TSTP Solution File: GRP477-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP477-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n012.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 01:18:35 EDT 2023
% Result : Unsatisfiable 0.20s 0.69s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP477-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n012.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon Aug 28 23:28:24 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.20/0.69 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.69
% 0.20/0.69 % SZS status Unsatisfiable
% 0.20/0.69
% 0.20/0.73 % SZS output start Proof
% 0.20/0.73 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.20/0.73 Axiom 2 (single_axiom): divide(inverse(divide(divide(divide(X, Y), Z), divide(W, Z))), divide(Y, X)) = W.
% 0.20/0.73
% 0.20/0.73 Lemma 3: divide(inverse(divide(multiply(divide(X, Y), Z), multiply(W, Z))), divide(Y, X)) = W.
% 0.20/0.73 Proof:
% 0.20/0.73 divide(inverse(divide(multiply(divide(X, Y), Z), multiply(W, Z))), divide(Y, X))
% 0.20/0.73 = { by axiom 1 (multiply) }
% 0.20/0.73 divide(inverse(divide(multiply(divide(X, Y), Z), divide(W, inverse(Z)))), divide(Y, X))
% 0.20/0.73 = { by axiom 1 (multiply) }
% 0.20/0.73 divide(inverse(divide(divide(divide(X, Y), inverse(Z)), divide(W, inverse(Z)))), divide(Y, X))
% 0.20/0.73 = { by axiom 2 (single_axiom) }
% 0.20/0.73 W
% 0.20/0.73
% 0.20/0.73 Lemma 4: multiply(inverse(divide(divide(multiply(divide(X, Y), divide(multiply(divide(Y, X), Z), multiply(inverse(W), Z))), V), divide(U, V))), W) = U.
% 0.20/0.73 Proof:
% 0.20/0.73 multiply(inverse(divide(divide(multiply(divide(X, Y), divide(multiply(divide(Y, X), Z), multiply(inverse(W), Z))), V), divide(U, V))), W)
% 0.20/0.73 = { by axiom 1 (multiply) }
% 0.20/0.73 divide(inverse(divide(divide(multiply(divide(X, Y), divide(multiply(divide(Y, X), Z), multiply(inverse(W), Z))), V), divide(U, V))), inverse(W))
% 0.20/0.73 = { by axiom 1 (multiply) }
% 0.20/0.73 divide(inverse(divide(divide(divide(divide(X, Y), inverse(divide(multiply(divide(Y, X), Z), multiply(inverse(W), Z)))), V), divide(U, V))), inverse(W))
% 0.20/0.73 = { by lemma 3 R->L }
% 0.20/0.73 divide(inverse(divide(divide(divide(divide(X, Y), inverse(divide(multiply(divide(Y, X), Z), multiply(inverse(W), Z)))), V), divide(U, V))), divide(inverse(divide(multiply(divide(Y, X), Z), multiply(inverse(W), Z))), divide(X, Y)))
% 0.20/0.73 = { by axiom 2 (single_axiom) }
% 0.20/0.73 U
% 0.20/0.73
% 0.20/0.73 Lemma 5: inverse(divide(multiply(divide(X, Y), Z), multiply(divide(W, divide(Y, X)), Z))) = W.
% 0.20/0.73 Proof:
% 0.20/0.73 inverse(divide(multiply(divide(X, Y), Z), multiply(divide(W, divide(Y, X)), Z)))
% 0.20/0.73 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.73 divide(inverse(divide(divide(divide(V, U), divide(Y, X)), divide(inverse(divide(multiply(divide(X, Y), Z), multiply(divide(W, divide(Y, X)), Z))), divide(Y, X)))), divide(U, V))
% 0.20/0.73 = { by lemma 3 }
% 0.20/0.73 divide(inverse(divide(divide(divide(V, U), divide(Y, X)), divide(W, divide(Y, X)))), divide(U, V))
% 0.20/0.73 = { by axiom 2 (single_axiom) }
% 0.20/0.73 W
% 0.20/0.73
% 0.20/0.73 Lemma 6: divide(X, multiply(divide(Y, Z), divide(multiply(divide(Z, Y), W), multiply(divide(V, U), W)))) = divide(X, divide(U, V)).
% 0.20/0.73 Proof:
% 0.20/0.73 divide(X, multiply(divide(Y, Z), divide(multiply(divide(Z, Y), W), multiply(divide(V, U), W))))
% 0.20/0.73 = { by lemma 5 R->L }
% 0.20/0.73 divide(inverse(divide(multiply(divide(V, U), T), multiply(divide(X, divide(U, V)), T))), multiply(divide(Y, Z), divide(multiply(divide(Z, Y), W), multiply(divide(V, U), W))))
% 0.20/0.73 = { by axiom 1 (multiply) }
% 0.20/0.73 divide(inverse(divide(multiply(divide(V, U), T), multiply(divide(X, divide(U, V)), T))), divide(divide(Y, Z), inverse(divide(multiply(divide(Z, Y), W), multiply(divide(V, U), W)))))
% 0.20/0.73 = { by lemma 3 R->L }
% 0.20/0.73 divide(inverse(divide(multiply(divide(inverse(divide(multiply(divide(Z, Y), W), multiply(divide(V, U), W))), divide(Y, Z)), T), multiply(divide(X, divide(U, V)), T))), divide(divide(Y, Z), inverse(divide(multiply(divide(Z, Y), W), multiply(divide(V, U), W)))))
% 0.20/0.73 = { by lemma 3 }
% 0.20/0.73 divide(X, divide(U, V))
% 0.20/0.73
% 0.20/0.73 Lemma 7: multiply(divide(X, Y), divide(multiply(divide(Y, X), Z), multiply(divide(W, V), Z))) = divide(V, W).
% 0.20/0.73 Proof:
% 0.20/0.73 multiply(divide(X, Y), divide(multiply(divide(Y, X), Z), multiply(divide(W, V), Z)))
% 0.20/0.73 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.73 divide(inverse(divide(divide(divide(U, T), S), divide(multiply(divide(X, Y), divide(multiply(divide(Y, X), Z), multiply(divide(W, V), Z))), S))), divide(T, U))
% 0.20/0.73 = { by lemma 6 R->L }
% 0.20/0.73 divide(inverse(divide(divide(divide(U, T), S), multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(S, multiply(divide(X, Y), divide(multiply(divide(Y, X), Z), multiply(divide(W, V), Z)))), Z2))))), divide(T, U))
% 0.20/0.73 = { by lemma 6 }
% 0.20/0.73 divide(inverse(divide(divide(divide(U, T), S), multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(S, divide(V, W)), Z2))))), divide(T, U))
% 0.20/0.73 = { by lemma 6 }
% 0.20/0.73 divide(inverse(divide(divide(divide(U, T), S), divide(divide(V, W), S))), divide(T, U))
% 0.20/0.73 = { by axiom 2 (single_axiom) }
% 0.20/0.73 divide(V, W)
% 0.20/0.73
% 0.20/0.73 Lemma 8: inverse(divide(multiply(X, W), multiply(Z, W))) = inverse(divide(multiply(X, Y), multiply(Z, Y))).
% 0.20/0.73 Proof:
% 0.20/0.73 inverse(divide(multiply(X, W), multiply(Z, W)))
% 0.20/0.73 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.73 inverse(divide(multiply(divide(inverse(divide(divide(divide(V, U), T), divide(X, T))), divide(U, V)), W), multiply(Z, W)))
% 0.20/0.73 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.73 divide(inverse(divide(divide(divide(S, X2), divide(divide(U, V), inverse(divide(divide(divide(V, U), T), divide(X, T))))), divide(inverse(divide(multiply(divide(inverse(divide(divide(divide(V, U), T), divide(X, T))), divide(U, V)), W), multiply(Z, W))), divide(divide(U, V), inverse(divide(divide(divide(V, U), T), divide(X, T))))))), divide(X2, S))
% 0.20/0.73 = { by lemma 3 }
% 0.20/0.73 divide(inverse(divide(divide(divide(S, X2), divide(divide(U, V), inverse(divide(divide(divide(V, U), T), divide(X, T))))), Z)), divide(X2, S))
% 0.20/0.73 = { by lemma 3 R->L }
% 0.20/0.73 divide(inverse(divide(divide(divide(S, X2), divide(divide(U, V), inverse(divide(divide(divide(V, U), T), divide(X, T))))), divide(inverse(divide(multiply(divide(inverse(divide(divide(divide(V, U), T), divide(X, T))), divide(U, V)), Y), multiply(Z, Y))), divide(divide(U, V), inverse(divide(divide(divide(V, U), T), divide(X, T))))))), divide(X2, S))
% 0.20/0.73 = { by axiom 2 (single_axiom) }
% 0.20/0.73 inverse(divide(multiply(divide(inverse(divide(divide(divide(V, U), T), divide(X, T))), divide(U, V)), Y), multiply(Z, Y)))
% 0.20/0.73 = { by axiom 2 (single_axiom) }
% 0.20/0.73 inverse(divide(multiply(X, Y), multiply(Z, Y)))
% 0.20/0.73
% 0.20/0.73 Lemma 9: multiply(X, divide(multiply(divide(Y, Z), W), multiply(divide(V, divide(Z, Y)), W))) = divide(X, V).
% 0.20/0.73 Proof:
% 0.20/0.73 multiply(X, divide(multiply(divide(Y, Z), W), multiply(divide(V, divide(Z, Y)), W)))
% 0.20/0.73 = { by axiom 1 (multiply) }
% 0.20/0.73 divide(X, inverse(divide(multiply(divide(Y, Z), W), multiply(divide(V, divide(Z, Y)), W))))
% 0.20/0.73 = { by lemma 5 }
% 0.20/0.73 divide(X, V)
% 0.20/0.73
% 0.20/0.73 Lemma 10: multiply(X, divide(multiply(Y, Z), multiply(Y, Z))) = X.
% 0.20/0.73 Proof:
% 0.20/0.73 multiply(X, divide(multiply(Y, Z), multiply(Y, Z)))
% 0.20/0.73 = { by lemma 4 R->L }
% 0.20/0.73 multiply(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), divide(multiply(Y, Z), multiply(Y, Z)))
% 0.20/0.73 = { by axiom 1 (multiply) }
% 0.20/0.73 divide(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), inverse(divide(multiply(Y, Z), multiply(Y, Z))))
% 0.20/0.73 = { by lemma 7 R->L }
% 0.20/0.73 multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(inverse(divide(multiply(Y, Z), multiply(Y, Z))), multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T)), Z2)))
% 0.20/0.73 = { by lemma 8 }
% 0.20/0.73 multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(inverse(divide(multiply(Y, divide(multiply(divide(W2, V2), U2), multiply(divide(T2, divide(V2, W2)), U2))), multiply(Y, divide(multiply(divide(W2, V2), U2), multiply(divide(T2, divide(V2, W2)), U2))))), multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T)), Z2)))
% 0.20/0.73 = { by lemma 9 }
% 0.20/0.73 multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(inverse(divide(divide(Y, T2), multiply(Y, divide(multiply(divide(W2, V2), U2), multiply(divide(T2, divide(V2, W2)), U2))))), multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T)), Z2)))
% 0.20/0.73 = { by lemma 9 }
% 0.20/0.73 multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(inverse(divide(divide(Y, T2), divide(Y, T2))), multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T)), Z2)))
% 0.20/0.74 = { by lemma 7 R->L }
% 0.20/0.74 multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(inverse(divide(divide(Y, T2), multiply(divide(inverse(T), inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S)))), divide(multiply(divide(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), inverse(T)), S2), multiply(divide(T2, Y), S2))))), multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T)), Z2)))
% 0.20/0.74 = { by axiom 1 (multiply) R->L }
% 0.20/0.74 multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(inverse(divide(divide(Y, T2), multiply(divide(inverse(T), inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S)))), divide(multiply(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), S2), multiply(divide(T2, Y), S2))))), multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T)), Z2)))
% 0.20/0.74 = { by lemma 3 R->L }
% 0.20/0.74 multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(inverse(divide(divide(Y, T2), multiply(divide(inverse(T), inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S)))), divide(multiply(divide(inverse(divide(multiply(divide(X3, Y3), Z3), multiply(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), Z3))), divide(Y3, X3)), S2), multiply(divide(T2, Y), S2))))), multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T)), Z2)))
% 0.20/0.74 = { by lemma 7 R->L }
% 0.20/0.74 multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(inverse(divide(multiply(divide(divide(Y3, X3), inverse(divide(multiply(divide(X3, Y3), Z3), multiply(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), Z3)))), divide(multiply(divide(inverse(divide(multiply(divide(X3, Y3), Z3), multiply(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), Z3))), divide(Y3, X3)), S2), multiply(divide(T2, Y), S2))), multiply(divide(inverse(T), inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S)))), divide(multiply(divide(inverse(divide(multiply(divide(X3, Y3), Z3), multiply(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), Z3))), divide(Y3, X3)), S2), multiply(divide(T2, Y), S2))))), multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T)), Z2)))
% 0.20/0.74 = { by lemma 3 R->L }
% 0.20/0.74 multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(inverse(divide(multiply(divide(divide(Y3, X3), inverse(divide(multiply(divide(X3, Y3), Z3), multiply(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), Z3)))), divide(multiply(divide(inverse(divide(multiply(divide(X3, Y3), Z3), multiply(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), Z3))), divide(Y3, X3)), S2), multiply(divide(T2, Y), S2))), multiply(divide(inverse(T), inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S)))), divide(multiply(divide(inverse(divide(multiply(divide(X3, Y3), Z3), multiply(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), Z3))), divide(Y3, X3)), S2), multiply(divide(T2, Y), S2))))), divide(inverse(divide(multiply(divide(X3, Y3), Z3), multiply(multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T), Z3))), divide(Y3, X3))), Z2)))
% 0.20/0.74 = { by lemma 3 }
% 0.20/0.74 multiply(divide(X2, Y2), divide(multiply(divide(Y2, X2), Z2), multiply(divide(inverse(T), inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S)))), Z2)))
% 0.20/0.74 = { by lemma 7 }
% 0.20/0.74 divide(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), inverse(T))
% 0.20/0.74 = { by axiom 1 (multiply) R->L }
% 0.20/0.74 multiply(inverse(divide(divide(multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(inverse(T), U))), S), divide(X, S))), T)
% 0.20/0.74 = { by lemma 4 }
% 0.20/0.74 X
% 0.20/0.74
% 0.20/0.74 Lemma 11: multiply(X, divide(multiply(Y, Z), multiply(W, Z))) = multiply(X, divide(Y, W)).
% 0.20/0.74 Proof:
% 0.20/0.74 multiply(X, divide(multiply(Y, Z), multiply(W, Z)))
% 0.20/0.74 = { by axiom 1 (multiply) }
% 0.20/0.74 divide(X, inverse(divide(multiply(Y, Z), multiply(W, Z))))
% 0.20/0.74 = { by lemma 8 }
% 0.20/0.74 divide(X, inverse(divide(multiply(Y, divide(multiply(V, U), multiply(V, U))), multiply(W, divide(multiply(V, U), multiply(V, U))))))
% 0.20/0.74 = { by axiom 1 (multiply) R->L }
% 0.20/0.74 multiply(X, divide(multiply(Y, divide(multiply(V, U), multiply(V, U))), multiply(W, divide(multiply(V, U), multiply(V, U)))))
% 0.20/0.74 = { by lemma 10 }
% 0.20/0.74 multiply(X, divide(Y, multiply(W, divide(multiply(V, U), multiply(V, U)))))
% 0.20/0.74 = { by lemma 10 }
% 0.20/0.74 multiply(X, divide(Y, W))
% 0.20/0.74
% 0.20/0.74 Lemma 12: multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W))) = divide(W, Z).
% 0.20/0.74 Proof:
% 0.20/0.74 multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W)))
% 0.20/0.74 = { by lemma 11 R->L }
% 0.20/0.74 multiply(divide(X, Y), divide(multiply(divide(Y, X), V), multiply(divide(Z, W), V)))
% 0.20/0.74 = { by lemma 7 }
% 0.20/0.74 divide(W, Z)
% 0.20/0.74
% 0.20/0.74 Lemma 13: multiply(divide(X, Y), multiply(Y, Z)) = multiply(X, Z).
% 0.20/0.74 Proof:
% 0.20/0.74 multiply(divide(X, Y), multiply(Y, Z))
% 0.20/0.74 = { by axiom 1 (multiply) }
% 0.20/0.74 multiply(divide(X, Y), divide(Y, inverse(Z)))
% 0.20/0.74 = { by lemma 11 R->L }
% 0.20/0.74 multiply(divide(X, Y), divide(multiply(Y, divide(multiply(divide(W, V), U), multiply(divide(X, divide(V, W)), U))), multiply(inverse(Z), divide(multiply(divide(W, V), U), multiply(divide(X, divide(V, W)), U)))))
% 0.20/0.74 = { by lemma 9 }
% 0.20/0.74 multiply(divide(X, Y), divide(divide(Y, X), multiply(inverse(Z), divide(multiply(divide(W, V), U), multiply(divide(X, divide(V, W)), U)))))
% 0.20/0.74 = { by lemma 9 }
% 0.20/0.74 multiply(divide(X, Y), divide(divide(Y, X), divide(inverse(Z), X)))
% 0.20/0.74 = { by lemma 12 }
% 0.20/0.74 divide(X, inverse(Z))
% 0.20/0.74 = { by axiom 1 (multiply) R->L }
% 0.20/0.74 multiply(X, Z)
% 0.20/0.74
% 0.20/0.74 Lemma 14: multiply(divide(X, Y), Y) = X.
% 0.20/0.74 Proof:
% 0.20/0.74 multiply(divide(X, Y), Y)
% 0.20/0.74 = { by lemma 10 R->L }
% 0.20/0.74 multiply(divide(X, Y), multiply(Y, divide(multiply(Z, W), multiply(Z, W))))
% 0.20/0.74 = { by lemma 13 }
% 0.20/0.74 multiply(X, divide(multiply(Z, W), multiply(Z, W)))
% 0.20/0.74 = { by lemma 10 }
% 0.20/0.74 X
% 0.20/0.74
% 0.20/0.74 Lemma 15: divide(X, divide(Y, Y)) = X.
% 0.20/0.74 Proof:
% 0.20/0.74 divide(X, divide(Y, Y))
% 0.20/0.74 = { by lemma 10 R->L }
% 0.20/0.74 multiply(divide(X, divide(Y, Y)), divide(multiply(inverse(divide(divide(multiply(divide(Z, W), divide(multiply(divide(W, Z), V), multiply(inverse(U), V))), T), divide(Y, T))), U), multiply(inverse(divide(divide(multiply(divide(Z, W), divide(multiply(divide(W, Z), V), multiply(inverse(U), V))), T), divide(Y, T))), U)))
% 0.20/0.74 = { by lemma 4 }
% 0.20/0.74 multiply(divide(X, divide(Y, Y)), divide(Y, multiply(inverse(divide(divide(multiply(divide(Z, W), divide(multiply(divide(W, Z), V), multiply(inverse(U), V))), T), divide(Y, T))), U)))
% 0.20/0.74 = { by lemma 4 }
% 0.20/0.74 multiply(divide(X, divide(Y, Y)), divide(Y, Y))
% 0.20/0.74 = { by lemma 14 }
% 0.20/0.74 X
% 0.20/0.74
% 0.20/0.74 Lemma 16: multiply(divide(X, X), Y) = Y.
% 0.20/0.74 Proof:
% 0.20/0.74 multiply(divide(X, X), Y)
% 0.20/0.74 = { by lemma 12 R->L }
% 0.20/0.74 multiply(multiply(divide(Z, W), divide(divide(W, Z), divide(X, X))), Y)
% 0.20/0.74 = { by lemma 15 }
% 0.20/0.74 multiply(multiply(divide(Z, W), divide(W, Z)), Y)
% 0.20/0.74 = { by lemma 15 R->L }
% 0.20/0.74 multiply(multiply(divide(Z, W), divide(divide(W, Z), divide(Y, Y))), Y)
% 0.20/0.74 = { by lemma 12 }
% 0.20/0.74 multiply(divide(Y, Y), Y)
% 0.20/0.74 = { by lemma 14 }
% 0.20/0.74 Y
% 0.20/0.74
% 0.20/0.74 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.74 Proof:
% 0.20/0.74 multiply(multiply(a3, b3), c3)
% 0.20/0.74 = { by lemma 13 R->L }
% 0.20/0.74 multiply(divide(multiply(a3, b3), b3), multiply(b3, c3))
% 0.20/0.74 = { by lemma 16 R->L }
% 0.20/0.74 multiply(multiply(divide(X, X), divide(multiply(a3, b3), b3)), multiply(b3, c3))
% 0.20/0.74 = { by lemma 16 R->L }
% 0.20/0.74 multiply(multiply(divide(X, X), divide(multiply(a3, b3), multiply(divide(Y, Y), b3))), multiply(b3, c3))
% 0.20/0.74 = { by lemma 11 }
% 0.20/0.74 multiply(multiply(divide(X, X), divide(a3, divide(Y, Y))), multiply(b3, c3))
% 0.20/0.74 = { by lemma 15 }
% 0.20/0.74 multiply(multiply(divide(X, X), a3), multiply(b3, c3))
% 0.20/0.74 = { by lemma 16 }
% 0.20/0.74 multiply(a3, multiply(b3, c3))
% 0.20/0.74 % SZS output end Proof
% 0.20/0.74
% 0.20/0.74 RESULT: Unsatisfiable (the axioms are contradictory).
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