%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP106-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 10:09:16 AM UTC 2026
% Result : Unsatisfiable 0.59s 0.53s
% Output : Proof 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP106-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 09:22:06 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.59/0.53 Command-line arguments: --no-flatten-goal
% 0.59/0.53
% 0.59/0.53 % SZS status Unsatisfiable
% 0.59/0.53
% 0.59/0.59 % SZS output start Proof
% 0.59/0.59 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.59/0.59 Axiom 2 (single_axiom): inverse(double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(Z, Y)))))) = Z.
% 0.59/0.59
% 0.59/0.59 Lemma 3: multiply(multiply(multiply(X, Y), Z), double_divide(Z, X)) = Y.
% 0.59/0.59 Proof:
% 0.59/0.59 multiply(multiply(multiply(X, Y), Z), double_divide(Z, X))
% 0.59/0.59 = { by axiom 1 (multiply) }
% 0.59/0.59 multiply(multiply(inverse(double_divide(Y, X)), Z), double_divide(Z, X))
% 0.59/0.59 = { by axiom 1 (multiply) }
% 0.59/0.59 multiply(inverse(double_divide(Z, inverse(double_divide(Y, X)))), double_divide(Z, X))
% 0.59/0.59 = { by axiom 1 (multiply) }
% 0.59/0.59 inverse(double_divide(double_divide(Z, X), inverse(double_divide(Z, inverse(double_divide(Y, X))))))
% 0.59/0.59 = { by axiom 2 (single_axiom) }
% 0.59/0.59 Y
% 0.59/0.59
% 0.59/0.59 Lemma 4: multiply(X, double_divide(double_divide(Y, Z), multiply(Z, X))) = Y.
% 0.59/0.59 Proof:
% 0.59/0.59 multiply(X, double_divide(double_divide(Y, Z), multiply(Z, X)))
% 0.59/0.59 = { by lemma 3 R->L }
% 0.59/0.59 multiply(multiply(multiply(multiply(Z, X), Y), double_divide(Y, Z)), double_divide(double_divide(Y, Z), multiply(Z, X)))
% 0.59/0.59 = { by lemma 3 }
% 0.59/0.59 Y
% 0.59/0.59
% 0.59/0.59 Lemma 5: multiply(multiply(X, Y), double_divide(Y, Z)) = double_divide(double_divide(X, W), multiply(W, Z)).
% 0.59/0.59 Proof:
% 0.59/0.59 multiply(multiply(X, Y), double_divide(Y, Z))
% 0.59/0.59 = { by lemma 4 R->L }
% 0.59/0.59 multiply(multiply(multiply(Z, double_divide(double_divide(X, W), multiply(W, Z))), Y), double_divide(Y, Z))
% 0.59/0.59 = { by lemma 3 }
% 0.59/0.59 double_divide(double_divide(X, W), multiply(W, Z))
% 0.59/0.59
% 0.59/0.59 Lemma 6: multiply(multiply(W, Y), double_divide(Z, W)) = multiply(multiply(X, Y), double_divide(Z, X)).
% 0.59/0.59 Proof:
% 0.59/0.59 multiply(multiply(W, Y), double_divide(Z, W))
% 0.59/0.59 = { by axiom 1 (multiply) }
% 0.59/0.59 inverse(double_divide(double_divide(Z, W), multiply(W, Y)))
% 0.59/0.59 = { by lemma 3 R->L }
% 0.59/0.59 inverse(multiply(multiply(multiply(Y, double_divide(double_divide(Z, W), multiply(W, Y))), V), double_divide(V, Y)))
% 0.59/0.59 = { by lemma 4 }
% 0.59/0.59 inverse(multiply(multiply(Z, V), double_divide(V, Y)))
% 0.59/0.59 = { by lemma 4 R->L }
% 0.59/0.59 inverse(multiply(multiply(multiply(Y, double_divide(double_divide(Z, X), multiply(X, Y))), V), double_divide(V, Y)))
% 0.59/0.59 = { by lemma 3 }
% 0.59/0.59 inverse(double_divide(double_divide(Z, X), multiply(X, Y)))
% 0.59/0.59 = { by axiom 1 (multiply) R->L }
% 0.59/0.59 multiply(multiply(X, Y), double_divide(Z, X))
% 0.59/0.59
% 0.59/0.59 Lemma 7: double_divide(double_divide(multiply(X, Y), Z), multiply(Z, X)) = Y.
% 0.59/0.59 Proof:
% 0.59/0.59 double_divide(double_divide(multiply(X, Y), Z), multiply(Z, X))
% 0.59/0.59 = { by lemma 5 R->L }
% 0.59/0.59 multiply(multiply(multiply(X, Y), W), double_divide(W, X))
% 0.59/0.59 = { by lemma 3 }
% 0.59/0.59 Y
% 0.59/0.59
% 0.59/0.59 Lemma 8: double_divide(multiply(X, double_divide(Y, multiply(Z, X))), Z) = Y.
% 0.59/0.59 Proof:
% 0.59/0.59 double_divide(multiply(X, double_divide(Y, multiply(Z, X))), Z)
% 0.59/0.59 = { by lemma 4 R->L }
% 0.59/0.59 multiply(W, double_divide(double_divide(double_divide(multiply(X, double_divide(Y, multiply(Z, X))), Z), multiply(Z, X)), multiply(multiply(Z, X), W)))
% 0.59/0.59 = { by lemma 7 }
% 0.59/0.59 multiply(W, double_divide(double_divide(Y, multiply(Z, X)), multiply(multiply(Z, X), W)))
% 0.59/0.59 = { by lemma 4 }
% 0.59/0.59 Y
% 0.59/0.59
% 0.59/0.59 Lemma 9: double_divide(double_divide(X, Y), multiply(Y, X)) = double_divide(Z, inverse(Z)).
% 0.59/0.59 Proof:
% 0.59/0.59 double_divide(double_divide(X, Y), multiply(Y, X))
% 0.59/0.59 = { by lemma 5 R->L }
% 0.59/0.59 multiply(multiply(X, W), double_divide(W, X))
% 0.59/0.59 = { by lemma 6 }
% 0.59/0.59 multiply(multiply(multiply(V, double_divide(Z, multiply(U, V))), W), double_divide(W, multiply(V, double_divide(Z, multiply(U, V)))))
% 0.59/0.59 = { by lemma 5 }
% 0.59/0.59 double_divide(double_divide(multiply(V, double_divide(Z, multiply(U, V))), U), multiply(U, multiply(V, double_divide(Z, multiply(U, V)))))
% 0.59/0.59 = { by axiom 1 (multiply) }
% 0.59/0.59 double_divide(double_divide(multiply(V, double_divide(Z, multiply(U, V))), U), inverse(double_divide(multiply(V, double_divide(Z, multiply(U, V))), U)))
% 0.59/0.59 = { by lemma 8 }
% 0.59/0.59 double_divide(double_divide(multiply(V, double_divide(Z, multiply(U, V))), U), inverse(Z))
% 0.59/0.59 = { by lemma 8 }
% 0.59/0.59 double_divide(Z, inverse(Z))
% 0.59/0.59
% 0.59/0.59 Lemma 10: multiply(multiply(inverse(X), Y), X) = Y.
% 0.59/0.59 Proof:
% 0.59/0.59 multiply(multiply(inverse(X), Y), X)
% 0.59/0.59 = { by lemma 4 R->L }
% 0.59/0.59 multiply(multiply(multiply(inverse(X), Y), X), double_divide(double_divide(multiply(multiply(inverse(X), Y), X), Z), multiply(Z, multiply(multiply(inverse(X), Y), X))))
% 0.59/0.59 = { by lemma 9 }
% 0.59/0.59 multiply(multiply(multiply(inverse(X), Y), X), double_divide(X, inverse(X)))
% 0.59/0.59 = { by lemma 3 }
% 0.59/0.59 Y
% 0.59/0.59
% 0.59/0.59 Lemma 11: double_divide(double_divide(X, Y), multiply(Y, multiply(multiply(Z, X), W))) = double_divide(W, Z).
% 0.59/0.59 Proof:
% 0.59/0.59 double_divide(double_divide(X, Y), multiply(Y, multiply(multiply(Z, X), W)))
% 0.59/0.59 = { by lemma 5 R->L }
% 0.59/0.59 multiply(multiply(X, V), double_divide(V, multiply(multiply(Z, X), W)))
% 0.59/0.59 = { by lemma 3 R->L }
% 0.59/0.59 multiply(multiply(multiply(multiply(multiply(Z, X), W), double_divide(W, Z)), V), double_divide(V, multiply(multiply(Z, X), W)))
% 0.59/0.59 = { by lemma 3 }
% 0.59/0.59 double_divide(W, Z)
% 0.59/0.59
% 0.59/0.59 Lemma 12: double_divide(double_divide(X, Y), Y) = X.
% 0.59/0.59 Proof:
% 0.59/0.59 double_divide(double_divide(X, Y), Y)
% 0.59/0.59 = { by lemma 10 R->L }
% 0.59/0.59 double_divide(double_divide(multiply(multiply(inverse(Z), X), Z), Y), Y)
% 0.59/0.59 = { by lemma 11 R->L }
% 0.59/0.59 double_divide(double_divide(multiply(inverse(Z), X), W), multiply(W, multiply(multiply(Y, multiply(inverse(Z), X)), double_divide(multiply(multiply(inverse(Z), X), Z), Y))))
% 0.59/0.59 = { by axiom 1 (multiply) }
% 0.59/0.59 double_divide(double_divide(multiply(inverse(Z), X), W), multiply(W, inverse(double_divide(double_divide(multiply(multiply(inverse(Z), X), Z), Y), multiply(Y, multiply(inverse(Z), X))))))
% 0.59/0.59 = { by lemma 7 }
% 0.59/0.59 double_divide(double_divide(multiply(inverse(Z), X), W), multiply(W, inverse(Z)))
% 0.59/0.59 = { by lemma 7 }
% 0.59/0.59 X
% 0.59/0.59
% 0.59/0.59 Lemma 13: multiply(X, double_divide(Y, X)) = inverse(Y).
% 0.59/0.59 Proof:
% 0.59/0.59 multiply(X, double_divide(Y, X))
% 0.59/0.59 = { by axiom 1 (multiply) }
% 0.59/0.59 inverse(double_divide(double_divide(Y, X), X))
% 0.59/0.59 = { by lemma 12 }
% 0.59/0.59 inverse(Y)
% 0.59/0.60
% 0.59/0.60 Lemma 14: multiply(inverse(X), Y) = double_divide(X, inverse(Y)).
% 0.59/0.60 Proof:
% 0.59/0.60 multiply(inverse(X), Y)
% 0.59/0.60 = { by lemma 13 R->L }
% 0.59/0.60 multiply(multiply(inverse(Y), double_divide(X, inverse(Y))), Y)
% 0.59/0.60 = { by lemma 10 }
% 0.59/0.60 double_divide(X, inverse(Y))
% 0.59/0.60
% 0.59/0.60 Lemma 15: double_divide(X, double_divide(X, inverse(Y))) = inverse(Y).
% 0.59/0.60 Proof:
% 0.59/0.60 double_divide(X, double_divide(X, inverse(Y)))
% 0.59/0.60 = { by lemma 14 R->L }
% 0.59/0.60 double_divide(X, multiply(inverse(X), Y))
% 0.59/0.60 = { by axiom 1 (multiply) }
% 0.59/0.60 double_divide(X, inverse(double_divide(Y, inverse(X))))
% 0.59/0.60 = { by lemma 14 R->L }
% 0.59/0.60 multiply(inverse(X), double_divide(Y, inverse(X)))
% 0.59/0.60 = { by lemma 13 }
% 0.59/0.60 inverse(Y)
% 0.59/0.60
% 0.59/0.60 Lemma 16: multiply(double_divide(X, inverse(Y)), X) = Y.
% 0.59/0.60 Proof:
% 0.59/0.60 multiply(double_divide(X, inverse(Y)), X)
% 0.59/0.60 = { by lemma 14 R->L }
% 0.59/0.60 multiply(multiply(inverse(X), Y), X)
% 0.59/0.60 = { by lemma 10 }
% 0.59/0.60 Y
% 0.59/0.60
% 0.59/0.60 Lemma 17: inverse(inverse(X)) = X.
% 0.59/0.60 Proof:
% 0.59/0.60 inverse(inverse(X))
% 0.59/0.60 = { by lemma 15 R->L }
% 0.59/0.60 inverse(double_divide(Y, double_divide(Y, inverse(X))))
% 0.59/0.60 = { by axiom 1 (multiply) R->L }
% 0.59/0.60 multiply(double_divide(Y, inverse(X)), Y)
% 0.59/0.60 = { by lemma 16 }
% 0.59/0.60 X
% 0.59/0.60
% 0.59/0.60 Lemma 18: double_divide(Y, X) = double_divide(X, Y).
% 0.59/0.60 Proof:
% 0.59/0.60 double_divide(Y, X)
% 0.59/0.60 = { by lemma 12 R->L }
% 0.59/0.60 double_divide(Y, double_divide(double_divide(X, V), V))
% 0.59/0.60 = { by lemma 11 R->L }
% 0.59/0.60 double_divide(Y, double_divide(double_divide(Z, W), multiply(W, multiply(multiply(V, Z), double_divide(X, V)))))
% 0.59/0.60 = { by lemma 6 }
% 0.59/0.60 double_divide(Y, double_divide(double_divide(Z, W), multiply(W, multiply(multiply(Y, Z), double_divide(X, Y)))))
% 0.59/0.60 = { by lemma 11 }
% 0.59/0.60 double_divide(Y, double_divide(double_divide(X, Y), Y))
% 0.59/0.60 = { by lemma 17 R->L }
% 0.59/0.60 double_divide(Y, double_divide(double_divide(X, Y), inverse(inverse(Y))))
% 0.59/0.60 = { by lemma 14 R->L }
% 0.59/0.60 double_divide(Y, multiply(inverse(double_divide(X, Y)), inverse(Y)))
% 0.59/0.60 = { by axiom 1 (multiply) }
% 0.59/0.60 double_divide(Y, inverse(double_divide(inverse(Y), inverse(double_divide(X, Y)))))
% 0.59/0.60 = { by lemma 14 R->L }
% 0.59/0.60 multiply(inverse(Y), double_divide(inverse(Y), inverse(double_divide(X, Y))))
% 0.59/0.60 = { by lemma 12 R->L }
% 0.59/0.60 multiply(double_divide(double_divide(inverse(Y), inverse(double_divide(X, Y))), inverse(double_divide(X, Y))), double_divide(inverse(Y), inverse(double_divide(X, Y))))
% 0.59/0.60 = { by lemma 16 }
% 0.59/0.60 double_divide(X, Y)
% 0.59/0.60
% 0.59/0.60 Lemma 19: multiply(X, Y) = double_divide(inverse(X), inverse(Y)).
% 0.59/0.60 Proof:
% 0.59/0.60 multiply(X, Y)
% 0.59/0.60 = { by lemma 17 R->L }
% 0.59/0.60 multiply(inverse(inverse(X)), Y)
% 0.59/0.60 = { by lemma 14 }
% 0.59/0.60 double_divide(inverse(X), inverse(Y))
% 0.59/0.60
% 0.59/0.60 Lemma 20: inverse(double_divide(X, Y)) = multiply(X, Y).
% 0.59/0.60 Proof:
% 0.59/0.60 inverse(double_divide(X, Y))
% 0.59/0.60 = { by lemma 18 }
% 0.59/0.60 inverse(double_divide(Y, X))
% 0.59/0.60 = { by axiom 1 (multiply) R->L }
% 0.59/0.60 multiply(X, Y)
% 0.59/0.60
% 0.59/0.60 Lemma 21: multiply(Y, X) = multiply(X, Y).
% 0.59/0.60 Proof:
% 0.59/0.60 multiply(Y, X)
% 0.59/0.60 = { by lemma 20 R->L }
% 0.59/0.60 inverse(double_divide(Y, X))
% 0.59/0.60 = { by axiom 1 (multiply) R->L }
% 0.59/0.60 multiply(X, Y)
% 0.59/0.60
% 0.59/0.60 Lemma 22: inverse(multiply(X, Y)) = double_divide(X, Y).
% 0.59/0.60 Proof:
% 0.59/0.60 inverse(multiply(X, Y))
% 0.59/0.60 = { by lemma 21 }
% 0.59/0.60 inverse(multiply(Y, X))
% 0.59/0.60 = { by lemma 20 R->L }
% 0.59/0.60 inverse(inverse(double_divide(Y, X)))
% 0.59/0.60 = { by lemma 17 }
% 0.59/0.60 double_divide(Y, X)
% 0.59/0.60 = { by lemma 18 R->L }
% 0.59/0.60 double_divide(X, Y)
% 0.59/0.60
% 0.59/0.60 Lemma 23: multiply(inverse(X), X) = double_divide(Y, inverse(Y)).
% 0.59/0.60 Proof:
% 0.59/0.60 multiply(inverse(X), X)
% 0.59/0.60 = { by axiom 1 (multiply) }
% 0.59/0.60 inverse(double_divide(X, inverse(X)))
% 0.59/0.60 = { by lemma 9 R->L }
% 0.59/0.60 inverse(double_divide(double_divide(Z, W), multiply(W, Z)))
% 0.59/0.60 = { by axiom 1 (multiply) R->L }
% 0.59/0.60 multiply(multiply(W, Z), double_divide(Z, W))
% 0.59/0.60 = { by lemma 5 }
% 0.59/0.60 double_divide(double_divide(W, V), multiply(V, W))
% 0.59/0.60 = { by lemma 9 }
% 0.59/0.60 double_divide(Y, inverse(Y))
% 0.59/0.60
% 0.59/0.60 Lemma 24: double_divide(double_divide(X, Y), double_divide(inverse(X), double_divide(Y, Z))) = inverse(Z).
% 0.59/0.60 Proof:
% 0.59/0.60 double_divide(double_divide(X, Y), double_divide(inverse(X), double_divide(Y, Z)))
% 0.59/0.60 = { by lemma 18 }
% 0.59/0.60 double_divide(double_divide(Y, X), double_divide(inverse(X), double_divide(Y, Z)))
% 0.59/0.60 = { by lemma 22 R->L }
% 0.59/0.60 double_divide(double_divide(Y, X), double_divide(inverse(X), inverse(multiply(Y, Z))))
% 0.59/0.60 = { by lemma 19 R->L }
% 0.59/0.60 double_divide(double_divide(Y, X), multiply(X, multiply(Y, Z)))
% 0.59/0.60 = { by lemma 5 R->L }
% 0.59/0.60 multiply(multiply(Y, Z), double_divide(Z, multiply(Y, Z)))
% 0.59/0.60 = { by lemma 13 }
% 0.59/0.60 inverse(Z)
% 0.59/0.60
% 0.59/0.60 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4)).
% 0.59/0.60 Proof:
% 0.59/0.60 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.59/0.60 = { by lemma 23 }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.59/0.60 = { by lemma 23 }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), multiply(double_divide(Y, inverse(Y)), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.59/0.60 = { by lemma 23 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), multiply(multiply(inverse(a2), a2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.59/0.60 = { by lemma 10 }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.59/0.60 = { by lemma 21 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.59/0.60 = { by lemma 19 }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), inverse(multiply(a3, b3))), multiply(a4, b4))
% 0.59/0.60 = { by lemma 22 }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), double_divide(a3, b3)), multiply(a4, b4))
% 0.59/0.60 = { by lemma 19 }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), double_divide(a3, b3)), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.60 = { by lemma 17 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), double_divide(a3, inverse(inverse(b3)))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.60 = { by lemma 14 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), multiply(inverse(a3), inverse(b3))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.60 = { by lemma 20 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), inverse(double_divide(inverse(a3), inverse(b3)))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.60 = { by lemma 19 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, multiply(c3, double_divide(inverse(a3), inverse(b3))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.60 = { by lemma 20 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(c3, double_divide(inverse(a3), inverse(b3)))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.60 = { by lemma 19 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(c3, multiply(a3, b3))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.60 = { by lemma 20 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(c3, inverse(double_divide(a3, b3)))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.60 = { by lemma 14 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, inverse(multiply(inverse(c3), double_divide(a3, b3))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.60 = { by lemma 20 R->L }
% 0.59/0.60 tuple(double_divide(X, inverse(X)), a2, inverse(inverse(double_divide(inverse(c3), double_divide(a3, b3)))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.60 = { by lemma 24 R->L }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(double_divide(c3, double_divide(c3, a3)), double_divide(inverse(c3), double_divide(double_divide(c3, a3), double_divide(inverse(c3), double_divide(a3, b3)))))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 24 }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(double_divide(c3, double_divide(c3, a3)), double_divide(inverse(c3), inverse(b3)))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 17 R->L }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(double_divide(c3, double_divide(c3, inverse(inverse(a3)))), double_divide(inverse(c3), inverse(b3)))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 15 }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(inverse(inverse(a3)), double_divide(inverse(c3), inverse(b3)))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 17 }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(a3, double_divide(inverse(c3), inverse(b3)))), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by axiom 1 (multiply) R->L }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, multiply(double_divide(inverse(c3), inverse(b3)), a3), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 19 }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(double_divide(inverse(c3), inverse(b3))), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 20 }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, double_divide(multiply(inverse(c3), inverse(b3)), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 14 }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, double_divide(double_divide(c3, inverse(inverse(b3))), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 17 }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, double_divide(double_divide(c3, b3), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 18 R->L }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), double_divide(c3, b3)), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 18 R->L }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), double_divide(b3, c3)), double_divide(inverse(a4), inverse(b4)))
% 0.59/0.61 = { by lemma 19 R->L }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.59/0.61 = { by lemma 22 R->L }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), inverse(multiply(b3, c3))), multiply(a4, b4))
% 0.59/0.61 = { by lemma 19 R->L }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.59/0.61 = { by lemma 21 }
% 0.59/0.61 tuple(double_divide(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.59/0.61 = { by lemma 23 R->L }
% 0.59/0.61 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.59/0.61 % SZS output end Proof
% 0.59/0.61
% 0.59/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------