide(X, X), Y)
% 0.50/0.49 = { by lemma 4 R->L }
% 0.50/0.49 divide(divide(X, X), inverse(Y))
% 0.50/0.49 = { by axiom 1 (inverse) R->L }
% 0.50/0.49 inverse(inverse(Y))
% 0.50/0.49
% 0.50/0.49 Lemma 6: divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z) = Y.
% 0.50/0.49 Proof:
% 0.50/0.49 divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z)
% 0.50/0.49 = { by axiom 1 (inverse) }
% 0.50/0.49 divide(inverse(divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z)
% 0.50/0.49 = { by axiom 1 (inverse) }
% 0.50/0.49 divide(divide(divide(X, X), divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z)
% 0.50/0.49 = { by axiom 3 (single_axiom) }
% 0.50/0.49 Y
% 0.50/0.49
% 0.50/0.49 Lemma 7: divide(inverse(inverse(multiply(X, Y))), Y) = X.
% 0.50/0.49 Proof:
% 0.50/0.49 divide(inverse(inverse(multiply(X, Y))), Y)
% 0.50/0.49 = { by lemma 4 R->L }
% 0.50/0.49 divide(inverse(inverse(divide(X, inverse(Y)))), Y)
% 0.50/0.49 = { by axiom 1 (inverse) }
% 0.50/0.49 divide(inverse(divide(divide(Z, Z), divide(X, inverse(Y)))), Y)
% 0.50/0.49 = { by axiom 1 (inverse) }
% 0.50/0.49 divide(inverse(divide(divide(Z, Z), divide(X, divide(divide(divide(Z, Z), divide(Z, Z)), Y)))), Y)
% 0.50/0.49 = { by axiom 1 (inverse) R->L }
% 0.50/0.49 divide(inverse(divide(divide(Z, Z), divide(X, divide(inverse(divide(Z, Z)), Y)))), Y)
% 0.50/0.49 = { by lemma 6 }
% 0.50/0.49 X
% 0.50/0.49
% 0.50/0.49 Lemma 8: multiply(inverse(inverse(multiply(X, inverse(Y)))), Y) = X.
% 0.50/0.49 Proof:
% 0.50/0.49 multiply(inverse(inverse(multiply(X, inverse(Y)))), Y)
% 0.50/0.49 = { by lemma 4 R->L }
% 0.50/0.49 divide(inverse(inverse(multiply(X, inverse(Y)))), inverse(Y))
% 0.50/0.49 = { by lemma 7 }
% 0.50/0.49 X
% 0.50/0.49
% 0.50/0.49 Lemma 9: inverse(inverse(multiply(X, inverse(Y)))) = divide(inverse(inverse(X)), Y).
% 0.50/0.49 Proof:
% 0.50/0.49 inverse(inverse(multiply(X, inverse(Y))))
% 0.50/0.49 = { by lemma 7 R->L }
% 0.50/0.49 divide(inverse(inverse(multiply(inverse(inverse(multiply(X, inverse(Y)))), Y))), Y)
% 0.50/0.49 = { by lemma 8 }
% 0.50/0.49 divide(inverse(inverse(X)), Y)
% 0.50/0.49
% 0.50/0.49 Lemma 10: multiply(divide(inverse(inverse(X)), Y), Y) = X.
% 0.50/0.49 Proof:
% 0.50/0.49 multiply(divide(inverse(inverse(X)), Y), Y)
% 0.50/0.49 = { by lemma 4 R->L }
% 0.50/0.49 divide(divide(inverse(inverse(X)), Y), inverse(Y))
% 0.50/0.49 = { by lemma 9 R->L }
% 0.50/0.49 divide(inverse(inverse(multiply(X, inverse(Y)))), inverse(Y))
% 0.50/0.49 = { by lemma 7 }
% 0.50/0.49 X
% 0.50/0.49
% 0.50/0.49 Lemma 11: inverse(inverse(inverse(inverse(X)))) = X.
% 0.50/0.49 Proof:
% 0.50/0.49 inverse(inverse(inverse(inverse(X))))
% 0.50/0.49 = { by lemma 5 R->L }
% 0.50/0.49 multiply(divide(inverse(inverse(X)), inverse(inverse(X))), inverse(inverse(X)))
% 0.50/0.49 = { by lemma 10 }
% 0.50/0.49 X
% 0.50/0.49
% 0.50/0.49 Lemma 12: divide(X, Y) = multiply(X, inverse(inverse(inverse(Y)))).
% 0.50/0.49 Proof:
% 0.50/0.49 divide(X, Y)
% 0.50/0.49 = { by lemma 11 R->L }
% 0.50/0.49 divide(X, inverse(inverse(inverse(inverse(Y)))))
% 0.50/0.49 = { by lemma 4 }
% 0.50/0.49 multiply(X, inverse(inverse(inverse(Y))))
% 0.50/0.49
% 0.50/0.49 Lemma 13: multiply(inverse(X), X) = multiply(Y, inverse(inverse(inverse(Y)))).
% 0.50/0.49 Proof:
% 0.50/0.49 multiply(inverse(X), X)
% 0.50/0.49 = { by lemma 4 R->L }
% 0.50/0.49 divide(inverse(X), inverse(X))
% 0.50/0.49 = { by lemma 7 R->L }
% 0.50/0.49 divide(inverse(inverse(multiply(divide(inverse(X), inverse(X)), Z))), Z)
% 0.50/0.49 = { by lemma 5 }
% 0.50/0.49 divide(inverse(inverse(inverse(inverse(Z)))), Z)
% 0.50/0.49 = { by lemma 5 R->L }
% 0.50/0.49 divide(inverse(inverse(multiply(divide(inverse(inverse(inverse(inverse(Y)))), inverse(inverse(inverse(inverse(Y))))), Z))), Z)
% 0.50/0.49 = { by lemma 7 }
% 0.50/0.49 divide(inverse(inverse(inverse(inverse(Y)))), inverse(inverse(inverse(inverse(Y)))))
% 0.50/0.49 = { by lemma 4 }
% 0.50/0.49 multiply(inverse(inverse(inverse(inverse(Y)))), inverse(inverse(inverse(Y))))
% 0.50/0.49 = { by lemma 11 }
% 0.50/0.49 multiply(Y, inverse(inverse(inverse(Y))))
% 0.50/0.49
% 0.50/0.50 Lemma 14: inverse(multiply(X, multiply(inverse(X), Y))) = inverse(Y).
% 0.50/0.50 Proof:
% 0.50/0.50 inverse(multiply(X, multiply(inverse(X), Y)))
% 0.50/0.50 = { by lemma 7 R->L }
% 0.50/0.50 divide(inverse(inverse(multiply(inverse(multiply(X, multiply(inverse(X), Y))), Y))), Y)
% 0.50/0.50 = { by lemma 4 R->L }
% 0.50/0.50 divide(inverse(inverse(multiply(inverse(multiply(X, divide(inverse(X), inverse(Y)))), Y))), Y)
% 0.50/0.50 = { by lemma 4 R->L }
% 0.50/0.50 divide(inverse(inverse(divide(inverse(multiply(X, divide(inverse(X), inverse(Y)))), inverse(Y)))), Y)
% 0.50/0.50 = { by lemma 4 R->L }
% 0.50/0.50 divide(inverse(inverse(divide(inverse(divide(X, inverse(divide(inverse(X), inverse(Y))))), inverse(Y)))), Y)
% 0.50/0.50 = { by axiom 1 (inverse) }
% 0.50/0.50 divide(inverse(inverse(divide(inverse(divide(X, divide(divide(inverse(Z), inverse(Z)), divide(inverse(X), inverse(Y))))), inverse(Y)))), Y)
% 0.50/0.50 = { by lemma 6 }
% 0.50/0.50 divide(inverse(inverse(divide(inverse(Z), inverse(Z)))), Y)
% 0.50/0.50 = { by lemma 4 }
% 0.50/0.50 divide(inverse(inverse(multiply(inverse(Z), Z))), Y)
% 0.50/0.50 = { by lemma 13 }
% 0.50/0.50 divide(inverse(inverse(multiply(W, inverse(inverse(inverse(W)))))), Y)
% 0.50/0.50 = { by lemma 12 }
% 0.50/0.50 multiply(inverse(inverse(multiply(W, inverse(inverse(inverse(W)))))), inverse(inverse(inverse(Y))))
% 0.50/0.50 = { by lemma 9 }
% 0.50/0.50 multiply(divide(inverse(inverse(W)), inverse(inverse(W))), inverse(inverse(inverse(Y))))
% 0.50/0.50 = { by lemma 5 }
% 0.50/0.50 inverse(inverse(inverse(inverse(inverse(Y)))))
% 0.50/0.50 = { by lemma 11 }
% 0.50/0.50 inverse(Y)
% 0.50/0.50
% 0.50/0.50 Lemma 15: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.50/0.50 Proof:
% 0.50/0.50 multiply(X, multiply(inverse(X), Y))
% 0.50/0.50 = { by lemma 10 R->L }
% 0.50/0.50 multiply(divide(inverse(inverse(multiply(X, multiply(inverse(X), Y)))), Z), Z)
% 0.50/0.50 = { by lemma 14 }
% 0.50/0.50 multiply(divide(inverse(inverse(Y)), Z), Z)
% 0.50/0.50 = { by lemma 10 }
% 0.50/0.50 Y
% 0.50/0.50
% 0.50/0.50 Lemma 16: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 0.50/0.50 Proof:
% 0.50/0.50 multiply(inverse(inverse(X)), Y)
% 0.50/0.50 = { by lemma 15 R->L }
% 0.50/0.50 multiply(X, multiply(inverse(X), multiply(inverse(inverse(X)), Y)))
% 0.50/0.50 = { by lemma 15 }
% 0.50/0.50 multiply(X, Y)
% 0.50/0.50
% 0.50/0.50 Lemma 17: inverse(inverse(X)) = X.
% 0.50/0.50 Proof:
% 0.50/0.50 inverse(inverse(X))
% 0.50/0.50 = { by lemma 7 R->L }
% 0.50/0.50 divide(inverse(inverse(multiply(inverse(inverse(X)), Y))), Y)
% 0.50/0.50 = { by lemma 16 }
% 0.50/0.50 divide(inverse(inverse(multiply(X, Y))), Y)
% 0.50/0.50 = { by lemma 7 }
% 0.50/0.50 X
% 0.50/0.50
% 0.50/0.50 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1)).
% 0.50/0.50 Proof:
% 0.50/0.50 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.50/0.50 = { by lemma 4 R->L }
% 0.50/0.50 tuple(multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.50/0.50 = { by lemma 5 }
% 0.50/0.50 tuple(inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.50/0.50 = { by lemma 13 }
% 0.50/0.50 tuple(inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(X, inverse(inverse(inverse(X)))))
% 0.50/0.50 = { by lemma 17 }
% 0.50/0.50 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(inverse(inverse(X)))))
% 0.50/0.50 = { by lemma 17 }
% 0.50/0.50 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 11 R->L }
% 0.50/0.50 tuple(a2, multiply(multiply(a3, b3), inverse(inverse(inverse(inverse(c3))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 11 R->L }
% 0.50/0.50 tuple(a2, multiply(multiply(a3, inverse(inverse(inverse(inverse(b3))))), inverse(inverse(inverse(inverse(c3))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 17 R->L }
% 0.50/0.50 tuple(a2, multiply(multiply(a3, inverse(inverse(inverse(inverse(b3))))), inverse(inverse(inverse(inverse(inverse(inverse(c3))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 16 R->L }
% 0.50/0.50 tuple(a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(inverse(inverse(b3))))), inverse(inverse(inverse(inverse(inverse(inverse(c3))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 17 R->L }
% 0.50/0.50 tuple(a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(inverse(inverse(inverse(inverse(b3))))))), inverse(inverse(inverse(inverse(inverse(inverse(c3))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 16 R->L }
% 0.50/0.50 tuple(a2, multiply(multiply(inverse(inverse(inverse(inverse(a3)))), inverse(inverse(inverse(inverse(inverse(inverse(b3))))))), inverse(inverse(inverse(inverse(inverse(inverse(c3))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 12 R->L }
% 0.50/0.50 tuple(a2, multiply(divide(inverse(inverse(inverse(inverse(a3)))), inverse(inverse(inverse(b3)))), inverse(inverse(inverse(inverse(inverse(inverse(c3))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 14 R->L }
% 0.50/0.50 tuple(a2, multiply(divide(inverse(inverse(multiply(inverse(multiply(inverse(inverse(inverse(b3))), inverse(inverse(inverse(a3))))), multiply(inverse(inverse(multiply(inverse(inverse(inverse(b3))), inverse(inverse(inverse(a3)))))), inverse(inverse(a3)))))), inverse(inverse(inverse(b3)))), inverse(inverse(inverse(inverse(inverse(inverse(c3))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 8 }
% 0.50/0.50 tuple(a2, multiply(divide(inverse(inverse(multiply(inverse(multiply(inverse(inverse(inverse(b3))), inverse(inverse(inverse(a3))))), inverse(inverse(inverse(b3)))))), inverse(inverse(inverse(b3)))), inverse(inverse(inverse(inverse(inverse(inverse(c3))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 7 }
% 0.50/0.50 tuple(a2, multiply(inverse(multiply(inverse(inverse(inverse(b3))), inverse(inverse(inverse(a3))))), inverse(inverse(inverse(inverse(inverse(inverse(c3))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 12 R->L }
% 0.50/0.50 tuple(a2, multiply(inverse(divide(inverse(inverse(inverse(b3))), a3)), inverse(inverse(inverse(inverse(inverse(inverse(c3))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 12 R->L }
% 0.50/0.50 tuple(a2, divide(inverse(divide(inverse(inverse(inverse(b3))), a3)), inverse(inverse(inverse(c3)))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 7 R->L }
% 0.50/0.50 tuple(a2, divide(inverse(divide(inverse(inverse(inverse(b3))), divide(inverse(inverse(multiply(a3, divide(inverse(inverse(inverse(inverse(b3)))), inverse(inverse(inverse(c3))))))), divide(inverse(inverse(inverse(inverse(b3)))), inverse(inverse(inverse(c3))))))), inverse(inverse(inverse(c3)))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 6 }
% 0.50/0.50 tuple(a2, inverse(inverse(multiply(a3, divide(inverse(inverse(inverse(inverse(b3)))), inverse(inverse(inverse(c3))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 17 }
% 0.50/0.50 tuple(a2, multiply(a3, divide(inverse(inverse(inverse(inverse(b3)))), inverse(inverse(inverse(c3))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 12 }
% 0.50/0.50 tuple(a2, multiply(a3, multiply(inverse(inverse(inverse(inverse(b3)))), inverse(inverse(inverse(inverse(inverse(inverse(c3)))))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 17 }
% 0.50/0.50 tuple(a2, multiply(a3, multiply(inverse(inverse(inverse(inverse(b3)))), inverse(inverse(inverse(inverse(c3)))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 16 }
% 0.50/0.50 tuple(a2, multiply(a3, multiply(inverse(inverse(b3)), inverse(inverse(inverse(inverse(c3)))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 16 }
% 0.50/0.50 tuple(a2, multiply(a3, multiply(b3, inverse(inverse(inverse(inverse(c3)))))), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 11 }
% 0.50/0.50 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 0.50/0.50 = { by lemma 17 R->L }
% 0.50/0.50 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(inverse(inverse(X)))))
% 0.50/0.50 = { by lemma 13 R->L }
% 0.50/0.50 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 0.50/0.50 % SZS output end Proof
% 0.50/0.50
% 0.50/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------