TSTP Solution File: GRP105-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP105-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:17:00 EDT 2023
% Result : Unsatisfiable 0.17s 0.43s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP105-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.32 % Computer : n008.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon Aug 28 21:12:17 EDT 2023
% 0.15/0.33 % CPUTime :
% 0.17/0.43 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.17/0.43
% 0.17/0.43 % SZS status Unsatisfiable
% 0.17/0.43
% 0.17/0.46 % SZS output start Proof
% 0.17/0.46 Take the following subset of the input axioms:
% 0.17/0.46 fof(multiply, axiom, ![X, Y]: multiply(X, Y)=inverse(double_divide(Y, X))).
% 0.17/0.46 fof(prove_these_axioms, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1) | (multiply(multiply(inverse(b2), b2), a2)!=a2 | (multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3)) | multiply(a4, b4)!=multiply(b4, a4)))).
% 0.17/0.46 fof(single_axiom, axiom, ![Z, X2, Y2]: double_divide(inverse(double_divide(double_divide(X2, Y2), inverse(double_divide(X2, inverse(Z))))), Y2)=Z).
% 0.17/0.46
% 0.17/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.17/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.17/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.17/0.46 fresh(y, y, x1...xn) = u
% 0.17/0.46 C => fresh(s, t, x1...xn) = v
% 0.17/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.17/0.46 variables of u and v.
% 0.17/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.17/0.46 input problem has no model of domain size 1).
% 0.17/0.46
% 0.17/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.17/0.46
% 0.17/0.46 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.17/0.46 Axiom 2 (single_axiom): double_divide(inverse(double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(Z))))), Y) = Z.
% 0.17/0.46
% 0.17/0.46 Lemma 3: double_divide(multiply(multiply(inverse(X), Y), double_divide(Y, Z)), Z) = X.
% 0.17/0.46 Proof:
% 0.17/0.47 double_divide(multiply(multiply(inverse(X), Y), double_divide(Y, Z)), Z)
% 0.17/0.47 = { by axiom 1 (multiply) }
% 0.17/0.47 double_divide(multiply(inverse(double_divide(Y, inverse(X))), double_divide(Y, Z)), Z)
% 0.17/0.47 = { by axiom 1 (multiply) }
% 0.17/0.47 double_divide(inverse(double_divide(double_divide(Y, Z), inverse(double_divide(Y, inverse(X))))), Z)
% 0.17/0.47 = { by axiom 2 (single_axiom) }
% 0.17/0.47 X
% 0.17/0.47
% 0.17/0.47 Lemma 4: multiply(X, multiply(multiply(inverse(Y), Z), double_divide(Z, X))) = inverse(Y).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(X, multiply(multiply(inverse(Y), Z), double_divide(Z, X)))
% 0.17/0.47 = { by axiom 1 (multiply) }
% 0.17/0.47 inverse(double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, X)), X))
% 0.17/0.47 = { by lemma 3 }
% 0.17/0.47 inverse(Y)
% 0.17/0.47
% 0.17/0.47 Lemma 5: double_divide(multiply(inverse(X), X), inverse(Y)) = Y.
% 0.17/0.47 Proof:
% 0.17/0.47 double_divide(multiply(inverse(X), X), inverse(Y))
% 0.17/0.47 = { by lemma 3 R->L }
% 0.17/0.47 double_divide(multiply(inverse(X), double_divide(multiply(multiply(inverse(X), Z), double_divide(Z, inverse(Y))), inverse(Y))), inverse(Y))
% 0.17/0.47 = { by lemma 4 R->L }
% 0.17/0.47 double_divide(multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), double_divide(Z, inverse(Y)))), double_divide(multiply(multiply(inverse(X), Z), double_divide(Z, inverse(Y))), inverse(Y))), inverse(Y))
% 0.17/0.47 = { by lemma 3 }
% 0.17/0.47 Y
% 0.17/0.47
% 0.17/0.47 Lemma 6: multiply(inverse(X), multiply(inverse(Y), Y)) = inverse(X).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(inverse(X), multiply(inverse(Y), Y))
% 0.17/0.47 = { by axiom 1 (multiply) }
% 0.17/0.47 inverse(double_divide(multiply(inverse(Y), Y), inverse(X)))
% 0.17/0.47 = { by lemma 5 }
% 0.17/0.47 inverse(X)
% 0.17/0.47
% 0.17/0.47 Lemma 7: multiply(inverse(X), inverse(multiply(inverse(Y), Y))) = inverse(X).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(inverse(X), inverse(multiply(inverse(Y), Y)))
% 0.17/0.47 = { by lemma 6 R->L }
% 0.17/0.47 multiply(inverse(X), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y)))
% 0.17/0.47 = { by lemma 6 }
% 0.17/0.47 inverse(X)
% 0.17/0.47
% 0.17/0.47 Lemma 8: double_divide(inverse(multiply(inverse(X), X)), inverse(Y)) = Y.
% 0.17/0.47 Proof:
% 0.17/0.47 double_divide(inverse(multiply(inverse(X), X)), inverse(Y))
% 0.17/0.47 = { by lemma 6 R->L }
% 0.17/0.47 double_divide(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)), inverse(Y))
% 0.17/0.47 = { by lemma 5 }
% 0.17/0.47 Y
% 0.17/0.47
% 0.17/0.47 Lemma 9: multiply(inverse(X), multiply(inverse(Y), X)) = inverse(Y).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(inverse(X), multiply(inverse(Y), X))
% 0.17/0.47 = { by lemma 7 R->L }
% 0.17/0.47 multiply(inverse(X), multiply(multiply(inverse(Y), inverse(multiply(inverse(Z), Z))), X))
% 0.17/0.47 = { by lemma 8 R->L }
% 0.17/0.47 multiply(inverse(X), multiply(multiply(inverse(Y), inverse(multiply(inverse(Z), Z))), double_divide(inverse(multiply(inverse(Z), Z)), inverse(X))))
% 0.17/0.47 = { by lemma 4 }
% 0.17/0.47 inverse(Y)
% 0.17/0.47
% 0.17/0.47 Lemma 10: multiply(inverse(multiply(inverse(X), Y)), inverse(X)) = inverse(Y).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(inverse(multiply(inverse(X), Y)), inverse(X))
% 0.17/0.47 = { by lemma 9 R->L }
% 0.17/0.47 multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), multiply(inverse(X), Y)))
% 0.17/0.47 = { by lemma 9 }
% 0.17/0.47 inverse(Y)
% 0.17/0.47
% 0.17/0.47 Lemma 11: multiply(inverse(multiply(multiply(X, Y), Z)), multiply(X, Y)) = inverse(Z).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(inverse(multiply(multiply(X, Y), Z)), multiply(X, Y))
% 0.17/0.47 = { by axiom 1 (multiply) }
% 0.17/0.47 multiply(inverse(multiply(multiply(X, Y), Z)), inverse(double_divide(Y, X)))
% 0.17/0.47 = { by axiom 1 (multiply) }
% 0.17/0.47 multiply(inverse(multiply(inverse(double_divide(Y, X)), Z)), inverse(double_divide(Y, X)))
% 0.17/0.47 = { by lemma 10 }
% 0.17/0.47 inverse(Z)
% 0.17/0.47
% 0.17/0.47 Lemma 12: inverse(multiply(multiply(inverse(X), X), Y)) = inverse(Y).
% 0.17/0.47 Proof:
% 0.17/0.47 inverse(multiply(multiply(inverse(X), X), Y))
% 0.17/0.47 = { by lemma 6 R->L }
% 0.17/0.47 multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(inverse(X), X))
% 0.17/0.47 = { by lemma 11 }
% 0.17/0.47 inverse(Y)
% 0.17/0.47
% 0.17/0.47 Lemma 13: multiply(inverse(multiply(X, Y)), inverse(Z)) = inverse(multiply(multiply(X, Y), Z)).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(inverse(multiply(X, Y)), inverse(Z))
% 0.17/0.47 = { by lemma 11 R->L }
% 0.17/0.47 multiply(inverse(multiply(X, Y)), multiply(inverse(multiply(multiply(X, Y), Z)), multiply(X, Y)))
% 0.17/0.47 = { by lemma 9 }
% 0.17/0.47 inverse(multiply(multiply(X, Y), Z))
% 0.17/0.47
% 0.17/0.47 Lemma 14: multiply(multiply(inverse(X), X), Y) = Y.
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(multiply(inverse(X), X), Y)
% 0.17/0.47 = { by lemma 3 R->L }
% 0.17/0.47 double_divide(multiply(multiply(inverse(multiply(multiply(inverse(X), X), Y)), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 12 }
% 0.17/0.47 double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 3 }
% 0.17/0.47 Y
% 0.17/0.47
% 0.17/0.47 Lemma 15: multiply(inverse(X), inverse(Y)) = inverse(multiply(X, Y)).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(inverse(X), inverse(Y))
% 0.17/0.47 = { by lemma 12 R->L }
% 0.17/0.47 multiply(inverse(multiply(multiply(inverse(Z), Z), X)), inverse(Y))
% 0.17/0.47 = { by lemma 13 }
% 0.17/0.47 inverse(multiply(multiply(multiply(inverse(Z), Z), X), Y))
% 0.17/0.47 = { by lemma 14 }
% 0.17/0.47 inverse(multiply(X, Y))
% 0.17/0.47
% 0.17/0.47 Lemma 16: multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(multiply(Z, X)), Y)) = inverse(Z).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(multiply(Z, X)), Y))
% 0.17/0.47 = { by lemma 15 R->L }
% 0.17/0.47 multiply(inverse(multiply(inverse(X), Y)), multiply(multiply(inverse(Z), inverse(X)), Y))
% 0.17/0.47 = { by lemma 3 R->L }
% 0.17/0.47 multiply(inverse(multiply(inverse(X), Y)), multiply(multiply(inverse(Z), inverse(X)), double_divide(multiply(multiply(inverse(Y), inverse(multiply(inverse(W), W))), double_divide(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(X), Y)))), inverse(multiply(inverse(X), Y)))))
% 0.17/0.47 = { by lemma 8 }
% 0.17/0.47 multiply(inverse(multiply(inverse(X), Y)), multiply(multiply(inverse(Z), inverse(X)), double_divide(multiply(multiply(inverse(Y), inverse(multiply(inverse(W), W))), multiply(inverse(X), Y)), inverse(multiply(inverse(X), Y)))))
% 0.17/0.47 = { by lemma 7 }
% 0.17/0.47 multiply(inverse(multiply(inverse(X), Y)), multiply(multiply(inverse(Z), inverse(X)), double_divide(multiply(inverse(Y), multiply(inverse(X), Y)), inverse(multiply(inverse(X), Y)))))
% 0.17/0.47 = { by lemma 9 }
% 0.17/0.47 multiply(inverse(multiply(inverse(X), Y)), multiply(multiply(inverse(Z), inverse(X)), double_divide(inverse(X), inverse(multiply(inverse(X), Y)))))
% 0.17/0.47 = { by lemma 4 }
% 0.17/0.47 inverse(Z)
% 0.17/0.47
% 0.17/0.47 Lemma 17: multiply(multiply(X, Y), multiply(inverse(Z), Z)) = multiply(X, Y).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(multiply(X, Y), multiply(inverse(Z), Z))
% 0.17/0.47 = { by axiom 1 (multiply) }
% 0.17/0.47 multiply(inverse(double_divide(Y, X)), multiply(inverse(Z), Z))
% 0.17/0.47 = { by lemma 6 }
% 0.17/0.47 inverse(double_divide(Y, X))
% 0.17/0.47 = { by axiom 1 (multiply) R->L }
% 0.17/0.47 multiply(X, Y)
% 0.17/0.47
% 0.17/0.47 Lemma 18: multiply(Y, X) = multiply(X, Y).
% 0.17/0.47 Proof:
% 0.17/0.47 multiply(Y, X)
% 0.17/0.47 = { by lemma 3 R->L }
% 0.17/0.47 double_divide(multiply(multiply(inverse(multiply(Y, X)), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 15 R->L }
% 0.17/0.47 double_divide(multiply(multiply(multiply(inverse(Y), inverse(X)), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 16 R->L }
% 0.17/0.47 double_divide(multiply(multiply(multiply(inverse(Y), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(multiply(X, Y)), Y))), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 11 R->L }
% 0.17/0.47 double_divide(multiply(multiply(multiply(inverse(Y), multiply(multiply(inverse(multiply(multiply(multiply(inverse(U), U), V), multiply(inverse(Y), Y))), multiply(multiply(inverse(U), U), V)), multiply(inverse(multiply(X, Y)), Y))), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 17 }
% 0.17/0.47 double_divide(multiply(multiply(multiply(inverse(Y), multiply(multiply(inverse(multiply(multiply(inverse(U), U), V)), multiply(multiply(inverse(U), U), V)), multiply(inverse(multiply(X, Y)), Y))), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 12 }
% 0.17/0.47 double_divide(multiply(multiply(multiply(inverse(Y), multiply(multiply(inverse(V), multiply(multiply(inverse(U), U), V)), multiply(inverse(multiply(X, Y)), Y))), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 14 }
% 0.17/0.47 double_divide(multiply(multiply(multiply(inverse(Y), multiply(multiply(inverse(V), V), multiply(inverse(multiply(X, Y)), Y))), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 14 }
% 0.17/0.47 double_divide(multiply(multiply(multiply(inverse(Y), multiply(inverse(multiply(X, Y)), Y)), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 9 }
% 0.17/0.47 double_divide(multiply(multiply(inverse(multiply(X, Y)), Z), double_divide(Z, W)), W)
% 0.17/0.47 = { by lemma 3 }
% 0.17/0.48 multiply(X, Y)
% 0.17/0.48
% 0.17/0.48 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)).
% 0.17/0.48 Proof:
% 0.17/0.48 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.17/0.48 = { by lemma 14 }
% 0.17/0.48 tuple(multiply(inverse(a1), a1), a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.17/0.48 = { by lemma 18 R->L }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.17/0.48 = { by lemma 18 R->L }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.17/0.48 = { by lemma 3 R->L }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(inverse(multiply(c3, multiply(a3, b3))), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 15 R->L }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(multiply(inverse(c3), inverse(multiply(a3, b3))), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 18 }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(multiply(inverse(multiply(a3, b3)), inverse(c3)), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 3 R->L }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(double_divide(multiply(multiply(inverse(multiply(inverse(multiply(a3, b3)), inverse(c3))), Z), double_divide(Z, W)), W), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 10 R->L }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(double_divide(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(b3), inverse(c3))), multiply(inverse(multiply(a3, b3)), inverse(c3)))), inverse(multiply(inverse(b3), inverse(c3)))), Z), double_divide(Z, W)), W), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 13 }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(double_divide(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(b3), inverse(c3))), multiply(inverse(multiply(a3, b3)), inverse(c3))), multiply(inverse(b3), inverse(c3)))), Z), double_divide(Z, W)), W), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 3 }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(multiply(multiply(inverse(multiply(inverse(b3), inverse(c3))), multiply(inverse(multiply(a3, b3)), inverse(c3))), multiply(inverse(b3), inverse(c3))), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 16 }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(multiply(inverse(a3), multiply(inverse(b3), inverse(c3))), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 18 R->L }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(multiply(inverse(a3), multiply(inverse(c3), inverse(b3))), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 15 }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(multiply(inverse(a3), inverse(multiply(c3, b3))), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 15 }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, double_divide(multiply(multiply(inverse(multiply(a3, multiply(c3, b3))), X), double_divide(X, Y)), Y), multiply(a4, b4))
% 0.17/0.48 = { by lemma 3 }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, multiply(a3, multiply(c3, b3)), multiply(a4, b4))
% 0.17/0.48 = { by lemma 18 R->L }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.17/0.48 = { by lemma 18 }
% 0.17/0.48 tuple(multiply(a1, inverse(a1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.17/0.48 = { by lemma 18 }
% 0.17/0.48 tuple(multiply(inverse(a1), a1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.17/0.48 = { by lemma 3 R->L }
% 0.17/0.48 tuple(double_divide(multiply(multiply(inverse(multiply(inverse(a1), a1)), V), double_divide(V, U)), U), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.17/0.48 = { by lemma 11 R->L }
% 0.17/0.48 tuple(double_divide(multiply(multiply(multiply(inverse(multiply(multiply(T, S), multiply(inverse(a1), a1))), multiply(T, S)), V), double_divide(V, U)), U), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.17/0.48 = { by lemma 17 }
% 0.17/0.48 tuple(double_divide(multiply(multiply(multiply(inverse(multiply(T, S)), multiply(T, S)), V), double_divide(V, U)), U), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.17/0.48 = { by lemma 17 R->L }
% 0.17/0.48 tuple(double_divide(multiply(multiply(multiply(inverse(multiply(multiply(T, S), multiply(inverse(b1), b1))), multiply(T, S)), V), double_divide(V, U)), U), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.17/0.48 = { by lemma 11 }
% 0.17/0.48 tuple(double_divide(multiply(multiply(inverse(multiply(inverse(b1), b1)), V), double_divide(V, U)), U), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.17/0.48 = { by lemma 3 }
% 0.17/0.48 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.17/0.48 % SZS output end Proof
% 0.17/0.48
% 0.17/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------