%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP070-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 10:09:12 AM UTC 2026
% Result : Unsatisfiable 0.02s 0.46s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP070-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sun Sep 27 09:20:36 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.46 Command-line arguments: --no-flatten-goal
% 0.02/0.46
% 0.02/0.46 % SZS status Unsatisfiable
% 0.02/0.46
% 0.47/0.48 % SZS output start Proof
% 0.47/0.48 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.47/0.48 Axiom 2 (single_axiom): divide(divide(X, X), divide(Y, divide(divide(Z, divide(W, Y)), inverse(W)))) = Z.
% 0.47/0.48
% 0.47/0.48 Lemma 3: divide(Y, Y) = divide(X, X).
% 0.47/0.48 Proof:
% 0.47/0.48 divide(Y, Y)
% 0.47/0.48 = { by axiom 2 (single_axiom) R->L }
% 0.47/0.48 divide(divide(Z, Z), divide(divide(divide(W, divide(V, U)), inverse(V)), divide(divide(divide(Y, Y), divide(U, divide(divide(W, divide(V, U)), inverse(V)))), inverse(U))))
% 0.47/0.49 = { by axiom 2 (single_axiom) }
% 0.47/0.49 divide(divide(Z, Z), divide(divide(divide(W, divide(V, U)), inverse(V)), divide(W, inverse(U))))
% 0.47/0.49 = { by axiom 2 (single_axiom) R->L }
% 0.47/0.49 divide(divide(Z, Z), divide(divide(divide(W, divide(V, U)), inverse(V)), divide(divide(divide(X, X), divide(U, divide(divide(W, divide(V, U)), inverse(V)))), inverse(U))))
% 0.47/0.49 = { by axiom 2 (single_axiom) }
% 0.47/0.49 divide(X, X)
% 0.47/0.49
% 0.47/0.49 Lemma 4: divide(divide(X, X), divide(Y, divide(divide(Z, Z), inverse(W)))) = divide(W, Y).
% 0.47/0.49 Proof:
% 0.47/0.49 divide(divide(X, X), divide(Y, divide(divide(Z, Z), inverse(W))))
% 0.47/0.49 = { by lemma 3 }
% 0.47/0.49 divide(divide(X, X), divide(Y, divide(divide(divide(W, Y), divide(W, Y)), inverse(W))))
% 0.47/0.49 = { by axiom 2 (single_axiom) }
% 0.47/0.49 divide(W, Y)
% 0.47/0.49
% 0.47/0.49 Lemma 5: divide(divide(X, X), inverse(Y)) = Y.
% 0.47/0.49 Proof:
% 0.47/0.49 divide(divide(X, X), inverse(Y))
% 0.47/0.49 = { by lemma 4 R->L }
% 0.47/0.49 divide(divide(Z, Z), divide(inverse(Y), divide(divide(divide(divide(divide(X, X), inverse(Y)), divide(divide(X, X), inverse(Y))), divide(divide(divide(X, X), inverse(Y)), divide(divide(X, X), inverse(Y)))), inverse(divide(X, X)))))
% 0.47/0.49 = { by lemma 4 }
% 0.47/0.49 divide(divide(Z, Z), divide(inverse(Y), divide(divide(Y, divide(divide(X, X), inverse(Y))), inverse(divide(X, X)))))
% 0.47/0.49 = { by axiom 2 (single_axiom) }
% 0.47/0.49 Y
% 0.47/0.49
% 0.47/0.49 Lemma 6: divide(divide(X, X), divide(Y, Z)) = divide(Z, Y).
% 0.47/0.49 Proof:
% 0.47/0.49 divide(divide(X, X), divide(Y, Z))
% 0.47/0.49 = { by lemma 5 R->L }
% 0.47/0.49 divide(divide(X, X), divide(Y, divide(divide(W, W), inverse(Z))))
% 0.47/0.49 = { by lemma 4 }
% 0.47/0.49 divide(Z, Y)
% 0.47/0.49
% 0.47/0.49 Lemma 7: divide(X, divide(Y, Y)) = X.
% 0.47/0.49 Proof:
% 0.47/0.49 divide(X, divide(Y, Y))
% 0.47/0.49 = { by lemma 4 R->L }
% 0.47/0.49 divide(divide(Z, Z), divide(divide(Y, Y), divide(divide(W, W), inverse(X))))
% 0.47/0.49 = { by lemma 6 }
% 0.47/0.49 divide(divide(Z, Z), divide(inverse(X), divide(W, W)))
% 0.47/0.49 = { by lemma 6 }
% 0.47/0.49 divide(divide(W, W), inverse(X))
% 0.47/0.49 = { by lemma 5 }
% 0.47/0.49 X
% 0.47/0.49
% 0.47/0.49 Lemma 8: divide(divide(X, Y), inverse(Y)) = X.
% 0.47/0.49 Proof:
% 0.47/0.49 divide(divide(X, Y), inverse(Y))
% 0.47/0.49 = { by lemma 7 R->L }
% 0.47/0.49 divide(divide(divide(X, Y), inverse(Y)), divide(Z, Z))
% 0.47/0.49 = { by lemma 6 R->L }
% 0.47/0.49 divide(divide(W, W), divide(divide(Z, Z), divide(divide(X, Y), inverse(Y))))
% 0.47/0.49 = { by lemma 7 R->L }
% 0.47/0.49 divide(divide(W, W), divide(divide(Z, Z), divide(divide(X, divide(Y, divide(Z, Z))), inverse(Y))))
% 0.47/0.49 = { by axiom 2 (single_axiom) }
% 0.47/0.49 X
% 0.47/0.49
% 0.47/0.49 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 0.47/0.49 Proof:
% 0.47/0.49 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.47/0.49 = { by axiom 1 (multiply) }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.47/0.49 = { by axiom 1 (multiply) }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3))
% 0.47/0.49 = { by axiom 1 (multiply) }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.47/0.49 = { by axiom 1 (multiply) }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(divide(a3, inverse(b3)), c3))
% 0.47/0.49 = { by axiom 1 (multiply) }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 0.47/0.49 = { by lemma 5 }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, inverse(b3)), inverse(c3)))
% 0.47/0.49 = { by lemma 6 R->L }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(X, X), divide(inverse(c3), divide(a3, inverse(b3)))))
% 0.47/0.49 = { by lemma 8 R->L }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(X, X), divide(inverse(c3), divide(divide(divide(a3, inverse(divide(b3, inverse(c3)))), inverse(inverse(divide(b3, inverse(c3))))), inverse(b3)))))
% 0.47/0.49 = { by lemma 8 R->L }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(X, X), divide(inverse(c3), divide(divide(divide(divide(divide(a3, inverse(divide(b3, inverse(c3)))), divide(b3, inverse(c3))), inverse(divide(b3, inverse(c3)))), inverse(inverse(divide(b3, inverse(c3))))), inverse(b3)))))
% 0.47/0.49 = { by lemma 8 }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(X, X), divide(inverse(c3), divide(divide(divide(a3, inverse(divide(b3, inverse(c3)))), divide(b3, inverse(c3))), inverse(b3)))))
% 0.47/0.49 = { by axiom 2 (single_axiom) }
% 0.47/0.49 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.47/0.49 = { by lemma 3 }
% 0.47/0.49 tuple(divide(inverse(b1), inverse(b1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.47/0.49 = { by axiom 1 (multiply) R->L }
% 0.47/0.49 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, divide(b3, inverse(c3))))
% 0.47/0.49 = { by axiom 1 (multiply) R->L }
% 0.47/0.49 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, multiply(b3, c3)))
% 0.47/0.49 = { by axiom 1 (multiply) R->L }
% 0.47/0.49 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 0.47/0.49 % SZS output end Proof
% 0.47/0.49
% 0.47/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------