TSTP Solution File: GRP074-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP074-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 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 : n004.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 01:16:53 EDT 2023
% Result : Unsatisfiable 0.19s 0.58s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP074-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.07/0.13 % 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 : n004.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 : Tue Aug 29 00:22:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.58 Command-line arguments: --no-flatten-goal
% 0.19/0.58
% 0.19/0.58 % SZS status Unsatisfiable
% 0.19/0.58
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 Take the following subset of the input axioms:
% 0.19/0.64 fof(multiply, axiom, ![X, Y]: multiply(X, Y)=divide(X, inverse(Y))).
% 0.19/0.64 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)))).
% 0.19/0.64 fof(single_axiom, axiom, ![Z, U, X2, Y2]: divide(inverse(divide(divide(divide(X2, X2), Y2), divide(Z, divide(Y2, U)))), U)=Z).
% 0.19/0.64
% 0.19/0.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.64 fresh(y, y, x1...xn) = u
% 0.19/0.64 C => fresh(s, t, x1...xn) = v
% 0.19/0.64 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.64 variables of u and v.
% 0.19/0.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.64 input problem has no model of domain size 1).
% 0.19/0.64
% 0.19/0.64 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.64
% 0.19/0.64 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.19/0.64 Axiom 2 (single_axiom): divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, W)))), W) = Z.
% 0.19/0.64
% 0.19/0.64 Lemma 3: inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V))))) = divide(inverse(divide(divide(divide(U, U), W), Z)), V).
% 0.19/0.64 Proof:
% 0.19/0.64 inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V)))))
% 0.19/0.64 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.64 divide(inverse(divide(divide(divide(U, U), W), divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V))))), divide(W, V)))), V)
% 0.19/0.64 = { by axiom 2 (single_axiom) }
% 0.19/0.64 divide(inverse(divide(divide(divide(U, U), W), Z)), V)
% 0.19/0.64
% 0.19/0.64 Lemma 4: divide(divide(inverse(divide(divide(divide(X, X), Y), Z)), W), divide(Y, W)) = Z.
% 0.19/0.64 Proof:
% 0.19/0.64 divide(divide(inverse(divide(divide(divide(X, X), Y), Z)), W), divide(Y, W))
% 0.19/0.64 = { by lemma 3 R->L }
% 0.19/0.64 divide(inverse(divide(divide(divide(V, V), U), divide(Z, divide(U, divide(Y, W))))), divide(Y, W))
% 0.19/0.64 = { by axiom 2 (single_axiom) }
% 0.19/0.64 Z
% 0.19/0.64
% 0.19/0.64 Lemma 5: divide(divide(divide(inverse(divide(divide(divide(X, X), Y), Z)), W), V), divide(U, V)) = divide(Z, divide(U, divide(Y, W))).
% 0.19/0.64 Proof:
% 0.19/0.64 divide(divide(divide(inverse(divide(divide(divide(X, X), Y), Z)), W), V), divide(U, V))
% 0.19/0.64 = { by lemma 3 R->L }
% 0.19/0.64 divide(divide(inverse(divide(divide(divide(T, T), U), divide(Z, divide(U, divide(Y, W))))), V), divide(U, V))
% 0.19/0.64 = { by lemma 4 }
% 0.19/0.64 divide(Z, divide(U, divide(Y, W)))
% 0.19/0.64
% 0.19/0.64 Lemma 6: divide(divide(inverse(multiply(divide(divide(X, X), Y), Z)), W), divide(Y, W)) = inverse(Z).
% 0.19/0.64 Proof:
% 0.19/0.64 divide(divide(inverse(multiply(divide(divide(X, X), Y), Z)), W), divide(Y, W))
% 0.19/0.64 = { by axiom 1 (multiply) }
% 0.19/0.64 divide(divide(inverse(divide(divide(divide(X, X), Y), inverse(Z))), W), divide(Y, W))
% 0.19/0.64 = { by lemma 4 }
% 0.19/0.64 inverse(Z)
% 0.19/0.64
% 0.19/0.64 Lemma 7: multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))) = W.
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W)))
% 0.19/0.64 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.64 divide(inverse(divide(divide(divide(V, V), U), divide(multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))), divide(U, T)))), T)
% 0.19/0.64 = { by lemma 4 R->L }
% 0.19/0.64 divide(inverse(divide(divide(inverse(divide(divide(divide(Z, Z), W), divide(divide(divide(V, V), U), divide(multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))), divide(U, T))))), divide(U, T)), divide(W, divide(U, T)))), T)
% 0.19/0.64 = { by axiom 1 (multiply) }
% 0.19/0.64 divide(inverse(divide(divide(inverse(divide(divide(divide(Z, Z), W), divide(divide(divide(V, V), U), divide(divide(X, inverse(divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W)))), divide(U, T))))), divide(U, T)), divide(W, divide(U, T)))), T)
% 0.19/0.64 = { by lemma 4 R->L }
% 0.19/0.64 divide(inverse(divide(divide(inverse(divide(divide(divide(inverse(divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))), inverse(divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W)))), divide(X, inverse(divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))))), divide(divide(divide(V, V), U), divide(divide(X, inverse(divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W)))), divide(U, T))))), divide(U, T)), divide(W, divide(U, T)))), T)
% 0.19/0.64 = { by axiom 2 (single_axiom) }
% 0.19/0.64 divide(inverse(divide(divide(divide(V, V), U), divide(W, divide(U, T)))), T)
% 0.19/0.64 = { by axiom 2 (single_axiom) }
% 0.19/0.64 W
% 0.19/0.64
% 0.19/0.64 Lemma 8: multiply(X, divide(divide(divide(Y, Y), Z), divide(divide(W, W), Z))) = X.
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(X, divide(divide(divide(Y, Y), Z), divide(divide(W, W), Z)))
% 0.19/0.64 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.64 multiply(X, divide(divide(divide(inverse(divide(divide(divide(V, V), U), divide(divide(Y, Y), divide(U, T)))), T), Z), divide(divide(W, W), Z)))
% 0.19/0.64 = { by lemma 5 }
% 0.19/0.64 multiply(X, divide(divide(divide(Y, Y), divide(U, T)), divide(divide(W, W), divide(U, T))))
% 0.19/0.64 = { by lemma 5 R->L }
% 0.19/0.64 multiply(X, divide(divide(divide(inverse(divide(divide(divide(S, S), U), divide(divide(Y, Y), divide(U, T)))), T), X), divide(divide(W, W), X)))
% 0.19/0.64 = { by axiom 2 (single_axiom) }
% 0.19/0.64 multiply(X, divide(divide(divide(Y, Y), X), divide(divide(W, W), X)))
% 0.19/0.64 = { by lemma 7 }
% 0.19/0.64 X
% 0.19/0.64
% 0.19/0.64 Lemma 9: divide(divide(X, Y), divide(Z, Y)) = divide(X, Z).
% 0.19/0.64 Proof:
% 0.19/0.64 divide(divide(X, Y), divide(Z, Y))
% 0.19/0.65 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.65 divide(divide(divide(inverse(divide(divide(divide(W, W), divide(inverse(multiply(divide(divide(V, V), U), divide(divide(divide(T, T), S), divide(divide(X2, X2), S)))), Y2)), divide(X, divide(divide(inverse(multiply(divide(divide(V, V), U), divide(divide(divide(T, T), S), divide(divide(X2, X2), S)))), Y2), divide(U, Y2))))), divide(U, Y2)), Y), divide(Z, Y))
% 0.19/0.65 = { by lemma 5 }
% 0.19/0.65 divide(divide(X, divide(divide(inverse(multiply(divide(divide(V, V), U), divide(divide(divide(T, T), S), divide(divide(X2, X2), S)))), Y2), divide(U, Y2))), divide(Z, divide(divide(inverse(multiply(divide(divide(V, V), U), divide(divide(divide(T, T), S), divide(divide(X2, X2), S)))), Y2), divide(U, Y2))))
% 0.19/0.65 = { by lemma 6 }
% 0.19/0.65 divide(divide(X, inverse(divide(divide(divide(T, T), S), divide(divide(X2, X2), S)))), divide(Z, divide(divide(inverse(multiply(divide(divide(V, V), U), divide(divide(divide(T, T), S), divide(divide(X2, X2), S)))), Y2), divide(U, Y2))))
% 0.19/0.65 = { by axiom 1 (multiply) R->L }
% 0.19/0.65 divide(multiply(X, divide(divide(divide(T, T), S), divide(divide(X2, X2), S))), divide(Z, divide(divide(inverse(multiply(divide(divide(V, V), U), divide(divide(divide(T, T), S), divide(divide(X2, X2), S)))), Y2), divide(U, Y2))))
% 0.19/0.65 = { by lemma 6 }
% 0.19/0.65 divide(multiply(X, divide(divide(divide(T, T), S), divide(divide(X2, X2), S))), divide(Z, inverse(divide(divide(divide(T, T), S), divide(divide(X2, X2), S)))))
% 0.19/0.65 = { by axiom 1 (multiply) R->L }
% 0.19/0.65 divide(multiply(X, divide(divide(divide(T, T), S), divide(divide(X2, X2), S))), multiply(Z, divide(divide(divide(T, T), S), divide(divide(X2, X2), S))))
% 0.19/0.65 = { by lemma 8 }
% 0.19/0.65 divide(X, multiply(Z, divide(divide(divide(T, T), S), divide(divide(X2, X2), S))))
% 0.19/0.65 = { by lemma 8 }
% 0.19/0.65 divide(X, Z)
% 0.19/0.65
% 0.19/0.65 Lemma 10: multiply(inverse(divide(divide(divide(X, X), Y), divide(Z, multiply(Y, W)))), W) = Z.
% 0.19/0.65 Proof:
% 0.19/0.65 multiply(inverse(divide(divide(divide(X, X), Y), divide(Z, multiply(Y, W)))), W)
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 multiply(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, inverse(W))))), W)
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, inverse(W))))), inverse(W))
% 0.19/0.65 = { by axiom 2 (single_axiom) }
% 0.19/0.65 Z
% 0.19/0.65
% 0.19/0.65 Lemma 11: inverse(divide(divide(X, X), Y)) = Y.
% 0.19/0.65 Proof:
% 0.19/0.65 inverse(divide(divide(X, X), Y))
% 0.19/0.65 = { by lemma 9 R->L }
% 0.19/0.65 inverse(divide(divide(divide(X, X), Z), divide(Y, Z)))
% 0.19/0.65 = { by lemma 9 R->L }
% 0.19/0.65 inverse(divide(divide(divide(X, X), Z), divide(divide(Y, divide(W, inverse(V))), divide(Z, divide(W, inverse(V))))))
% 0.19/0.65 = { by lemma 3 }
% 0.19/0.65 divide(inverse(divide(divide(divide(U, U), W), divide(Y, divide(W, inverse(V))))), inverse(V))
% 0.19/0.65 = { by axiom 1 (multiply) R->L }
% 0.19/0.65 multiply(inverse(divide(divide(divide(U, U), W), divide(Y, divide(W, inverse(V))))), V)
% 0.19/0.65 = { by axiom 1 (multiply) R->L }
% 0.19/0.65 multiply(inverse(divide(divide(divide(U, U), W), divide(Y, multiply(W, V)))), V)
% 0.19/0.65 = { by lemma 10 }
% 0.19/0.65 Y
% 0.19/0.65
% 0.19/0.65 Lemma 12: divide(divide(X, X), Y) = inverse(Y).
% 0.19/0.65 Proof:
% 0.19/0.65 divide(divide(X, X), Y)
% 0.19/0.65 = { by lemma 11 R->L }
% 0.19/0.65 inverse(divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(X, X), Y)))
% 0.19/0.65 = { by lemma 11 R->L }
% 0.19/0.65 inverse(divide(divide(Z, Z), inverse(divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(X, X), Y)))))
% 0.19/0.65 = { by axiom 1 (multiply) R->L }
% 0.19/0.65 inverse(multiply(divide(Z, Z), divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(X, X), Y))))
% 0.19/0.65 = { by lemma 7 }
% 0.19/0.65 inverse(Y)
% 0.19/0.65
% 0.19/0.65 Lemma 13: inverse(inverse(X)) = X.
% 0.19/0.65 Proof:
% 0.19/0.65 inverse(inverse(X))
% 0.19/0.65 = { by lemma 12 R->L }
% 0.19/0.65 inverse(divide(divide(Y, Y), X))
% 0.19/0.65 = { by lemma 11 }
% 0.19/0.65 X
% 0.19/0.65
% 0.19/0.65 Lemma 14: multiply(inverse(X), X) = divide(Y, Y).
% 0.19/0.65 Proof:
% 0.19/0.65 multiply(inverse(X), X)
% 0.19/0.65 = { by lemma 13 R->L }
% 0.19/0.65 inverse(inverse(multiply(inverse(X), X)))
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 inverse(inverse(divide(inverse(X), inverse(X))))
% 0.19/0.65 = { by lemma 8 R->L }
% 0.19/0.65 inverse(inverse(multiply(divide(inverse(X), inverse(X)), divide(divide(divide(Z, Z), W), divide(divide(V, V), W)))))
% 0.19/0.65 = { by lemma 8 R->L }
% 0.19/0.65 inverse(inverse(multiply(multiply(divide(inverse(X), inverse(X)), divide(divide(divide(Z, Z), W), divide(divide(V, V), W))), divide(divide(divide(U, U), T), divide(divide(S, S), T)))))
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 inverse(inverse(multiply(divide(divide(inverse(X), inverse(X)), inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W)))), divide(divide(divide(U, U), T), divide(divide(S, S), T)))))
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 inverse(inverse(divide(divide(divide(inverse(X), inverse(X)), inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W)))), inverse(divide(divide(divide(U, U), T), divide(divide(S, S), T))))))
% 0.19/0.65 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.65 inverse(divide(inverse(divide(divide(divide(X2, X2), Y2), divide(inverse(divide(divide(divide(inverse(X), inverse(X)), inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W)))), inverse(divide(divide(divide(U, U), T), divide(divide(S, S), T))))), divide(Y2, Z2)))), Z2))
% 0.19/0.65 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.66 inverse(divide(inverse(divide(divide(divide(X2, X2), Y2), divide(inverse(divide(divide(divide(inverse(X), inverse(X)), inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W)))), divide(inverse(divide(divide(divide(W2, W2), V2), divide(inverse(divide(divide(divide(U, U), T), divide(divide(S, S), T))), divide(V2, divide(inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W))), divide(Y2, Z2)))))), divide(inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W))), divide(Y2, Z2))))), divide(Y2, Z2)))), Z2))
% 0.19/0.66 = { by axiom 2 (single_axiom) }
% 0.19/0.66 inverse(divide(inverse(divide(divide(divide(X2, X2), Y2), inverse(divide(divide(divide(W2, W2), V2), divide(inverse(divide(divide(divide(U, U), T), divide(divide(S, S), T))), divide(V2, divide(inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W))), divide(Y2, Z2)))))))), Z2))
% 0.19/0.66 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.66 inverse(divide(inverse(divide(divide(divide(X2, X2), Y2), divide(inverse(divide(divide(divide(Y, Y), inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W)))), divide(inverse(divide(divide(divide(W2, W2), V2), divide(inverse(divide(divide(divide(U, U), T), divide(divide(S, S), T))), divide(V2, divide(inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W))), divide(Y2, Z2)))))), divide(inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W))), divide(Y2, Z2))))), divide(Y2, Z2)))), Z2))
% 0.19/0.66 = { by axiom 2 (single_axiom) }
% 0.19/0.66 inverse(divide(inverse(divide(divide(divide(X2, X2), Y2), divide(inverse(divide(divide(divide(Y, Y), inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W)))), inverse(divide(divide(divide(U, U), T), divide(divide(S, S), T))))), divide(Y2, Z2)))), Z2))
% 0.19/0.66 = { by axiom 2 (single_axiom) }
% 0.19/0.66 inverse(inverse(divide(divide(divide(Y, Y), inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W)))), inverse(divide(divide(divide(U, U), T), divide(divide(S, S), T))))))
% 0.19/0.66 = { by axiom 1 (multiply) R->L }
% 0.19/0.66 inverse(inverse(multiply(divide(divide(Y, Y), inverse(divide(divide(divide(Z, Z), W), divide(divide(V, V), W)))), divide(divide(divide(U, U), T), divide(divide(S, S), T)))))
% 0.19/0.66 = { by axiom 1 (multiply) R->L }
% 0.19/0.66 inverse(inverse(multiply(multiply(divide(Y, Y), divide(divide(divide(Z, Z), W), divide(divide(V, V), W))), divide(divide(divide(U, U), T), divide(divide(S, S), T)))))
% 0.19/0.66 = { by lemma 8 }
% 0.19/0.66 inverse(inverse(multiply(divide(Y, Y), divide(divide(divide(Z, Z), W), divide(divide(V, V), W)))))
% 0.19/0.66 = { by lemma 8 }
% 0.19/0.66 inverse(inverse(divide(Y, Y)))
% 0.19/0.66 = { by lemma 13 }
% 0.19/0.66 divide(Y, Y)
% 0.19/0.66
% 0.19/0.66 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 0.19/0.66 Proof:
% 0.19/0.66 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.19/0.66 = { by lemma 14 }
% 0.19/0.66 tuple(divide(X, X), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.19/0.66 = { by lemma 14 }
% 0.19/0.66 tuple(divide(X, X), multiply(divide(Y, Y), a2), multiply(multiply(a3, b3), c3))
% 0.19/0.66 = { by axiom 1 (multiply) }
% 0.19/0.66 tuple(divide(X, X), divide(divide(Y, Y), inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.19/0.66 = { by lemma 12 }
% 0.19/0.66 tuple(divide(X, X), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.19/0.66 = { by lemma 13 }
% 0.19/0.66 tuple(divide(X, X), a2, multiply(multiply(a3, b3), c3))
% 0.19/0.66 = { by axiom 1 (multiply) }
% 0.19/0.66 tuple(divide(X, X), a2, multiply(divide(a3, inverse(b3)), c3))
% 0.19/0.66 = { by lemma 12 R->L }
% 0.19/0.66 tuple(divide(X, X), a2, multiply(divide(a3, divide(divide(Z, Z), b3)), c3))
% 0.19/0.66 = { by lemma 11 R->L }
% 0.19/0.66 tuple(divide(X, X), a2, multiply(inverse(divide(divide(divide(divide(Z, Z), b3), divide(divide(Z, Z), b3)), divide(a3, divide(divide(Z, Z), b3)))), c3))
% 0.19/0.66 = { by lemma 9 }
% 0.19/0.66 tuple(divide(X, X), a2, multiply(inverse(divide(divide(divide(Z, Z), b3), a3)), c3))
% 0.19/0.66 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.66 tuple(divide(X, X), a2, multiply(inverse(divide(divide(divide(Z, Z), b3), divide(inverse(divide(divide(divide(W, W), divide(W, W)), divide(a3, divide(divide(W, W), multiply(b3, c3))))), multiply(b3, c3)))), c3))
% 0.19/0.66 = { by lemma 12 }
% 0.19/0.66 tuple(divide(X, X), a2, multiply(inverse(divide(divide(divide(Z, Z), b3), divide(inverse(divide(divide(divide(W, W), divide(W, W)), divide(a3, inverse(multiply(b3, c3))))), multiply(b3, c3)))), c3))
% 0.19/0.66 = { by lemma 11 }
% 0.19/0.66 tuple(divide(X, X), a2, multiply(inverse(divide(divide(divide(Z, Z), b3), divide(divide(a3, inverse(multiply(b3, c3))), multiply(b3, c3)))), c3))
% 0.19/0.66 = { by axiom 1 (multiply) R->L }
% 0.19/0.66 tuple(divide(X, X), a2, multiply(inverse(divide(divide(divide(Z, Z), b3), divide(multiply(a3, multiply(b3, c3)), multiply(b3, c3)))), c3))
% 0.19/0.66 = { by lemma 10 }
% 0.19/0.66 tuple(divide(X, X), a2, multiply(a3, multiply(b3, c3)))
% 0.19/0.66 = { by lemma 14 R->L }
% 0.19/0.66 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 0.19/0.66 % SZS output end Proof
% 0.19/0.66
% 0.19/0.66 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------