%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP100-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 10:09:16 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : Proof 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP100-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:21:41 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.47 Command-line arguments: --no-flatten-goal
% 0.13/0.47
% 0.13/0.47 % SZS status Unsatisfiable
% 0.13/0.47
% 0.13/0.50 % SZS output start Proof
% 0.13/0.50 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.13/0.50 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.13/0.50 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.13/0.50 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(Z, identity))), double_divide(identity, identity)) = Y.
% 0.13/0.50
% 0.13/0.50 Lemma 5: double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), inverse(Z))), inverse(identity)) = Y.
% 0.13/0.50 Proof:
% 0.13/0.50 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), inverse(Z))), inverse(identity))
% 0.13/0.50 = { by axiom 1 (inverse) }
% 0.13/0.50 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), inverse(Z))), double_divide(identity, identity))
% 0.13/0.50 = { by axiom 1 (inverse) }
% 0.13/0.50 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(Z, identity))), double_divide(identity, identity))
% 0.13/0.50 = { by axiom 4 (single_axiom) }
% 0.13/0.50 Y
% 0.13/0.50
% 0.13/0.50 Lemma 6: double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), inverse(identity)) = Y.
% 0.13/0.50 Proof:
% 0.13/0.50 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), inverse(identity))
% 0.13/0.50 = { by axiom 1 (inverse) }
% 0.13/0.50 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, identity)), inverse(identity))), inverse(identity))
% 0.13/0.50 = { by lemma 5 }
% 0.13/0.50 Y
% 0.13/0.50
% 0.13/0.50 Lemma 7: double_divide(inverse(X), inverse(identity)) = X.
% 0.13/0.50 Proof:
% 0.13/0.50 double_divide(inverse(X), inverse(identity))
% 0.13/0.50 = { by axiom 1 (inverse) }
% 0.13/0.50 double_divide(double_divide(X, identity), inverse(identity))
% 0.13/0.50 = { by axiom 2 (identity) }
% 0.13/0.50 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.13/0.50 = { by axiom 2 (identity) }
% 0.13/0.50 double_divide(double_divide(X, double_divide(double_divide(X, inverse(X)), inverse(identity))), inverse(identity))
% 0.13/0.50 = { by lemma 6 }
% 0.13/0.50 X
% 0.13/0.50
% 0.13/0.50 Lemma 8: double_divide(double_divide(identity, double_divide(X, inverse(identity))), inverse(identity)) = inverse(X).
% 0.13/0.50 Proof:
% 0.13/0.50 double_divide(double_divide(identity, double_divide(X, inverse(identity))), inverse(identity))
% 0.13/0.50 = { by lemma 7 R->L }
% 0.13/0.50 double_divide(double_divide(identity, double_divide(double_divide(inverse(X), inverse(identity)), inverse(identity))), inverse(identity))
% 0.13/0.50 = { by lemma 6 }
% 0.13/0.50 inverse(X)
% 0.13/0.50
% 0.13/0.50 Lemma 9: inverse(identity) = identity.
% 0.13/0.50 Proof:
% 0.13/0.50 inverse(identity)
% 0.13/0.50 = { by lemma 8 R->L }
% 0.13/0.50 double_divide(double_divide(identity, double_divide(identity, inverse(identity))), inverse(identity))
% 0.13/0.50 = { by axiom 2 (identity) R->L }
% 0.13/0.50 double_divide(double_divide(identity, identity), inverse(identity))
% 0.13/0.50 = { by axiom 1 (inverse) R->L }
% 0.13/0.50 double_divide(inverse(identity), inverse(identity))
% 0.13/0.50 = { by lemma 7 }
% 0.13/0.50 identity
% 0.13/0.50
% 0.58/0.50 Lemma 10: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.58/0.50 Proof:
% 0.58/0.50 inverse(double_divide(X, Y))
% 0.58/0.50 = { by axiom 1 (inverse) }
% 0.58/0.50 double_divide(double_divide(X, Y), identity)
% 0.58/0.50 = { by axiom 3 (multiply) R->L }
% 0.58/0.50 multiply(Y, X)
% 0.58/0.50
% 0.58/0.50 Lemma 11: double_divide(multiply(X, Y), inverse(identity)) = double_divide(Y, X).
% 0.58/0.50 Proof:
% 0.58/0.50 double_divide(multiply(X, Y), inverse(identity))
% 0.58/0.50 = { by lemma 10 R->L }
% 0.58/0.50 double_divide(inverse(double_divide(Y, X)), inverse(identity))
% 0.58/0.50 = { by lemma 7 }
% 0.58/0.50 double_divide(Y, X)
% 0.58/0.50
% 0.58/0.50 Lemma 12: multiply(identity, X) = inverse(inverse(X)).
% 0.58/0.50 Proof:
% 0.58/0.50 multiply(identity, X)
% 0.58/0.50 = { by lemma 10 R->L }
% 0.58/0.50 inverse(double_divide(X, identity))
% 0.58/0.50 = { by axiom 1 (inverse) R->L }
% 0.58/0.50 inverse(inverse(X))
% 0.58/0.50
% 0.58/0.50 Lemma 13: inverse(inverse(X)) = X.
% 0.58/0.50 Proof:
% 0.58/0.50 inverse(inverse(X))
% 0.58/0.50 = { by lemma 12 R->L }
% 0.58/0.50 multiply(identity, X)
% 0.58/0.50 = { by lemma 10 R->L }
% 0.58/0.50 inverse(double_divide(X, identity))
% 0.58/0.50 = { by lemma 8 R->L }
% 0.58/0.50 double_divide(double_divide(identity, double_divide(double_divide(X, identity), inverse(identity))), inverse(identity))
% 0.58/0.50 = { by lemma 9 R->L }
% 0.58/0.50 double_divide(double_divide(identity, double_divide(double_divide(X, inverse(identity)), inverse(identity))), inverse(identity))
% 0.58/0.50 = { by lemma 6 }
% 0.58/0.50 X
% 0.58/0.50
% 0.58/0.50 Lemma 14: double_divide(identity, X) = inverse(X).
% 0.58/0.50 Proof:
% 0.58/0.50 double_divide(identity, X)
% 0.58/0.50 = { by lemma 11 R->L }
% 0.58/0.50 double_divide(multiply(X, identity), inverse(identity))
% 0.58/0.50 = { by lemma 13 R->L }
% 0.58/0.50 double_divide(multiply(inverse(inverse(X)), identity), inverse(identity))
% 0.58/0.50 = { by lemma 10 R->L }
% 0.58/0.50 double_divide(inverse(double_divide(identity, inverse(inverse(X)))), inverse(identity))
% 0.58/0.50 = { by axiom 1 (inverse) }
% 0.58/0.50 double_divide(double_divide(double_divide(identity, inverse(inverse(X))), identity), inverse(identity))
% 0.58/0.50 = { by lemma 9 R->L }
% 0.58/0.50 double_divide(double_divide(double_divide(identity, inverse(inverse(X))), inverse(identity)), inverse(identity))
% 0.58/0.50 = { by axiom 1 (inverse) }
% 0.58/0.50 double_divide(double_divide(double_divide(identity, double_divide(inverse(X), identity)), inverse(identity)), inverse(identity))
% 0.58/0.50 = { by lemma 9 R->L }
% 0.58/0.50 double_divide(double_divide(double_divide(identity, double_divide(inverse(X), inverse(identity))), inverse(identity)), inverse(identity))
% 0.58/0.50 = { by lemma 8 }
% 0.58/0.50 double_divide(inverse(inverse(X)), inverse(identity))
% 0.58/0.50 = { by lemma 13 }
% 0.58/0.50 double_divide(X, inverse(identity))
% 0.58/0.50 = { by lemma 9 }
% 0.58/0.50 double_divide(X, identity)
% 0.58/0.50 = { by axiom 1 (inverse) R->L }
% 0.58/0.50 inverse(X)
% 0.58/0.50
% 0.58/0.50 Lemma 15: multiply(multiply(X, Y), inverse(X)) = Y.
% 0.58/0.50 Proof:
% 0.58/0.50 multiply(multiply(X, Y), inverse(X))
% 0.58/0.50 = { by lemma 10 R->L }
% 0.58/0.50 multiply(inverse(double_divide(Y, X)), inverse(X))
% 0.58/0.50 = { by axiom 1 (inverse) }
% 0.58/0.50 multiply(double_divide(double_divide(Y, X), identity), inverse(X))
% 0.58/0.50 = { by lemma 10 R->L }
% 0.58/0.50 inverse(double_divide(inverse(X), double_divide(double_divide(Y, X), identity)))
% 0.58/0.50 = { by axiom 1 (inverse) }
% 0.58/0.50 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), identity)), identity)
% 0.58/0.51 = { by lemma 9 R->L }
% 0.58/0.51 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), inverse(identity))), identity)
% 0.58/0.51 = { by lemma 9 R->L }
% 0.58/0.51 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), inverse(identity))), inverse(identity))
% 0.58/0.51 = { by lemma 13 R->L }
% 0.58/0.51 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, inverse(inverse(X))), inverse(identity))), inverse(identity))
% 0.58/0.51 = { by lemma 6 }
% 0.58/0.51 Y
% 0.58/0.51
% 0.58/0.51 Lemma 16: multiply(X, double_divide(X, Y)) = inverse(Y).
% 0.58/0.51 Proof:
% 0.58/0.51 multiply(X, double_divide(X, Y))
% 0.58/0.51 = { by lemma 11 R->L }
% 0.58/0.51 multiply(X, double_divide(multiply(Y, X), inverse(identity)))
% 0.58/0.51 = { by lemma 9 }
% 0.58/0.51 multiply(X, double_divide(multiply(Y, X), identity))
% 0.58/0.51 = { by axiom 1 (inverse) R->L }
% 0.58/0.51 multiply(X, inverse(multiply(Y, X)))
% 0.58/0.51 = { by lemma 15 R->L }
% 0.58/0.51 multiply(multiply(multiply(Y, X), inverse(Y)), inverse(multiply(Y, X)))
% 0.58/0.51 = { by lemma 15 }
% 0.58/0.51 inverse(Y)
% 0.58/0.51
% 0.58/0.51 Lemma 17: multiply(multiply(inverse(X), Y), X) = Y.
% 0.58/0.51 Proof:
% 0.58/0.51 multiply(multiply(inverse(X), Y), X)
% 0.58/0.51 = { by lemma 10 R->L }
% 0.58/0.51 inverse(double_divide(X, multiply(inverse(X), Y)))
% 0.58/0.51 = { by axiom 1 (inverse) }
% 0.58/0.51 double_divide(double_divide(X, multiply(inverse(X), Y)), identity)
% 0.58/0.51 = { by lemma 9 R->L }
% 0.58/0.51 double_divide(double_divide(X, multiply(inverse(X), Y)), inverse(identity))
% 0.58/0.51 = { by axiom 1 (inverse) }
% 0.58/0.51 double_divide(double_divide(X, multiply(double_divide(X, identity), Y)), inverse(identity))
% 0.58/0.51 = { by lemma 10 R->L }
% 0.58/0.51 double_divide(double_divide(X, inverse(double_divide(Y, double_divide(X, identity)))), inverse(identity))
% 0.58/0.51 = { by axiom 1 (inverse) }
% 0.58/0.51 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, identity)), identity)), inverse(identity))
% 0.58/0.51 = { by lemma 9 R->L }
% 0.58/0.51 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, identity)), inverse(identity))), inverse(identity))
% 0.58/0.51 = { by lemma 5 }
% 0.58/0.51 Y
% 0.58/0.51
% 0.58/0.51 Lemma 18: double_divide(X, inverse(Y)) = multiply(Y, inverse(X)).
% 0.58/0.51 Proof:
% 0.58/0.51 double_divide(X, inverse(Y))
% 0.58/0.51 = { by lemma 16 R->L }
% 0.58/0.51 double_divide(X, multiply(inverse(X), double_divide(inverse(X), Y)))
% 0.58/0.51 = { by lemma 11 R->L }
% 0.58/0.51 double_divide(multiply(multiply(inverse(X), double_divide(inverse(X), Y)), X), inverse(identity))
% 0.58/0.51 = { by lemma 17 }
% 0.58/0.51 double_divide(double_divide(inverse(X), Y), inverse(identity))
% 0.58/0.51 = { by lemma 9 }
% 0.58/0.51 double_divide(double_divide(inverse(X), Y), identity)
% 0.58/0.51 = { by axiom 1 (inverse) R->L }
% 0.58/0.51 inverse(double_divide(inverse(X), Y))
% 0.58/0.51 = { by lemma 10 }
% 0.58/0.51 multiply(Y, inverse(X))
% 0.58/0.51
% 0.58/0.51 Lemma 19: multiply(Y, X) = multiply(X, Y).
% 0.58/0.51 Proof:
% 0.58/0.51 multiply(Y, X)
% 0.58/0.51 = { by lemma 5 R->L }
% 0.58/0.51 multiply(double_divide(double_divide(identity, double_divide(double_divide(Y, double_divide(identity, inverse(X))), inverse(inverse(X)))), inverse(identity)), X)
% 0.58/0.51 = { by lemma 14 }
% 0.58/0.51 multiply(double_divide(inverse(double_divide(double_divide(Y, double_divide(identity, inverse(X))), inverse(inverse(X)))), inverse(identity)), X)
% 0.58/0.51 = { by lemma 7 }
% 0.58/0.51 multiply(double_divide(double_divide(Y, double_divide(identity, inverse(X))), inverse(inverse(X))), X)
% 0.58/0.51 = { by lemma 18 }
% 0.58/0.51 multiply(multiply(inverse(X), inverse(double_divide(Y, double_divide(identity, inverse(X))))), X)
% 0.58/0.51 = { by lemma 10 }
% 0.58/0.51 multiply(multiply(inverse(X), multiply(double_divide(identity, inverse(X)), Y)), X)
% 0.58/0.51 = { by lemma 14 }
% 0.58/0.51 multiply(multiply(inverse(X), multiply(inverse(inverse(X)), Y)), X)
% 0.58/0.51 = { by lemma 17 }
% 0.58/0.51 multiply(inverse(inverse(X)), Y)
% 0.58/0.51 = { by lemma 13 }
% 0.58/0.51 multiply(X, Y)
% 0.58/0.51
% 0.58/0.51 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3), multiply(a4, b4)) = tuple(identity, a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4)).
% 0.58/0.51 Proof:
% 0.58/0.51 tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.58/0.51 = { by lemma 12 }
% 0.58/0.51 tuple(multiply(inverse(a1), a1), inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.58/0.51 = { by lemma 10 R->L }
% 0.58/0.51 tuple(inverse(double_divide(a1, inverse(a1))), inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.58/0.51 = { by axiom 2 (identity) R->L }
% 0.58/0.51 tuple(inverse(identity), inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.58/0.51 = { by lemma 9 }
% 0.58/0.51 tuple(identity, inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.58/0.51 = { by lemma 13 }
% 0.58/0.51 tuple(identity, a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.58/0.51 = { by lemma 19 R->L }
% 0.58/0.51 tuple(identity, a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.58/0.51 = { by lemma 13 R->L }
% 0.58/0.51 tuple(identity, a2, multiply(inverse(inverse(c3)), multiply(a3, b3)), multiply(a4, b4))
% 0.58/0.51 = { by lemma 19 }
% 0.58/0.51 tuple(identity, a2, multiply(inverse(inverse(c3)), multiply(b3, a3)), multiply(a4, b4))
% 0.58/0.51 = { by lemma 10 R->L }
% 0.58/0.51 tuple(identity, a2, multiply(inverse(inverse(c3)), inverse(double_divide(a3, b3))), multiply(a4, b4))
% 0.58/0.51 = { by lemma 16 R->L }
% 0.58/0.51 tuple(identity, a2, multiply(multiply(double_divide(a3, b3), double_divide(double_divide(a3, b3), inverse(c3))), inverse(double_divide(a3, b3))), multiply(a4, b4))
% 0.58/0.51 = { by lemma 15 }
% 0.58/0.51 tuple(identity, a2, double_divide(double_divide(a3, b3), inverse(c3)), multiply(a4, b4))
% 0.58/0.51 = { by lemma 5 R->L }
% 0.58/0.51 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(double_divide(double_divide(a3, b3), inverse(c3)), double_divide(a3, b3)), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.58/0.51 = { by lemma 11 R->L }
% 0.58/0.51 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(multiply(double_divide(a3, b3), double_divide(double_divide(a3, b3), inverse(c3))), inverse(identity)), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.58/0.51 = { by lemma 16 }
% 0.58/0.51 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(inverse(inverse(c3)), inverse(identity)), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.58/0.51 = { by lemma 7 }
% 0.58/0.51 tuple(identity, a2, double_divide(double_divide(a3, double_divide(inverse(c3), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.58/0.51 = { by lemma 18 }
% 0.58/0.51 tuple(identity, a2, multiply(identity, inverse(double_divide(a3, double_divide(inverse(c3), inverse(b3))))), multiply(a4, b4))
% 0.58/0.51 = { by lemma 12 }
% 0.58/0.51 tuple(identity, a2, inverse(inverse(inverse(double_divide(a3, double_divide(inverse(c3), inverse(b3)))))), multiply(a4, b4))
% 0.58/0.51 = { by lemma 13 }
% 0.58/0.51 tuple(identity, a2, inverse(double_divide(a3, double_divide(inverse(c3), inverse(b3)))), multiply(a4, b4))
% 0.58/0.51 = { by lemma 10 }
% 0.58/0.51 tuple(identity, a2, multiply(double_divide(inverse(c3), inverse(b3)), a3), multiply(a4, b4))
% 0.58/0.51 = { by lemma 18 }
% 0.58/0.51 tuple(identity, a2, multiply(multiply(b3, inverse(inverse(c3))), a3), multiply(a4, b4))
% 0.58/0.51 = { by lemma 19 R->L }
% 0.58/0.51 tuple(identity, a2, multiply(a3, multiply(b3, inverse(inverse(c3)))), multiply(a4, b4))
% 0.58/0.51 = { by lemma 13 }
% 0.58/0.51 tuple(identity, a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.58/0.51 = { by lemma 19 }
% 0.58/0.51 tuple(identity, a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.58/0.51 % SZS output end Proof
% 0.58/0.51
% 0.58/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------