TSTP Solution File: GRP107-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP107-1 : 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 : n002.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 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP107-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:55:34 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Command-line arguments: --no-flatten-goal
% 0.19/0.47
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 Take the following subset of the input axioms:
% 0.19/0.49 fof(multiply, axiom, ![X, Y]: multiply(X, Y)=inverse(double_divide(Y, X))).
% 0.19/0.49 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)))).
% 0.19/0.49 fof(single_axiom, axiom, ![Z, X2, Y2]: double_divide(double_divide(X2, Y2), inverse(double_divide(X2, inverse(double_divide(inverse(Z), Y2)))))=Z).
% 0.19/0.49
% 0.19/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.49 fresh(y, y, x1...xn) = u
% 0.19/0.49 C => fresh(s, t, x1...xn) = v
% 0.19/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.49 variables of u and v.
% 0.19/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.49 input problem has no model of domain size 1).
% 0.19/0.49
% 0.19/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.49
% 0.19/0.49 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.19/0.49 Axiom 2 (single_axiom): double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y))))) = Z.
% 0.19/0.49
% 0.19/0.49 Lemma 3: double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X)) = Z.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X))
% 0.19/0.49 = { by axiom 1 (multiply) }
% 0.19/0.49 double_divide(double_divide(X, Y), multiply(inverse(double_divide(inverse(Z), Y)), X))
% 0.19/0.49 = { by axiom 1 (multiply) }
% 0.19/0.49 double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y)))))
% 0.19/0.49 = { by axiom 2 (single_axiom) }
% 0.19/0.49 Z
% 0.19/0.49
% 0.19/0.49 Lemma 4: multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X)) = inverse(Y).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X))
% 0.19/0.49 = { by axiom 1 (multiply) }
% 0.19/0.49 inverse(double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.19/0.49 = { by lemma 3 }
% 0.19/0.49 inverse(Y)
% 0.19/0.49
% 0.19/0.49 Lemma 5: multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y) = inverse(W).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y)
% 0.19/0.49 = { by lemma 3 R->L }
% 0.19/0.49 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.19/0.49 = { by lemma 4 }
% 0.19/0.49 inverse(W)
% 0.19/0.49
% 0.19/0.49 Lemma 6: multiply(multiply(inverse(X), inverse(Y)), X) = inverse(Y).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(multiply(inverse(X), inverse(Y)), X)
% 0.19/0.49 = { by lemma 3 R->L }
% 0.19/0.49 multiply(multiply(inverse(X), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))), X)
% 0.19/0.49 = { by lemma 5 R->L }
% 0.19/0.49 multiply(multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))), X)
% 0.19/0.49 = { by lemma 5 }
% 0.19/0.49 inverse(Y)
% 0.19/0.49
% 0.19/0.49 Lemma 7: double_divide(double_divide(X, inverse(X)), multiply(Y, Z)) = double_divide(Z, Y).
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(double_divide(X, inverse(X)), multiply(Y, Z))
% 0.19/0.49 = { by axiom 1 (multiply) }
% 0.19/0.49 double_divide(double_divide(X, inverse(X)), inverse(double_divide(Z, Y)))
% 0.19/0.49 = { by lemma 6 R->L }
% 0.19/0.49 double_divide(double_divide(X, inverse(X)), multiply(multiply(inverse(X), inverse(double_divide(Z, Y))), X))
% 0.19/0.49 = { by lemma 3 }
% 0.19/0.49 double_divide(Z, Y)
% 0.19/0.49
% 0.19/0.49 Lemma 8: double_divide(X, multiply(inverse(X), inverse(Y))) = Y.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(X, multiply(inverse(X), inverse(Y)))
% 0.19/0.49 = { by lemma 3 R->L }
% 0.19/0.49 double_divide(X, multiply(inverse(X), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))))
% 0.19/0.49 = { by lemma 5 R->L }
% 0.19/0.49 double_divide(X, multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))))
% 0.19/0.49 = { by lemma 3 R->L }
% 0.19/0.49 double_divide(double_divide(double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z)), multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W))), multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))))
% 0.19/0.49 = { by lemma 3 }
% 0.19/0.49 Y
% 0.19/0.49
% 0.19/0.49 Lemma 9: double_divide(inverse(X), multiply(inverse(Y), Y)) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(inverse(X), multiply(inverse(Y), Y))
% 0.19/0.49 = { by axiom 1 (multiply) }
% 0.19/0.49 double_divide(inverse(X), inverse(double_divide(Y, inverse(Y))))
% 0.19/0.49 = { by lemma 7 R->L }
% 0.19/0.49 double_divide(double_divide(Y, inverse(Y)), multiply(inverse(double_divide(Y, inverse(Y))), inverse(X)))
% 0.19/0.49 = { by lemma 8 }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 10: multiply(inverse(X), double_divide(Y, inverse(Y))) = inverse(X).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(X), double_divide(Y, inverse(Y)))
% 0.19/0.49 = { by lemma 6 R->L }
% 0.19/0.49 multiply(multiply(multiply(inverse(Y), inverse(X)), Y), double_divide(Y, inverse(Y)))
% 0.19/0.49 = { by lemma 4 }
% 0.19/0.49 inverse(X)
% 0.19/0.49
% 0.19/0.49 Lemma 11: multiply(multiply(inverse(X), X), inverse(Y)) = inverse(Y).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(multiply(inverse(X), X), inverse(Y))
% 0.19/0.49 = { by axiom 1 (multiply) }
% 0.19/0.49 multiply(inverse(double_divide(X, inverse(X))), inverse(Y))
% 0.19/0.49 = { by axiom 1 (multiply) }
% 0.19/0.49 inverse(double_divide(inverse(Y), inverse(double_divide(X, inverse(X)))))
% 0.19/0.49 = { by lemma 10 R->L }
% 0.19/0.49 multiply(inverse(double_divide(inverse(Y), inverse(double_divide(X, inverse(X))))), double_divide(X, inverse(X)))
% 0.19/0.49 = { by axiom 1 (multiply) R->L }
% 0.19/0.49 multiply(multiply(inverse(double_divide(X, inverse(X))), inverse(Y)), double_divide(X, inverse(X)))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 inverse(Y)
% 0.19/0.49
% 0.19/0.49 Lemma 12: double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), inverse(Z)) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), inverse(Z))
% 0.19/0.49 = { by lemma 4 R->L }
% 0.19/0.49 double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), multiply(multiply(multiply(Y, inverse(Z)), inverse(X)), double_divide(inverse(X), Y)))
% 0.19/0.49 = { by lemma 3 }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 13: double_divide(double_divide(X, inverse(Y)), inverse(Y)) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(double_divide(X, inverse(Y)), inverse(Y))
% 0.19/0.49 = { by lemma 9 R->L }
% 0.19/0.49 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(Z), Z)), inverse(Y)), inverse(Y))
% 0.19/0.49 = { by lemma 11 R->L }
% 0.19/0.49 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(Y))), inverse(Y))
% 0.19/0.49 = { by lemma 12 }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 14: double_divide(double_divide(inverse(X), inverse(inverse(Y))), inverse(X)) = Y.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(double_divide(inverse(X), inverse(inverse(Y))), inverse(X))
% 0.19/0.49 = { by lemma 7 R->L }
% 0.19/0.49 double_divide(double_divide(double_divide(inverse(Y), inverse(inverse(Y))), multiply(inverse(inverse(Y)), inverse(X))), inverse(X))
% 0.19/0.49 = { by lemma 12 }
% 0.19/0.49 Y
% 0.19/0.49
% 0.19/0.49 Lemma 15: inverse(inverse(X)) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(inverse(X))
% 0.19/0.49 = { by lemma 13 R->L }
% 0.19/0.49 double_divide(double_divide(inverse(inverse(X)), inverse(inverse(X))), inverse(inverse(X)))
% 0.19/0.49 = { by lemma 14 }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 16: double_divide(double_divide(X, Y), X) = Y.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(double_divide(X, Y), X)
% 0.19/0.49 = { by lemma 15 R->L }
% 0.19/0.49 double_divide(double_divide(X, Y), inverse(inverse(X)))
% 0.19/0.49 = { by lemma 15 R->L }
% 0.19/0.49 double_divide(double_divide(X, inverse(inverse(Y))), inverse(inverse(X)))
% 0.19/0.49 = { by lemma 15 R->L }
% 0.19/0.49 double_divide(double_divide(inverse(inverse(X)), inverse(inverse(Y))), inverse(inverse(X)))
% 0.19/0.49 = { by lemma 14 }
% 0.19/0.49 Y
% 0.19/0.49
% 0.19/0.49 Lemma 17: double_divide(Y, X) = double_divide(X, Y).
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(Y, X)
% 0.19/0.49 = { by lemma 16 R->L }
% 0.19/0.49 double_divide(double_divide(double_divide(X, Y), X), X)
% 0.19/0.49 = { by lemma 15 R->L }
% 0.19/0.49 double_divide(double_divide(double_divide(X, Y), X), inverse(inverse(X)))
% 0.19/0.49 = { by lemma 15 R->L }
% 0.19/0.49 double_divide(double_divide(double_divide(X, Y), inverse(inverse(X))), inverse(inverse(X)))
% 0.19/0.49 = { by lemma 13 }
% 0.19/0.49 double_divide(X, Y)
% 0.19/0.49
% 0.19/0.49 Lemma 18: multiply(Y, X) = multiply(X, Y).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(Y, X)
% 0.19/0.49 = { by axiom 1 (multiply) }
% 0.19/0.49 inverse(double_divide(X, Y))
% 0.19/0.49 = { by lemma 17 }
% 0.19/0.49 inverse(double_divide(Y, X))
% 0.19/0.49 = { by axiom 1 (multiply) R->L }
% 0.19/0.49 multiply(X, Y)
% 0.19/0.49
% 0.19/0.49 Lemma 19: inverse(multiply(X, Y)) = double_divide(Y, X).
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(multiply(X, Y))
% 0.19/0.49 = { by axiom 1 (multiply) }
% 0.19/0.49 inverse(inverse(double_divide(Y, X)))
% 0.19/0.49 = { by lemma 15 }
% 0.19/0.49 double_divide(Y, X)
% 0.19/0.49
% 0.19/0.49 Lemma 20: multiply(X, inverse(X)) = double_divide(Y, inverse(Y)).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, inverse(X))
% 0.19/0.49 = { by lemma 18 }
% 0.19/0.49 multiply(inverse(X), X)
% 0.19/0.49 = { by lemma 16 R->L }
% 0.19/0.49 double_divide(double_divide(inverse(Y), multiply(inverse(X), X)), inverse(Y))
% 0.19/0.49 = { by lemma 9 }
% 0.19/0.49 double_divide(Y, inverse(Y))
% 0.19/0.49
% 0.19/0.49 Lemma 21: multiply(X, inverse(Y)) = double_divide(Y, inverse(X)).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, inverse(Y))
% 0.19/0.49 = { by lemma 15 R->L }
% 0.19/0.49 multiply(inverse(inverse(X)), inverse(Y))
% 0.19/0.49 = { by lemma 18 }
% 0.19/0.49 multiply(inverse(Y), inverse(inverse(X)))
% 0.19/0.49 = { by lemma 16 R->L }
% 0.19/0.49 double_divide(double_divide(Y, multiply(inverse(Y), inverse(inverse(X)))), Y)
% 0.19/0.49 = { by lemma 8 }
% 0.19/0.49 double_divide(inverse(X), Y)
% 0.19/0.49 = { by lemma 17 R->L }
% 0.19/0.49 double_divide(Y, inverse(X))
% 0.19/0.49
% 0.19/0.49 Lemma 22: multiply(X, double_divide(X, Y)) = inverse(Y).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(X, double_divide(X, Y))
% 0.19/0.49 = { by lemma 17 }
% 0.19/0.49 multiply(X, double_divide(Y, X))
% 0.19/0.49 = { by lemma 15 R->L }
% 0.19/0.49 multiply(X, double_divide(Y, inverse(inverse(X))))
% 0.19/0.49 = { by lemma 15 R->L }
% 0.19/0.49 multiply(inverse(inverse(X)), double_divide(Y, inverse(inverse(X))))
% 0.19/0.49 = { by lemma 9 R->L }
% 0.19/0.49 multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), multiply(inverse(Z), Z)), inverse(inverse(X))))
% 0.19/0.49 = { by lemma 11 R->L }
% 0.19/0.49 multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(inverse(X)))))
% 0.19/0.49 = { by lemma 4 R->L }
% 0.19/0.49 multiply(multiply(multiply(multiply(multiply(inverse(Z), Z), inverse(inverse(X))), inverse(Y)), double_divide(inverse(Y), multiply(inverse(Z), Z))), double_divide(double_divide(inverse(Y), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(inverse(X)))))
% 0.19/0.49 = { by lemma 4 }
% 0.19/0.49 inverse(Y)
% 0.19/0.49
% 0.19/0.49 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)).
% 0.19/0.49 Proof:
% 0.19/0.49 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.19/0.49 = { by lemma 18 R->L }
% 0.19/0.49 tuple(multiply(a1, inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.19/0.49 = { by lemma 18 R->L }
% 0.19/0.49 tuple(multiply(a1, inverse(a1)), multiply(multiply(b2, inverse(b2)), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.19/0.49 = { by lemma 18 R->L }
% 0.19/0.49 tuple(multiply(a1, inverse(a1)), multiply(a2, multiply(b2, inverse(b2))), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.19/0.49 = { by lemma 18 R->L }
% 0.19/0.49 tuple(multiply(a1, inverse(a1)), multiply(a2, multiply(b2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.19/0.49 = { by lemma 20 }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), multiply(a2, multiply(b2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.19/0.50 = { by lemma 20 }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), multiply(a2, double_divide(Y, inverse(Y))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.19/0.50 = { by lemma 15 R->L }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), multiply(inverse(inverse(a2)), double_divide(Y, inverse(Y))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.19/0.50 = { by lemma 10 }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), inverse(inverse(a2)), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.19/0.50 = { by lemma 15 }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.19/0.50 = { by lemma 18 }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.19/0.50 = { by axiom 1 (multiply) }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(c3, multiply(a3, b3))), multiply(a4, b4))
% 0.19/0.50 = { by lemma 18 }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(c3, multiply(b3, a3))), multiply(a4, b4))
% 0.19/0.50 = { by lemma 8 R->L }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(c3, multiply(b3, double_divide(b3, multiply(inverse(b3), inverse(a3)))))), multiply(a4, b4))
% 0.19/0.50 = { by lemma 22 }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(c3, inverse(multiply(inverse(b3), inverse(a3))))), multiply(a4, b4))
% 0.19/0.50 = { by lemma 19 }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(c3, double_divide(inverse(a3), inverse(b3)))), multiply(a4, b4))
% 0.19/0.50 = { by lemma 21 R->L }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(c3, multiply(b3, inverse(inverse(a3))))), multiply(a4, b4))
% 0.19/0.50 = { by lemma 19 R->L }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(inverse(multiply(multiply(b3, inverse(inverse(a3))), c3))), multiply(a4, b4))
% 0.19/0.50 = { by lemma 22 R->L }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(multiply(double_divide(c3, b3), double_divide(double_divide(c3, b3), multiply(multiply(b3, inverse(inverse(a3))), c3)))), multiply(a4, b4))
% 0.19/0.50 = { by lemma 3 }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(multiply(double_divide(c3, b3), inverse(a3))), multiply(a4, b4))
% 0.19/0.50 = { by lemma 21 }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(a3, inverse(double_divide(c3, b3)))), multiply(a4, b4))
% 0.19/0.50 = { by axiom 1 (multiply) R->L }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(a3, multiply(b3, c3))), multiply(a4, b4))
% 0.19/0.50 = { by lemma 18 R->L }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, inverse(double_divide(a3, multiply(c3, b3))), multiply(a4, b4))
% 0.19/0.50 = { by axiom 1 (multiply) R->L }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, multiply(multiply(c3, b3), a3), multiply(a4, b4))
% 0.19/0.50 = { by lemma 18 R->L }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, multiply(a3, multiply(c3, b3)), multiply(a4, b4))
% 0.19/0.50 = { by lemma 18 R->L }
% 0.19/0.50 tuple(double_divide(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.19/0.50 = { by lemma 20 R->L }
% 0.19/0.50 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.19/0.50 = { by lemma 18 }
% 0.19/0.50 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.19/0.50 = { by lemma 18 }
% 0.19/0.50 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50
% 0.19/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------