TSTP Solution File: GRP108-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP108-1 : 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 : n026.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 01:17:01 EDT 2023
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP108-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 21:05:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.45 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.45
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 Take the following subset of the input axioms:
% 0.20/0.49 fof(multiply, axiom, ![X, Y]: multiply(X, Y)=inverse(double_divide(Y, X))).
% 0.20/0.49 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)))).
% 0.20/0.49 fof(single_axiom, axiom, ![Z, X2, Y2]: inverse(double_divide(inverse(double_divide(X2, inverse(double_divide(Y2, double_divide(X2, Z))))), Z))=Y2).
% 0.20/0.49
% 0.20/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.49 fresh(y, y, x1...xn) = u
% 0.20/0.49 C => fresh(s, t, x1...xn) = v
% 0.20/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.49 variables of u and v.
% 0.20/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.49 input problem has no model of domain size 1).
% 0.20/0.49
% 0.20/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.49
% 0.20/0.49 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.20/0.50 Axiom 2 (single_axiom): inverse(double_divide(inverse(double_divide(X, inverse(double_divide(Y, double_divide(X, Z))))), Z)) = Y.
% 0.20/0.50
% 0.20/0.50 Lemma 3: multiply(X, multiply(multiply(double_divide(Y, X), Z), Y)) = Z.
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(X, multiply(multiply(double_divide(Y, X), Z), Y))
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 multiply(X, multiply(inverse(double_divide(Z, double_divide(Y, X))), Y))
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 multiply(X, inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))))
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 inverse(double_divide(inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))), X))
% 0.20/0.50 = { by axiom 2 (single_axiom) }
% 0.20/0.50 Z
% 0.20/0.50
% 0.20/0.50 Lemma 4: multiply(double_divide(X, Y), multiply(Y, multiply(Z, X))) = Z.
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))
% 0.20/0.50 = { by lemma 3 R->L }
% 0.20/0.50 multiply(double_divide(X, Y), multiply(Y, multiply(multiply(double_divide(X, Y), multiply(multiply(double_divide(W, double_divide(X, Y)), Z), W)), X)))
% 0.20/0.50 = { by lemma 3 }
% 0.20/0.50 multiply(double_divide(X, Y), multiply(multiply(double_divide(W, double_divide(X, Y)), Z), W))
% 0.20/0.50 = { by lemma 3 }
% 0.20/0.50 Z
% 0.20/0.50
% 0.20/0.50 Lemma 5: multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, Y)) = double_divide(Z, X).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, Y))
% 0.20/0.50 = { by lemma 4 R->L }
% 0.20/0.50 multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, multiply(double_divide(Z, X), multiply(X, multiply(Y, Z)))))
% 0.20/0.50 = { by lemma 4 }
% 0.20/0.50 double_divide(Z, X)
% 0.20/0.50
% 0.20/0.50 Lemma 6: multiply(multiply(X, Y), multiply(inverse(X), Z)) = multiply(Y, Z).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(multiply(X, Y), multiply(inverse(X), Z))
% 0.20/0.50 = { by lemma 4 R->L }
% 0.20/0.50 multiply(multiply(X, Y), multiply(inverse(multiply(double_divide(multiply(multiply(double_divide(multiply(multiply(X, Y), multiply(Y, Z)), X), multiply(X, Y)), multiply(multiply(X, Y), multiply(Y, Z))), W), multiply(W, multiply(X, multiply(multiply(double_divide(multiply(multiply(X, Y), multiply(Y, Z)), X), multiply(X, Y)), multiply(multiply(X, Y), multiply(Y, Z))))))), Z))
% 0.20/0.50 = { by lemma 3 }
% 0.20/0.50 multiply(multiply(X, Y), multiply(inverse(multiply(double_divide(multiply(multiply(double_divide(multiply(multiply(X, Y), multiply(Y, Z)), X), multiply(X, Y)), multiply(multiply(X, Y), multiply(Y, Z))), W), multiply(W, multiply(X, Y)))), Z))
% 0.20/0.50 = { by lemma 5 }
% 0.20/0.50 multiply(multiply(X, Y), multiply(inverse(double_divide(multiply(Y, Z), multiply(double_divide(multiply(multiply(X, Y), multiply(Y, Z)), X), multiply(X, Y)))), Z))
% 0.20/0.50 = { by axiom 1 (multiply) R->L }
% 0.20/0.50 multiply(multiply(X, Y), multiply(multiply(multiply(double_divide(multiply(multiply(X, Y), multiply(Y, Z)), X), multiply(X, Y)), multiply(Y, Z)), Z))
% 0.20/0.50 = { by lemma 5 }
% 0.20/0.50 multiply(multiply(X, Y), multiply(multiply(double_divide(Z, multiply(X, Y)), multiply(Y, Z)), Z))
% 0.20/0.50 = { by lemma 3 }
% 0.20/0.50 multiply(Y, Z)
% 0.20/0.50
% 0.20/0.50 Lemma 7: multiply(multiply(X, multiply(Y, Z)), W) = multiply(Y, multiply(multiply(X, Z), W)).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(multiply(X, multiply(Y, Z)), W)
% 0.20/0.50 = { by lemma 6 R->L }
% 0.20/0.50 multiply(multiply(double_divide(Z, X), multiply(X, multiply(Y, Z))), multiply(inverse(double_divide(Z, X)), W))
% 0.20/0.50 = { by lemma 4 }
% 0.20/0.50 multiply(Y, multiply(inverse(double_divide(Z, X)), W))
% 0.20/0.50 = { by axiom 1 (multiply) R->L }
% 0.20/0.50 multiply(Y, multiply(multiply(X, Z), W))
% 0.20/0.50
% 0.20/0.50 Lemma 8: multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(multiply(X, Y), Z)
% 0.20/0.50 = { by lemma 6 R->L }
% 0.20/0.50 multiply(multiply(W, multiply(X, Y)), multiply(inverse(W), Z))
% 0.20/0.50 = { by lemma 7 }
% 0.20/0.50 multiply(X, multiply(multiply(W, Y), multiply(inverse(W), Z)))
% 0.20/0.50 = { by lemma 6 }
% 0.20/0.50 multiply(X, multiply(Y, Z))
% 0.20/0.50
% 0.20/0.50 Lemma 9: multiply(X, multiply(Y, multiply(inverse(X), Z))) = multiply(Y, Z).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(X, multiply(Y, multiply(inverse(X), Z)))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 multiply(multiply(X, Y), multiply(inverse(X), Z))
% 0.20/0.50 = { by lemma 6 }
% 0.20/0.50 multiply(Y, Z)
% 0.20/0.50
% 0.20/0.50 Lemma 10: multiply(X, multiply(inverse(multiply(Y, X)), Z)) = multiply(inverse(Y), Z).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(X, multiply(inverse(multiply(Y, X)), Z))
% 0.20/0.50 = { by lemma 6 R->L }
% 0.20/0.50 multiply(multiply(Y, X), multiply(inverse(Y), multiply(inverse(multiply(Y, X)), Z)))
% 0.20/0.50 = { by lemma 9 }
% 0.20/0.50 multiply(inverse(Y), Z)
% 0.20/0.50
% 0.20/0.50 Lemma 11: multiply(inverse(X), multiply(inverse(Y), Z)) = multiply(inverse(multiply(X, Y)), Z).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(inverse(X), multiply(inverse(Y), Z))
% 0.20/0.50 = { by lemma 10 R->L }
% 0.20/0.50 multiply(inverse(X), multiply(W, multiply(inverse(multiply(Y, W)), Z)))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 multiply(multiply(inverse(X), W), multiply(inverse(multiply(Y, W)), Z))
% 0.20/0.50 = { by lemma 6 R->L }
% 0.20/0.50 multiply(multiply(inverse(X), W), multiply(inverse(multiply(multiply(X, Y), multiply(inverse(X), W))), Z))
% 0.20/0.50 = { by lemma 10 }
% 0.20/0.50 multiply(inverse(multiply(X, Y)), Z)
% 0.20/0.50
% 0.20/0.50 Lemma 12: multiply(X, multiply(inverse(multiply(Y, multiply(Z, X))), W)) = multiply(inverse(multiply(Y, Z)), W).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(X, multiply(inverse(multiply(Y, multiply(Z, X))), W))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 multiply(X, multiply(inverse(multiply(multiply(Y, Z), X)), W))
% 0.20/0.50 = { by lemma 10 }
% 0.20/0.50 multiply(inverse(multiply(Y, Z)), W)
% 0.20/0.50
% 0.20/0.50 Lemma 13: inverse(multiply(Y, multiply(X, Z))) = inverse(multiply(X, multiply(Y, Z))).
% 0.20/0.50 Proof:
% 0.20/0.50 inverse(multiply(Y, multiply(X, Z)))
% 0.20/0.50 = { by lemma 4 R->L }
% 0.20/0.50 multiply(double_divide(W, V), multiply(V, multiply(inverse(multiply(Y, multiply(X, Z))), W)))
% 0.20/0.50 = { by lemma 11 R->L }
% 0.20/0.50 multiply(double_divide(W, V), multiply(V, multiply(inverse(Y), multiply(inverse(multiply(X, Z)), W))))
% 0.20/0.50 = { by lemma 12 R->L }
% 0.20/0.50 multiply(double_divide(W, V), multiply(V, multiply(inverse(Y), multiply(U, multiply(inverse(multiply(X, multiply(Z, U))), W)))))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 multiply(double_divide(W, V), multiply(V, multiply(multiply(inverse(Y), U), multiply(inverse(multiply(X, multiply(Z, U))), W))))
% 0.20/0.50 = { by lemma 6 R->L }
% 0.20/0.50 multiply(double_divide(W, V), multiply(V, multiply(multiply(inverse(Y), U), multiply(inverse(multiply(X, multiply(multiply(Y, Z), multiply(inverse(Y), U)))), W))))
% 0.20/0.50 = { by lemma 12 }
% 0.20/0.50 multiply(double_divide(W, V), multiply(V, multiply(inverse(multiply(X, multiply(Y, Z))), W)))
% 0.20/0.50 = { by lemma 4 }
% 0.20/0.50 inverse(multiply(X, multiply(Y, Z)))
% 0.20/0.50
% 0.20/0.50 Lemma 14: multiply(inverse(multiply(X, Y)), Z) = multiply(inverse(multiply(Y, X)), Z).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(inverse(multiply(X, Y)), Z)
% 0.20/0.50 = { by lemma 12 R->L }
% 0.20/0.50 multiply(multiply(W, multiply(inverse(Y), V)), multiply(inverse(multiply(X, multiply(Y, multiply(W, multiply(inverse(Y), V))))), Z))
% 0.20/0.50 = { by lemma 9 }
% 0.20/0.50 multiply(multiply(W, multiply(inverse(Y), V)), multiply(inverse(multiply(X, multiply(W, V))), Z))
% 0.20/0.50 = { by lemma 7 }
% 0.20/0.50 multiply(inverse(Y), multiply(multiply(W, V), multiply(inverse(multiply(X, multiply(W, V))), Z)))
% 0.20/0.50 = { by lemma 8 }
% 0.20/0.50 multiply(inverse(Y), multiply(W, multiply(V, multiply(inverse(multiply(X, multiply(W, V))), Z))))
% 0.20/0.50 = { by lemma 12 }
% 0.20/0.50 multiply(inverse(Y), multiply(W, multiply(inverse(multiply(X, W)), Z)))
% 0.20/0.50 = { by lemma 10 }
% 0.20/0.50 multiply(inverse(Y), multiply(inverse(X), Z))
% 0.20/0.50 = { by lemma 11 }
% 0.20/0.50 multiply(inverse(multiply(Y, X)), Z)
% 0.20/0.50
% 0.20/0.50 Lemma 15: inverse(multiply(Y, X)) = inverse(multiply(X, Y)).
% 0.20/0.50 Proof:
% 0.20/0.50 inverse(multiply(Y, X))
% 0.20/0.50 = { by lemma 4 R->L }
% 0.20/0.50 multiply(double_divide(Z, W), multiply(W, multiply(inverse(multiply(Y, X)), Z)))
% 0.20/0.50 = { by lemma 14 R->L }
% 0.20/0.50 multiply(double_divide(Z, W), multiply(W, multiply(inverse(multiply(X, Y)), Z)))
% 0.20/0.50 = { by lemma 4 }
% 0.20/0.50 inverse(multiply(X, Y))
% 0.20/0.50
% 0.20/0.50 Lemma 16: inverse(multiply(inverse(X), multiply(Y, X))) = inverse(Y).
% 0.20/0.50 Proof:
% 0.20/0.50 inverse(multiply(inverse(X), multiply(Y, X)))
% 0.20/0.50 = { by lemma 4 R->L }
% 0.20/0.50 multiply(double_divide(Z, W), multiply(W, multiply(inverse(multiply(inverse(X), multiply(Y, X))), Z)))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 multiply(double_divide(Z, W), multiply(W, multiply(inverse(multiply(multiply(inverse(X), Y), X)), Z)))
% 0.20/0.50 = { by lemma 14 R->L }
% 0.20/0.50 multiply(double_divide(Z, W), multiply(W, multiply(inverse(multiply(X, multiply(inverse(X), Y))), Z)))
% 0.20/0.50 = { by lemma 11 R->L }
% 0.20/0.50 multiply(double_divide(Z, W), multiply(W, multiply(inverse(X), multiply(inverse(multiply(inverse(X), Y)), Z))))
% 0.20/0.50 = { by lemma 14 R->L }
% 0.20/0.50 multiply(double_divide(Z, W), multiply(W, multiply(inverse(X), multiply(inverse(multiply(Y, inverse(X))), Z))))
% 0.20/0.50 = { by lemma 10 }
% 0.20/0.50 multiply(double_divide(Z, W), multiply(W, multiply(inverse(Y), Z)))
% 0.20/0.50 = { by lemma 4 }
% 0.20/0.50 inverse(Y)
% 0.20/0.50
% 0.20/0.50 Lemma 17: inverse(multiply(X, inverse(multiply(X, multiply(Y, Z))))) = multiply(Y, Z).
% 0.20/0.50 Proof:
% 0.20/0.50 inverse(multiply(X, inverse(multiply(X, multiply(Y, Z)))))
% 0.20/0.50 = { by lemma 13 R->L }
% 0.20/0.50 inverse(multiply(X, inverse(multiply(Y, multiply(X, Z)))))
% 0.20/0.50 = { by lemma 15 }
% 0.20/0.50 inverse(multiply(inverse(multiply(Y, multiply(X, Z))), X))
% 0.20/0.50 = { by lemma 4 R->L }
% 0.20/0.50 inverse(multiply(inverse(multiply(Y, multiply(X, Z))), multiply(double_divide(Z, Y), multiply(Y, multiply(X, Z)))))
% 0.20/0.50 = { by lemma 16 }
% 0.20/0.50 inverse(double_divide(Z, Y))
% 0.20/0.50 = { by axiom 1 (multiply) R->L }
% 0.20/0.50 multiply(Y, Z)
% 0.20/0.50
% 0.20/0.50 Lemma 18: multiply(Y, X) = multiply(X, Y).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(Y, X)
% 0.20/0.50 = { by lemma 17 R->L }
% 0.20/0.50 inverse(multiply(Z, inverse(multiply(Z, multiply(Y, X)))))
% 0.20/0.50 = { by lemma 13 }
% 0.20/0.50 inverse(multiply(Z, inverse(multiply(Y, multiply(Z, X)))))
% 0.20/0.50 = { by lemma 15 R->L }
% 0.20/0.50 inverse(multiply(Z, inverse(multiply(multiply(Z, X), Y))))
% 0.20/0.50 = { by lemma 8 }
% 0.20/0.50 inverse(multiply(Z, inverse(multiply(Z, multiply(X, Y)))))
% 0.20/0.50 = { by lemma 17 }
% 0.20/0.50 multiply(X, Y)
% 0.20/0.50
% 0.20/0.50 Lemma 19: multiply(inverse(X), multiply(X, Y)) = multiply(Z, multiply(inverse(Z), Y)).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(inverse(X), multiply(X, Y))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 multiply(multiply(inverse(X), X), Y)
% 0.20/0.50 = { by lemma 6 R->L }
% 0.20/0.50 multiply(multiply(multiply(X, X), multiply(inverse(X), X)), multiply(inverse(multiply(X, X)), Y))
% 0.20/0.50 = { by lemma 6 }
% 0.20/0.50 multiply(multiply(X, X), multiply(inverse(multiply(X, X)), Y))
% 0.20/0.50 = { by lemma 9 R->L }
% 0.20/0.50 multiply(Z, multiply(multiply(X, X), multiply(inverse(Z), multiply(inverse(multiply(X, X)), Y))))
% 0.20/0.50 = { by lemma 9 }
% 0.20/0.51 multiply(Z, multiply(inverse(Z), Y))
% 0.20/0.51
% 0.20/0.51 Lemma 20: inverse(multiply(X, multiply(Y, inverse(Y)))) = inverse(X).
% 0.20/0.51 Proof:
% 0.20/0.51 inverse(multiply(X, multiply(Y, inverse(Y))))
% 0.20/0.51 = { by lemma 13 }
% 0.20/0.51 inverse(multiply(Y, multiply(X, inverse(Y))))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 multiply(double_divide(Z, W), multiply(W, multiply(inverse(multiply(Y, multiply(X, inverse(Y)))), Z)))
% 0.20/0.51 = { by lemma 8 R->L }
% 0.20/0.51 multiply(double_divide(Z, W), multiply(W, multiply(inverse(multiply(multiply(Y, X), inverse(Y))), Z)))
% 0.20/0.51 = { by lemma 11 R->L }
% 0.20/0.51 multiply(double_divide(Z, W), multiply(W, multiply(inverse(multiply(Y, X)), multiply(inverse(inverse(Y)), Z))))
% 0.20/0.51 = { by lemma 11 R->L }
% 0.20/0.51 multiply(double_divide(Z, W), multiply(W, multiply(inverse(Y), multiply(inverse(X), multiply(inverse(inverse(Y)), Z)))))
% 0.20/0.51 = { by lemma 9 }
% 0.20/0.51 multiply(double_divide(Z, W), multiply(W, multiply(inverse(X), Z)))
% 0.20/0.51 = { by lemma 4 }
% 0.20/0.51 inverse(X)
% 0.20/0.51
% 0.20/0.51 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)).
% 0.20/0.51 Proof:
% 0.20/0.51 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.20/0.51 = { by lemma 8 }
% 0.20/0.51 tuple(multiply(inverse(a1), a1), multiply(inverse(b2), multiply(b2, a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.20/0.51 = { by lemma 8 }
% 0.20/0.51 tuple(multiply(inverse(a1), a1), multiply(inverse(b2), multiply(b2, a2)), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 19 }
% 0.20/0.51 tuple(multiply(inverse(a1), a1), multiply(X, multiply(inverse(X), a2)), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 18 R->L }
% 0.20/0.51 tuple(multiply(a1, inverse(a1)), multiply(X, multiply(inverse(X), a2)), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 18 R->L }
% 0.20/0.51 tuple(multiply(a1, inverse(a1)), multiply(X, multiply(a2, inverse(X))), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 8 R->L }
% 0.20/0.51 tuple(multiply(a1, inverse(a1)), multiply(multiply(X, a2), inverse(X)), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 18 }
% 0.20/0.51 tuple(multiply(a1, inverse(a1)), multiply(inverse(X), multiply(X, a2)), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 17 R->L }
% 0.20/0.51 tuple(multiply(a1, inverse(a1)), inverse(multiply(X, inverse(multiply(X, multiply(inverse(X), multiply(X, a2)))))), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 19 R->L }
% 0.20/0.51 tuple(multiply(a1, inverse(a1)), inverse(multiply(X, inverse(multiply(inverse(multiply(X, a2)), multiply(multiply(X, a2), multiply(X, a2)))))), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 16 }
% 0.20/0.51 tuple(multiply(a1, inverse(a1)), inverse(multiply(X, inverse(multiply(X, a2)))), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 3 R->L }
% 0.20/0.51 tuple(multiply(a1, inverse(a1)), inverse(multiply(X, inverse(multiply(X, multiply(Y, multiply(multiply(double_divide(Z, Y), a2), Z)))))), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 17 }
% 0.20/0.51 tuple(multiply(a1, inverse(a1)), multiply(Y, multiply(multiply(double_divide(Z, Y), a2), Z)), multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 3 }
% 0.20/0.51 tuple(multiply(a1, inverse(a1)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 17 R->L }
% 0.20/0.51 tuple(inverse(multiply(W, inverse(multiply(W, multiply(a1, inverse(a1)))))), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 20 }
% 0.20/0.51 tuple(inverse(multiply(W, inverse(W))), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 20 R->L }
% 0.20/0.51 tuple(inverse(multiply(W, inverse(multiply(W, multiply(b1, inverse(b1)))))), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 17 }
% 0.20/0.51 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.20/0.51 = { by lemma 18 }
% 0.20/0.51 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.20/0.51 = { by lemma 18 }
% 0.20/0.51 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51
% 0.20/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
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