%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP087-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 10:09:14 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP087-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:19:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 Command-line arguments: --no-flatten-goal
% 0.19/0.49
% 0.19/0.49 % SZS status Unsatisfiable
% 0.19/0.49
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 Axiom 1 (single_axiom): multiply(X, multiply(multiply(inverse(multiply(X, Y)), Z), Y)) = Z.
% 0.19/0.50
% 0.19/0.50 Lemma 2: multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W), Z) = multiply(X, multiply(W, Y)).
% 0.19/0.50 Proof:
% 0.19/0.50 multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W), Z)
% 0.19/0.50 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.50 multiply(X, multiply(multiply(inverse(multiply(X, Y)), multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W), Z)), Y))
% 0.19/0.50 = { by axiom 1 (single_axiom) }
% 0.19/0.50 multiply(X, multiply(W, Y))
% 0.19/0.50
% 0.19/0.50 Lemma 3: multiply(multiply(inverse(X), Y), multiply(Z, multiply(X, W))) = multiply(Z, multiply(Y, W)).
% 0.19/0.50 Proof:
% 0.19/0.50 multiply(multiply(inverse(X), Y), multiply(Z, multiply(X, W)))
% 0.19/0.50 = { by lemma 2 R->L }
% 0.19/0.50 multiply(multiply(inverse(X), Y), multiply(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), X), V))
% 0.19/0.50 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.50 multiply(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), X), V))), Y), multiply(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), X), V))
% 0.19/0.51 = { by lemma 2 }
% 0.19/0.51 multiply(Z, multiply(Y, W))
% 0.19/0.51
% 0.19/0.51 Lemma 4: multiply(multiply(inverse(X), Y), multiply(Z, multiply(X, W))) = multiply(multiply(inverse(V), Z), multiply(V, multiply(Y, W))).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(multiply(inverse(X), Y), multiply(Z, multiply(X, W)))
% 0.19/0.51 = { by lemma 3 R->L }
% 0.19/0.51 multiply(multiply(inverse(V), Z), multiply(multiply(inverse(X), Y), multiply(V, multiply(X, W))))
% 0.19/0.51 = { by lemma 3 }
% 0.19/0.51 multiply(multiply(inverse(V), Z), multiply(V, multiply(Y, W)))
% 0.19/0.51
% 0.19/0.51 Lemma 5: multiply(X, multiply(Y, Z)) = multiply(Y, multiply(X, Z)).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(X, multiply(Y, Z))
% 0.19/0.51 = { by lemma 3 R->L }
% 0.19/0.51 multiply(multiply(inverse(W), Y), multiply(X, multiply(W, Z)))
% 0.19/0.51 = { by lemma 4 }
% 0.19/0.51 multiply(multiply(inverse(Y), X), multiply(Y, multiply(Y, Z)))
% 0.19/0.51 = { by lemma 3 }
% 0.19/0.51 multiply(Y, multiply(X, Z))
% 0.19/0.51
% 0.19/0.51 Lemma 6: multiply(X, multiply(multiply(inverse(X), Y), Z)) = multiply(Y, Z).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(X, multiply(multiply(inverse(X), Y), Z))
% 0.19/0.51 = { by lemma 5 R->L }
% 0.19/0.51 multiply(multiply(inverse(X), Y), multiply(X, Z))
% 0.19/0.51 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.51 multiply(multiply(inverse(X), Y), multiply(X, multiply(W, multiply(multiply(inverse(multiply(W, V)), Z), V))))
% 0.19/0.51 = { by lemma 4 R->L }
% 0.19/0.51 multiply(multiply(inverse(U), W), multiply(Y, multiply(U, multiply(multiply(inverse(multiply(W, V)), Z), V))))
% 0.19/0.51 = { by lemma 3 }
% 0.19/0.51 multiply(Y, multiply(W, multiply(multiply(inverse(multiply(W, V)), Z), V)))
% 0.19/0.51 = { by axiom 1 (single_axiom) }
% 0.19/0.51 multiply(Y, Z)
% 0.19/0.51
% 0.19/0.51 Lemma 7: multiply(inverse(multiply(X, Y)), multiply(X, multiply(Z, Y))) = Z.
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(inverse(multiply(X, Y)), multiply(X, multiply(Z, Y)))
% 0.19/0.51 = { by lemma 2 R->L }
% 0.19/0.51 multiply(inverse(multiply(X, Y)), multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z), W))
% 0.19/0.51 = { by axiom 1 (single_axiom) }
% 0.19/0.51 Z
% 0.19/0.51
% 0.19/0.51 Lemma 8: multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(multiply(X, Y), Z)
% 0.19/0.51 = { by lemma 6 R->L }
% 0.19/0.51 multiply(W, multiply(multiply(inverse(W), multiply(X, Y)), Z))
% 0.19/0.51 = { by lemma 3 R->L }
% 0.19/0.51 multiply(multiply(inverse(multiply(inverse(W), Y)), multiply(inverse(W), multiply(X, Y))), multiply(W, multiply(multiply(inverse(W), Y), Z)))
% 0.19/0.51 = { by lemma 7 }
% 0.19/0.51 multiply(X, multiply(W, multiply(multiply(inverse(W), Y), Z)))
% 0.19/0.51 = { by lemma 6 }
% 0.19/0.51 multiply(X, multiply(Y, Z))
% 0.19/0.51
% 0.19/0.51 Lemma 9: multiply(X, multiply(inverse(X), multiply(Y, Z))) = multiply(Y, Z).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(X, multiply(inverse(X), multiply(Y, Z)))
% 0.19/0.51 = { by lemma 5 R->L }
% 0.19/0.51 multiply(inverse(X), multiply(X, multiply(Y, Z)))
% 0.19/0.51 = { by lemma 5 R->L }
% 0.19/0.51 multiply(inverse(X), multiply(Y, multiply(X, Z)))
% 0.19/0.51 = { by lemma 8 R->L }
% 0.19/0.51 multiply(multiply(inverse(X), Y), multiply(X, Z))
% 0.19/0.51 = { by lemma 7 R->L }
% 0.19/0.51 multiply(multiply(inverse(X), Y), multiply(X, multiply(inverse(multiply(W, V)), multiply(W, multiply(Z, V)))))
% 0.19/0.51 = { by lemma 4 R->L }
% 0.19/0.51 multiply(multiply(inverse(U), inverse(multiply(W, V))), multiply(Y, multiply(U, multiply(W, multiply(Z, V)))))
% 0.19/0.51 = { by lemma 3 }
% 0.19/0.51 multiply(Y, multiply(inverse(multiply(W, V)), multiply(W, multiply(Z, V))))
% 0.19/0.51 = { by lemma 7 }
% 0.19/0.51 multiply(Y, Z)
% 0.19/0.51
% 0.19/0.51 Lemma 10: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(X, multiply(inverse(X), Y))
% 0.19/0.51 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.51 multiply(X, multiply(inverse(X), multiply(Z, multiply(multiply(inverse(multiply(Z, W)), Y), W))))
% 0.19/0.51 = { by lemma 9 }
% 0.19/0.51 multiply(Z, multiply(multiply(inverse(multiply(Z, W)), Y), W))
% 0.19/0.51 = { by axiom 1 (single_axiom) }
% 0.19/0.51 Y
% 0.19/0.51
% 0.19/0.51 Lemma 11: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.19/0.51 Proof:
% 0.19/0.51 multiply(inverse(X), X)
% 0.19/0.51 = { by lemma 9 R->L }
% 0.19/0.51 multiply(Y, multiply(inverse(Y), multiply(inverse(X), X)))
% 0.19/0.51 = { by lemma 5 R->L }
% 0.19/0.51 multiply(Y, multiply(inverse(X), multiply(inverse(Y), X)))
% 0.19/0.51 = { by lemma 10 R->L }
% 0.19/0.51 multiply(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), X))), multiply(inverse(Y), X)))
% 0.19/0.51 = { by lemma 10 R->L }
% 0.19/0.51 multiply(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), X))), multiply(Y, multiply(inverse(Y), multiply(inverse(Y), X)))))
% 0.19/0.51 = { by lemma 7 }
% 0.19/0.51 multiply(Y, inverse(Y))
% 0.19/0.51
% 0.19/0.51 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4)).
% 0.19/0.51 Proof:
% 0.19/0.51 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.19/0.51 = { by lemma 8 }
% 0.19/0.51 tuple(multiply(inverse(b2), multiply(b2, a2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.19/0.51 = { by lemma 8 }
% 0.19/0.51 tuple(multiply(inverse(b2), multiply(b2, a2)), multiply(a3, multiply(b3, c3)), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.19/0.51 = { by lemma 5 }
% 0.19/0.51 tuple(multiply(b2, multiply(inverse(b2), a2)), multiply(a3, multiply(b3, c3)), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.19/0.51 = { by lemma 10 }
% 0.19/0.51 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.19/0.51 = { by lemma 11 }
% 0.19/0.51 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(a4, b4))
% 0.19/0.51 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.51 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(Y, multiply(multiply(inverse(multiply(Y, Z)), multiply(a4, b4)), Z)))
% 0.19/0.51 = { by lemma 8 R->L }
% 0.19/0.51 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(Y, multiply(multiply(multiply(inverse(multiply(Y, Z)), a4), b4), Z)))
% 0.19/0.51 = { by lemma 7 R->L }
% 0.19/0.51 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(Y, multiply(multiply(multiply(inverse(multiply(Y, Z)), a4), multiply(inverse(multiply(inverse(multiply(Y, Z)), a4)), multiply(inverse(multiply(Y, Z)), multiply(b4, a4)))), Z)))
% 0.19/0.51 = { by lemma 10 }
% 0.19/0.51 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(Y, multiply(multiply(inverse(multiply(Y, Z)), multiply(b4, a4)), Z)))
% 0.19/0.51 = { by axiom 1 (single_axiom) }
% 0.19/0.51 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)), multiply(b4, a4))
% 0.19/0.51 = { by lemma 11 R->L }
% 0.19/0.51 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51
% 0.19/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------