TSTP Solution File: GRP474-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP474-1 : 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 : n006.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 01:18:34 EDT 2023
% Result : Unsatisfiable 1.37s 0.62s
% Output : Proof 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP474-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 19:35:51 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.37/0.62 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 1.37/0.62
% 1.37/0.62 % SZS status Unsatisfiable
% 1.37/0.62
% 2.33/0.67 % SZS output start Proof
% 2.33/0.67 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 2.33/0.67 Axiom 2 (single_axiom): divide(divide(inverse(divide(X, Y)), divide(divide(Z, W), X)), divide(W, Z)) = Y.
% 2.33/0.67
% 2.33/0.67 Lemma 3: divide(divide(inverse(divide(divide(X, Y), Z)), W), multiply(divide(divide(Y, X), V), divide(V, W))) = Z.
% 2.33/0.67 Proof:
% 2.33/0.67 divide(divide(inverse(divide(divide(X, Y), Z)), W), multiply(divide(divide(Y, X), V), divide(V, W)))
% 2.33/0.67 = { by axiom 1 (multiply) }
% 2.33/0.67 divide(divide(inverse(divide(divide(X, Y), Z)), W), divide(divide(divide(Y, X), V), inverse(divide(V, W))))
% 2.33/0.67 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.67 divide(divide(inverse(divide(divide(X, Y), Z)), divide(divide(inverse(divide(V, W)), divide(divide(Y, X), V)), divide(X, Y))), divide(divide(divide(Y, X), V), inverse(divide(V, W))))
% 2.33/0.67 = { by axiom 2 (single_axiom) }
% 2.33/0.67 Z
% 2.33/0.67
% 2.33/0.67 Lemma 4: divide(multiply(inverse(X), Y), multiply(divide(multiply(divide(divide(Z, W), V), divide(V, X)), U), multiply(U, Y))) = divide(W, Z).
% 2.33/0.67 Proof:
% 2.33/0.67 divide(multiply(inverse(X), Y), multiply(divide(multiply(divide(divide(Z, W), V), divide(V, X)), U), multiply(U, Y)))
% 2.33/0.67 = { by axiom 1 (multiply) }
% 2.33/0.67 divide(multiply(inverse(X), Y), multiply(divide(divide(divide(divide(Z, W), V), inverse(divide(V, X))), U), multiply(U, Y)))
% 2.33/0.67 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.67 divide(multiply(inverse(divide(divide(inverse(divide(V, X)), divide(divide(Z, W), V)), divide(W, Z))), Y), multiply(divide(divide(divide(divide(Z, W), V), inverse(divide(V, X))), U), multiply(U, Y)))
% 2.33/0.67 = { by axiom 1 (multiply) }
% 2.33/0.67 divide(multiply(inverse(divide(divide(inverse(divide(V, X)), divide(divide(Z, W), V)), divide(W, Z))), Y), multiply(divide(divide(divide(divide(Z, W), V), inverse(divide(V, X))), U), divide(U, inverse(Y))))
% 2.33/0.67 = { by axiom 1 (multiply) }
% 2.33/0.67 divide(divide(inverse(divide(divide(inverse(divide(V, X)), divide(divide(Z, W), V)), divide(W, Z))), inverse(Y)), multiply(divide(divide(divide(divide(Z, W), V), inverse(divide(V, X))), U), divide(U, inverse(Y))))
% 2.33/0.67 = { by lemma 3 }
% 2.33/0.67 divide(W, Z)
% 2.33/0.67
% 2.33/0.67 Lemma 5: divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), multiply(W, V)), multiply(inverse(Z), V)) = X.
% 2.33/0.67 Proof:
% 2.33/0.67 divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), multiply(W, V)), multiply(inverse(Z), V))
% 2.33/0.67 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.67 divide(multiply(divide(multiply(divide(divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T)), Y), divide(Y, Z)), W), multiply(W, V)), multiply(inverse(Z), V))
% 2.33/0.67 = { by lemma 4 R->L }
% 2.33/0.67 divide(multiply(inverse(X2), Y2), multiply(divide(multiply(divide(divide(multiply(inverse(Z), V), multiply(divide(multiply(divide(divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T)), Y), divide(Y, Z)), W), multiply(W, V))), Z2), divide(Z2, X2)), W2), multiply(W2, Y2)))
% 2.33/0.67 = { by lemma 4 }
% 2.33/0.67 divide(multiply(inverse(X2), Y2), multiply(divide(multiply(divide(divide(divide(S, T), divide(inverse(divide(U, X)), divide(divide(T, S), U))), Z2), divide(Z2, X2)), W2), multiply(W2, Y2)))
% 2.33/0.67 = { by lemma 4 }
% 2.33/0.67 divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T))
% 2.33/0.67 = { by axiom 2 (single_axiom) }
% 2.33/0.67 X
% 2.33/0.67
% 2.33/0.67 Lemma 6: divide(divide(inverse(X), Y), multiply(divide(multiply(divide(divide(Z, W), V), divide(V, X)), U), divide(U, Y))) = divide(W, Z).
% 2.33/0.67 Proof:
% 2.33/0.67 divide(divide(inverse(X), Y), multiply(divide(multiply(divide(divide(Z, W), V), divide(V, X)), U), divide(U, Y)))
% 2.33/0.67 = { by axiom 1 (multiply) }
% 2.33/0.67 divide(divide(inverse(X), Y), multiply(divide(divide(divide(divide(Z, W), V), inverse(divide(V, X))), U), divide(U, Y)))
% 2.33/0.67 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.67 divide(divide(inverse(divide(divide(inverse(divide(V, X)), divide(divide(Z, W), V)), divide(W, Z))), Y), multiply(divide(divide(divide(divide(Z, W), V), inverse(divide(V, X))), U), divide(U, Y)))
% 2.33/0.67 = { by lemma 3 }
% 2.33/0.67 divide(W, Z)
% 2.33/0.67
% 2.33/0.67 Lemma 7: divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), divide(W, V)), divide(inverse(Z), V)) = X.
% 2.33/0.67 Proof:
% 2.33/0.67 divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), divide(W, V)), divide(inverse(Z), V))
% 2.33/0.67 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.67 divide(multiply(divide(multiply(divide(divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T)), Y), divide(Y, Z)), W), divide(W, V)), divide(inverse(Z), V))
% 2.33/0.67 = { by lemma 6 R->L }
% 2.33/0.67 divide(divide(inverse(X2), Y2), multiply(divide(multiply(divide(divide(divide(inverse(Z), V), multiply(divide(multiply(divide(divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T)), Y), divide(Y, Z)), W), divide(W, V))), Z2), divide(Z2, X2)), W2), divide(W2, Y2)))
% 2.33/0.67 = { by lemma 6 }
% 2.33/0.67 divide(divide(inverse(X2), Y2), multiply(divide(multiply(divide(divide(divide(S, T), divide(inverse(divide(U, X)), divide(divide(T, S), U))), Z2), divide(Z2, X2)), W2), divide(W2, Y2)))
% 2.33/0.67 = { by lemma 6 }
% 2.33/0.67 divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T))
% 2.33/0.67 = { by axiom 2 (single_axiom) }
% 2.33/0.67 X
% 2.33/0.67
% 2.33/0.67 Lemma 8: multiply(divide(X, W), divide(W, Z)) = multiply(divide(X, Y), divide(Y, Z)).
% 2.33/0.67 Proof:
% 2.33/0.67 multiply(divide(X, W), divide(W, Z))
% 2.33/0.67 = { by lemma 5 R->L }
% 2.33/0.67 divide(multiply(divide(multiply(divide(multiply(divide(X, W), divide(W, Z)), S), divide(S, U)), divide(inverse(Z), U)), multiply(divide(inverse(Z), U), T)), multiply(inverse(U), T))
% 2.33/0.67 = { by lemma 7 }
% 2.33/0.67 divide(multiply(X, multiply(divide(inverse(Z), U), T)), multiply(inverse(U), T))
% 2.33/0.67 = { by lemma 7 R->L }
% 2.33/0.67 divide(multiply(divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), V), divide(V, U)), divide(inverse(Z), U)), multiply(divide(inverse(Z), U), T)), multiply(inverse(U), T))
% 2.33/0.67 = { by lemma 5 }
% 2.33/0.67 multiply(divide(X, Y), divide(Y, Z))
% 2.33/0.67
% 2.33/0.67 Lemma 9: multiply(multiply(X, Y), divide(inverse(Y), Z)) = multiply(divide(X, W), divide(W, Z)).
% 2.33/0.67 Proof:
% 2.33/0.67 multiply(multiply(X, Y), divide(inverse(Y), Z))
% 2.33/0.67 = { by axiom 1 (multiply) }
% 2.33/0.67 multiply(divide(X, inverse(Y)), divide(inverse(Y), Z))
% 2.33/0.67 = { by lemma 8 R->L }
% 2.33/0.67 multiply(divide(X, W), divide(W, Z))
% 2.33/0.67
% 2.33/0.67 Lemma 10: multiply(divide(divide(X, Y), Z), divide(Z, divide(divide(W, V), divide(Y, X)))) = divide(V, W).
% 2.33/0.67 Proof:
% 2.33/0.67 multiply(divide(divide(X, Y), Z), divide(Z, divide(divide(W, V), divide(Y, X))))
% 2.33/0.67 = { by lemma 3 R->L }
% 2.33/0.67 divide(divide(inverse(divide(divide(inverse(divide(divide(Y, X), U)), divide(divide(W, V), divide(Y, X))), multiply(divide(divide(X, Y), Z), divide(Z, divide(divide(W, V), divide(Y, X)))))), T), multiply(divide(divide(divide(divide(W, V), divide(Y, X)), inverse(divide(divide(Y, X), U))), S), divide(S, T)))
% 2.33/0.67 = { by lemma 3 }
% 2.33/0.67 divide(divide(inverse(U), T), multiply(divide(divide(divide(divide(W, V), divide(Y, X)), inverse(divide(divide(Y, X), U))), S), divide(S, T)))
% 2.33/0.67 = { by axiom 1 (multiply) R->L }
% 2.33/0.67 divide(divide(inverse(U), T), multiply(divide(multiply(divide(divide(W, V), divide(Y, X)), divide(divide(Y, X), U)), S), divide(S, T)))
% 2.33/0.67 = { by lemma 6 }
% 2.33/0.67 divide(V, W)
% 2.33/0.67
% 2.33/0.67 Lemma 11: divide(inverse(divide(X, Y)), divide(multiply(divide(Z, W), divide(W, V)), X)) = multiply(divide(multiply(Y, V), U), divide(U, Z)).
% 2.33/0.67 Proof:
% 2.33/0.67 divide(inverse(divide(X, Y)), divide(multiply(divide(Z, W), divide(W, V)), X))
% 2.33/0.67 = { by lemma 10 R->L }
% 2.33/0.67 multiply(divide(divide(Y, inverse(V)), U), divide(U, divide(divide(divide(multiply(divide(Z, W), divide(W, V)), X), inverse(divide(X, Y))), divide(inverse(V), Y))))
% 2.33/0.67 = { by axiom 1 (multiply) R->L }
% 2.33/0.67 multiply(divide(divide(Y, inverse(V)), U), divide(U, divide(multiply(divide(multiply(divide(Z, W), divide(W, V)), X), divide(X, Y)), divide(inverse(V), Y))))
% 2.33/0.67 = { by lemma 7 }
% 2.33/0.67 multiply(divide(divide(Y, inverse(V)), U), divide(U, Z))
% 2.33/0.67 = { by axiom 1 (multiply) R->L }
% 2.33/0.67 multiply(divide(multiply(Y, V), U), divide(U, Z))
% 2.33/0.67
% 2.33/0.67 Lemma 12: divide(multiply(divide(multiply(X, Y), Z), divide(Z, multiply(W, V))), multiply(divide(multiply(divide(Y, U), divide(U, V)), T), divide(T, W))) = X.
% 2.33/0.67 Proof:
% 2.33/0.67 divide(multiply(divide(multiply(X, Y), Z), divide(Z, multiply(W, V))), multiply(divide(multiply(divide(Y, U), divide(U, V)), T), divide(T, W)))
% 2.33/0.67 = { by axiom 1 (multiply) }
% 2.33/0.67 divide(multiply(divide(multiply(X, Y), Z), divide(Z, multiply(W, V))), divide(divide(multiply(divide(Y, U), divide(U, V)), T), inverse(divide(T, W))))
% 2.33/0.67 = { by lemma 11 R->L }
% 2.33/0.67 divide(divide(inverse(divide(S, X)), divide(multiply(divide(multiply(W, V), X2), divide(X2, Y)), S)), divide(divide(multiply(divide(Y, U), divide(U, V)), T), inverse(divide(T, W))))
% 2.33/0.67 = { by lemma 11 R->L }
% 2.33/0.67 divide(divide(inverse(divide(S, X)), divide(divide(inverse(divide(T, W)), divide(multiply(divide(Y, U), divide(U, V)), T)), S)), divide(divide(multiply(divide(Y, U), divide(U, V)), T), inverse(divide(T, W))))
% 2.33/0.67 = { by axiom 2 (single_axiom) }
% 2.33/0.67 X
% 2.33/0.67
% 2.33/0.67 Lemma 13: divide(multiply(divide(multiply(X, divide(Y, divide(Z, W))), V), divide(V, divide(W, Z))), Y) = X.
% 2.33/0.67 Proof:
% 2.33/0.67 divide(multiply(divide(multiply(X, divide(Y, divide(Z, W))), V), divide(V, divide(W, Z))), Y)
% 2.33/0.67 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.67 divide(multiply(divide(multiply(X, divide(Y, divide(Z, W))), V), divide(V, divide(W, Z))), divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T)))
% 2.33/0.67 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.67 divide(multiply(divide(multiply(X, divide(divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T)), divide(Z, W))), V), divide(V, divide(W, Z))), divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T)))
% 2.33/0.67 = { by lemma 10 R->L }
% 2.33/0.68 divide(multiply(divide(multiply(X, divide(divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T)), divide(Z, W))), V), divide(V, multiply(divide(divide(divide(S, T), divide(inverse(divide(U, Y)), divide(divide(T, S), U))), divide(X2, Y2)), divide(divide(X2, Y2), divide(divide(Z, W), divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T))))))), divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T)))
% 2.33/0.68 = { by lemma 10 R->L }
% 2.33/0.68 divide(multiply(divide(multiply(X, divide(divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T)), divide(Z, W))), V), divide(V, multiply(divide(divide(divide(S, T), divide(inverse(divide(U, Y)), divide(divide(T, S), U))), divide(X2, Y2)), divide(divide(X2, Y2), divide(divide(Z, W), divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T))))))), multiply(divide(divide(Y2, X2), Z2), divide(Z2, divide(divide(divide(S, T), divide(inverse(divide(U, Y)), divide(divide(T, S), U))), divide(X2, Y2)))))
% 2.33/0.68 = { by lemma 10 R->L }
% 2.33/0.68 divide(multiply(divide(multiply(X, divide(divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T)), divide(Z, W))), V), divide(V, multiply(divide(divide(divide(S, T), divide(inverse(divide(U, Y)), divide(divide(T, S), U))), divide(X2, Y2)), divide(divide(X2, Y2), divide(divide(Z, W), divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T))))))), multiply(divide(multiply(divide(divide(divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T)), divide(Z, W)), W2), divide(W2, divide(divide(X2, Y2), divide(divide(Z, W), divide(divide(inverse(divide(U, Y)), divide(divide(T, S), U)), divide(S, T)))))), Z2), divide(Z2, divide(divide(divide(S, T), divide(inverse(divide(U, Y)), divide(divide(T, S), U))), divide(X2, Y2)))))
% 2.33/0.68 = { by lemma 12 }
% 2.33/0.68 X
% 2.33/0.68
% 2.33/0.68 Lemma 14: multiply(divide(multiply(divide(X, Y), divide(Y, divide(Z, W))), V), divide(V, divide(W, Z))) = X.
% 2.33/0.68 Proof:
% 2.33/0.68 multiply(divide(multiply(divide(X, Y), divide(Y, divide(Z, W))), V), divide(V, divide(W, Z)))
% 2.33/0.68 = { by lemma 12 R->L }
% 2.33/0.68 divide(multiply(divide(multiply(multiply(divide(multiply(divide(X, Y), divide(Y, divide(Z, W))), V), divide(V, divide(W, Z))), U), T), divide(T, multiply(S, X2))), multiply(divide(multiply(divide(U, Y2), divide(Y2, X2)), Z2), divide(Z2, S)))
% 2.33/0.68 = { by axiom 1 (multiply) }
% 2.33/0.68 divide(multiply(divide(divide(multiply(divide(multiply(divide(X, Y), divide(Y, divide(Z, W))), V), divide(V, divide(W, Z))), inverse(U)), T), divide(T, multiply(S, X2))), multiply(divide(multiply(divide(U, Y2), divide(Y2, X2)), Z2), divide(Z2, S)))
% 2.33/0.68 = { by lemma 9 R->L }
% 2.33/0.68 divide(multiply(divide(divide(multiply(divide(multiply(multiply(X, U), divide(inverse(U), divide(Z, W))), V), divide(V, divide(W, Z))), inverse(U)), T), divide(T, multiply(S, X2))), multiply(divide(multiply(divide(U, Y2), divide(Y2, X2)), Z2), divide(Z2, S)))
% 2.33/0.68 = { by lemma 13 }
% 2.33/0.68 divide(multiply(divide(multiply(X, U), T), divide(T, multiply(S, X2))), multiply(divide(multiply(divide(U, Y2), divide(Y2, X2)), Z2), divide(Z2, S)))
% 2.33/0.68 = { by lemma 12 }
% 2.33/0.68 X
% 2.33/0.68
% 2.33/0.68 Lemma 15: multiply(X, multiply(divide(Y, Z), divide(Z, Y))) = X.
% 2.33/0.68 Proof:
% 2.33/0.68 multiply(X, multiply(divide(Y, Z), divide(Z, Y)))
% 2.33/0.68 = { by axiom 1 (multiply) }
% 2.33/0.68 divide(X, inverse(multiply(divide(Y, Z), divide(Z, Y))))
% 2.33/0.68 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.68 divide(divide(inverse(divide(W, divide(X, inverse(multiply(divide(Y, Z), divide(Z, Y)))))), divide(divide(inverse(divide(V, divide(Y, Z))), divide(multiply(divide(divide(inverse(multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y))), U), divide(U, divide(Z, Y))), V)), W)), divide(divide(multiply(divide(divide(inverse(multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y))), U), divide(U, divide(Z, Y))), V), inverse(divide(V, divide(Y, Z)))))
% 2.33/0.68 = { by axiom 1 (multiply) R->L }
% 2.33/0.68 divide(divide(inverse(divide(W, divide(X, inverse(multiply(divide(Y, Z), divide(Z, Y)))))), divide(divide(inverse(divide(V, divide(Y, Z))), divide(multiply(divide(divide(inverse(multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y))), U), divide(U, divide(Z, Y))), V)), W)), multiply(divide(multiply(divide(divide(inverse(multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y))), U), divide(U, divide(Z, Y))), V), divide(V, divide(Y, Z))))
% 2.33/0.68 = { by lemma 14 }
% 2.33/0.68 divide(divide(inverse(divide(W, divide(X, inverse(multiply(divide(Y, Z), divide(Z, Y)))))), divide(divide(inverse(divide(V, divide(Y, Z))), divide(multiply(divide(divide(inverse(multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y))), U), divide(U, divide(Z, Y))), V)), W)), divide(inverse(multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y))))
% 2.33/0.68 = { by lemma 11 }
% 2.33/0.68 divide(divide(inverse(divide(W, divide(X, inverse(multiply(divide(Y, Z), divide(Z, Y)))))), divide(multiply(divide(multiply(divide(Y, Z), divide(Z, Y)), T), divide(T, divide(inverse(multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y))))), W)), divide(inverse(multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y))))
% 2.33/0.68 = { by lemma 11 }
% 2.33/0.68 divide(multiply(divide(multiply(divide(X, inverse(multiply(divide(Y, Z), divide(Z, Y)))), divide(inverse(multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y)))), S), divide(S, multiply(divide(Y, Z), divide(Z, Y)))), divide(inverse(multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y))))
% 2.33/0.68 = { by lemma 7 }
% 2.33/0.68 X
% 2.33/0.68
% 2.33/0.68 Lemma 16: multiply(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), W), Z) = X.
% 2.33/0.68 Proof:
% 2.33/0.68 multiply(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), W), Z)
% 2.33/0.68 = { by axiom 1 (multiply) }
% 2.33/0.68 divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), W), inverse(Z))
% 2.33/0.68 = { by lemma 15 R->L }
% 2.33/0.68 divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), W), multiply(inverse(Z), multiply(divide(V, U), divide(U, V))))
% 2.33/0.68 = { by lemma 15 R->L }
% 2.33/0.68 divide(multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), multiply(W, multiply(divide(V, U), divide(U, V)))), multiply(inverse(Z), multiply(divide(V, U), divide(U, V))))
% 2.33/0.68 = { by lemma 5 }
% 2.33/0.68 X
% 2.33/0.68
% 2.33/0.68 Lemma 17: multiply(divide(X, Y), divide(Y, Z)) = multiply(X, divide(W, multiply(Z, W))).
% 2.33/0.68 Proof:
% 2.33/0.68 multiply(divide(X, Y), divide(Y, Z))
% 2.33/0.68 = { by lemma 9 R->L }
% 2.33/0.68 multiply(multiply(X, W), divide(inverse(W), Z))
% 2.33/0.68 = { by lemma 13 R->L }
% 2.33/0.68 multiply(multiply(divide(multiply(divide(multiply(X, divide(W, divide(Z, inverse(W)))), V), divide(V, divide(inverse(W), Z))), W), W), divide(inverse(W), Z))
% 2.33/0.68 = { by lemma 16 }
% 2.33/0.68 multiply(X, divide(W, divide(Z, inverse(W))))
% 2.33/0.68 = { by axiom 1 (multiply) R->L }
% 2.33/0.68 multiply(X, divide(W, multiply(Z, W)))
% 2.33/0.68
% 2.33/0.68 Lemma 18: multiply(X, multiply(Y, divide(Z, multiply(Y, Z)))) = X.
% 2.33/0.68 Proof:
% 2.33/0.68 multiply(X, multiply(Y, divide(Z, multiply(Y, Z))))
% 2.33/0.68 = { by lemma 17 R->L }
% 2.33/0.68 multiply(X, multiply(divide(Y, W), divide(W, Y)))
% 2.33/0.68 = { by lemma 15 }
% 2.33/0.68 X
% 2.33/0.68
% 2.33/0.68 Lemma 19: multiply(divide(X, Y), Y) = X.
% 2.33/0.68 Proof:
% 2.33/0.68 multiply(divide(X, Y), Y)
% 2.33/0.68 = { by axiom 2 (single_axiom) R->L }
% 2.33/0.68 divide(divide(inverse(divide(Z, multiply(divide(X, Y), Y))), divide(divide(W, V), Z)), divide(V, W))
% 2.33/0.68 = { by lemma 18 R->L }
% 2.33/0.68 divide(divide(inverse(multiply(divide(Z, multiply(divide(X, Y), Y)), multiply(multiply(divide(X, Y), Y), divide(U, multiply(multiply(divide(X, Y), Y), U))))), divide(divide(W, V), Z)), divide(V, W))
% 2.33/0.68 = { by axiom 1 (multiply) }
% 2.33/0.68 divide(divide(inverse(multiply(divide(Z, multiply(divide(X, Y), Y)), divide(multiply(divide(X, Y), Y), inverse(divide(U, multiply(multiply(divide(X, Y), Y), U)))))), divide(divide(W, V), Z)), divide(V, W))
% 2.33/0.68 = { by lemma 8 R->L }
% 2.33/0.68 divide(divide(inverse(multiply(divide(Z, X), divide(X, inverse(divide(U, multiply(multiply(divide(X, Y), Y), U)))))), divide(divide(W, V), Z)), divide(V, W))
% 2.33/0.68 = { by axiom 1 (multiply) R->L }
% 2.33/0.68 divide(divide(inverse(multiply(divide(Z, X), multiply(X, divide(U, multiply(multiply(divide(X, Y), Y), U))))), divide(divide(W, V), Z)), divide(V, W))
% 2.33/0.68 = { by lemma 17 R->L }
% 2.33/0.68 divide(divide(inverse(multiply(divide(Z, X), multiply(divide(X, Y), divide(Y, multiply(divide(X, Y), Y))))), divide(divide(W, V), Z)), divide(V, W))
% 2.33/0.68 = { by lemma 18 }
% 2.33/0.68 divide(divide(inverse(divide(Z, X)), divide(divide(W, V), Z)), divide(V, W))
% 2.33/0.68 = { by axiom 2 (single_axiom) }
% 2.33/0.68 X
% 2.33/0.68
% 2.33/0.68 Lemma 20: divide(multiply(X, Y), Y) = X.
% 2.33/0.68 Proof:
% 2.33/0.68 divide(multiply(X, Y), Y)
% 2.33/0.68 = { by lemma 19 R->L }
% 2.33/0.68 divide(multiply(divide(multiply(X, Y), Z), Z), Y)
% 2.33/0.68 = { by lemma 19 R->L }
% 2.33/0.68 divide(multiply(divide(multiply(X, Y), Z), multiply(divide(Z, multiply(divide(W, V), divide(V, W))), multiply(divide(W, V), divide(V, W)))), Y)
% 2.33/0.68 = { by lemma 14 R->L }
% 2.33/0.68 divide(multiply(divide(multiply(X, Y), Z), multiply(divide(Z, multiply(divide(W, V), divide(V, W))), multiply(divide(W, V), divide(V, W)))), multiply(divide(multiply(divide(Y, U), divide(U, divide(V, W))), T), divide(T, divide(W, V))))
% 2.33/0.68 = { by lemma 15 }
% 2.33/0.68 divide(multiply(divide(multiply(X, Y), Z), divide(Z, multiply(divide(W, V), divide(V, W)))), multiply(divide(multiply(divide(Y, U), divide(U, divide(V, W))), T), divide(T, divide(W, V))))
% 2.33/0.68 = { by lemma 12 }
% 2.33/0.68 X
% 2.33/0.68
% 2.33/0.68 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 2.33/0.68 Proof:
% 2.33/0.68 multiply(multiply(a3, b3), c3)
% 2.33/0.68 = { by axiom 1 (multiply) }
% 2.33/0.68 divide(multiply(a3, b3), inverse(c3))
% 2.33/0.68 = { by lemma 16 R->L }
% 2.33/0.68 divide(multiply(multiply(divide(multiply(divide(multiply(a3, b3), b3), divide(b3, inverse(c3))), X), X), inverse(c3)), inverse(c3))
% 2.33/0.68 = { by lemma 20 }
% 2.33/0.68 multiply(divide(multiply(divide(multiply(a3, b3), b3), divide(b3, inverse(c3))), X), X)
% 2.33/0.68 = { by lemma 19 }
% 2.33/0.68 multiply(divide(multiply(a3, b3), b3), divide(b3, inverse(c3)))
% 2.33/0.68 = { by lemma 20 }
% 2.33/0.68 multiply(a3, divide(b3, inverse(c3)))
% 2.33/0.68 = { by axiom 1 (multiply) R->L }
% 2.33/0.68 multiply(a3, multiply(b3, c3))
% 2.33/0.68 % SZS output end Proof
% 2.33/0.68
% 2.33/0.68 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------