TSTP Solution File: GRP480-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP480-1 : 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 : n010.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 01:18:36 EDT 2023
% Result : Unsatisfiable 0.22s 0.47s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP480-1 : 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
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 02:16:49 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.47 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.47
% 0.22/0.47 % SZS status Unsatisfiable
% 0.22/0.47
% 0.22/0.52 % SZS output start Proof
% 0.22/0.52 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.22/0.52 Axiom 2 (single_axiom): divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, W)))), W) = Z.
% 0.22/0.52
% 0.22/0.52 Lemma 3: multiply(inverse(divide(divide(divide(X, X), Y), divide(Z, multiply(Y, W)))), W) = Z.
% 0.22/0.52 Proof:
% 0.22/0.52 multiply(inverse(divide(divide(divide(X, X), Y), divide(Z, multiply(Y, W)))), W)
% 0.22/0.52 = { by axiom 1 (multiply) }
% 0.22/0.52 multiply(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, inverse(W))))), W)
% 0.22/0.52 = { by axiom 1 (multiply) }
% 0.22/0.52 divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, inverse(W))))), inverse(W))
% 0.22/0.52 = { by axiom 2 (single_axiom) }
% 0.22/0.52 Z
% 0.22/0.52
% 0.22/0.52 Lemma 4: multiply(inverse(divide(multiply(divide(X, X), divide(divide(divide(Y, Y), Z), divide(inverse(W), multiply(Z, V)))), multiply(U, W))), V) = U.
% 0.22/0.52 Proof:
% 0.22/0.52 multiply(inverse(divide(multiply(divide(X, X), divide(divide(divide(Y, Y), Z), divide(inverse(W), multiply(Z, V)))), multiply(U, W))), V)
% 0.22/0.52 = { by axiom 1 (multiply) }
% 0.22/0.52 multiply(inverse(divide(multiply(divide(X, X), divide(divide(divide(Y, Y), Z), divide(inverse(W), multiply(Z, V)))), divide(U, inverse(W)))), V)
% 0.22/0.52 = { by axiom 1 (multiply) }
% 0.22/0.52 multiply(inverse(divide(divide(divide(X, X), inverse(divide(divide(divide(Y, Y), Z), divide(inverse(W), multiply(Z, V))))), divide(U, inverse(W)))), V)
% 0.22/0.52 = { by lemma 3 R->L }
% 0.22/0.52 multiply(inverse(divide(divide(divide(X, X), inverse(divide(divide(divide(Y, Y), Z), divide(inverse(W), multiply(Z, V))))), divide(U, multiply(inverse(divide(divide(divide(Y, Y), Z), divide(inverse(W), multiply(Z, V)))), V)))), V)
% 0.22/0.52 = { by lemma 3 }
% 0.22/0.52 U
% 0.22/0.52
% 0.22/0.52 Lemma 5: divide(multiply(inverse(divide(divide(divide(X, X), Y), Z)), W), multiply(Y, W)) = Z.
% 0.22/0.52 Proof:
% 0.22/0.52 divide(multiply(inverse(divide(divide(divide(X, X), Y), Z)), W), multiply(Y, W))
% 0.22/0.52 = { by axiom 2 (single_axiom) R->L }
% 0.22/0.52 divide(multiply(inverse(divide(divide(divide(X, X), Y), divide(inverse(divide(divide(divide(V, V), U), divide(Z, divide(U, multiply(Y, W))))), multiply(Y, W)))), W), multiply(Y, W))
% 0.22/0.52 = { by lemma 3 }
% 0.22/0.52 divide(inverse(divide(divide(divide(V, V), U), divide(Z, divide(U, multiply(Y, W))))), multiply(Y, W))
% 0.22/0.52 = { by axiom 2 (single_axiom) }
% 0.22/0.52 Z
% 0.22/0.52
% 0.22/0.52 Lemma 6: multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))) = W.
% 0.22/0.52 Proof:
% 0.22/0.52 multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W)))
% 0.22/0.52 = { by lemma 4 R->L }
% 0.22/0.52 multiply(inverse(divide(multiply(divide(V, V), divide(divide(divide(U, U), T), divide(inverse(S), multiply(T, X2)))), multiply(multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))), S))), X2)
% 0.22/0.52 = { by lemma 5 R->L }
% 0.22/0.52 multiply(inverse(divide(multiply(inverse(divide(divide(divide(Z, Z), W), divide(multiply(divide(V, V), divide(divide(divide(U, U), T), divide(inverse(S), multiply(T, X2)))), multiply(multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))), S)))), S), multiply(W, S))), X2)
% 0.22/0.52 = { by lemma 5 R->L }
% 0.22/0.52 multiply(inverse(divide(multiply(inverse(divide(divide(multiply(inverse(divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))), divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))), multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W)))), divide(multiply(divide(V, V), divide(divide(divide(U, U), T), divide(inverse(S), multiply(T, X2)))), multiply(multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))), S)))), S), multiply(W, S))), X2)
% 0.22/0.52 = { by axiom 1 (multiply) }
% 0.22/0.52 multiply(inverse(divide(multiply(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)))), multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W)))), divide(multiply(divide(V, V), divide(divide(divide(U, U), T), divide(inverse(S), multiply(T, X2)))), multiply(multiply(X, divide(divide(divide(Y, Y), X), divide(divide(Z, Z), W))), S)))), S), multiply(W, S))), X2)
% 0.22/0.52 = { by lemma 3 }
% 0.22/0.52 multiply(inverse(divide(multiply(divide(V, V), divide(divide(divide(U, U), T), divide(inverse(S), multiply(T, X2)))), multiply(W, S))), X2)
% 0.22/0.52 = { by lemma 4 }
% 0.22/0.52 W
% 0.22/0.52
% 0.22/0.52 Lemma 7: multiply(divide(X, X), divide(Y, divide(divide(Z, Z), divide(W, W)))) = Y.
% 0.22/0.52 Proof:
% 0.22/0.52 multiply(divide(X, X), divide(Y, divide(divide(Z, Z), divide(W, W))))
% 0.22/0.52 = { by lemma 6 R->L }
% 0.22/0.52 multiply(V, divide(divide(divide(U, U), V), divide(divide(W, W), multiply(divide(X, X), divide(Y, divide(divide(Z, Z), divide(W, W)))))))
% 0.22/0.52 = { by lemma 6 R->L }
% 0.22/0.52 multiply(V, divide(divide(divide(U, U), V), divide(divide(W, W), multiply(divide(X, X), divide(multiply(divide(X, X), divide(divide(divide(T, T), divide(X, X)), divide(divide(S, S), Y))), divide(divide(Z, Z), divide(W, W)))))))
% 0.22/0.52 = { by axiom 1 (multiply) }
% 0.22/0.52 multiply(V, divide(divide(divide(U, U), V), divide(divide(W, W), multiply(divide(X, X), divide(divide(divide(X, X), inverse(divide(divide(divide(T, T), divide(X, X)), divide(divide(S, S), Y)))), divide(divide(Z, Z), divide(W, W)))))))
% 0.22/0.52 = { by lemma 6 R->L }
% 0.22/0.52 multiply(V, divide(divide(divide(U, U), V), divide(multiply(inverse(divide(divide(divide(T, T), divide(X, X)), divide(divide(S, S), Y))), divide(divide(divide(X, X), inverse(divide(divide(divide(T, T), divide(X, X)), divide(divide(S, S), Y)))), divide(divide(Z, Z), divide(W, W)))), multiply(divide(X, X), divide(divide(divide(X, X), inverse(divide(divide(divide(T, T), divide(X, X)), divide(divide(S, S), Y)))), divide(divide(Z, Z), divide(W, W)))))))
% 0.22/0.52 = { by lemma 5 }
% 0.22/0.52 multiply(V, divide(divide(divide(U, U), V), divide(divide(S, S), Y)))
% 0.22/0.52 = { by lemma 6 }
% 0.22/0.52 Y
% 0.22/0.52
% 0.22/0.52 Lemma 8: multiply(X, divide(multiply(divide(V, V), Z), W)) = multiply(X, divide(multiply(divide(Y, Y), Z), W)).
% 0.22/0.52 Proof:
% 0.22/0.52 multiply(X, divide(multiply(divide(V, V), Z), W))
% 0.22/0.52 = { by axiom 1 (multiply) }
% 0.22/0.52 divide(X, inverse(divide(multiply(divide(V, V), Z), W)))
% 0.22/0.52 = { by lemma 4 R->L }
% 0.22/0.52 divide(X, multiply(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), multiply(S, Y2)))), multiply(inverse(divide(multiply(divide(V, V), Z), W)), X2))), Y2))
% 0.22/0.52 = { by axiom 1 (multiply) }
% 0.22/0.52 divide(X, multiply(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), multiply(S, Y2)))), multiply(inverse(divide(divide(divide(V, V), inverse(Z)), W)), X2))), Y2))
% 0.22/0.52 = { by axiom 2 (single_axiom) R->L }
% 0.22/0.52 divide(X, multiply(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), multiply(S, Y2)))), multiply(inverse(divide(divide(divide(V, V), inverse(Z)), divide(inverse(divide(divide(divide(Z2, Z2), W2), divide(W, divide(W2, multiply(inverse(Z), X2))))), multiply(inverse(Z), X2)))), X2))), Y2))
% 0.22/0.52 = { by lemma 3 }
% 0.22/0.52 divide(X, multiply(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), multiply(S, Y2)))), inverse(divide(divide(divide(Z2, Z2), W2), divide(W, divide(W2, multiply(inverse(Z), X2))))))), Y2))
% 0.22/0.52 = { by lemma 3 R->L }
% 0.22/0.52 divide(X, multiply(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), multiply(S, Y2)))), multiply(inverse(divide(divide(divide(Y, Y), inverse(Z)), divide(inverse(divide(divide(divide(Z2, Z2), W2), divide(W, divide(W2, multiply(inverse(Z), X2))))), multiply(inverse(Z), X2)))), X2))), Y2))
% 0.22/0.52 = { by axiom 2 (single_axiom) }
% 0.22/0.52 divide(X, multiply(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), multiply(S, Y2)))), multiply(inverse(divide(divide(divide(Y, Y), inverse(Z)), W)), X2))), Y2))
% 0.22/0.52 = { by axiom 1 (multiply) R->L }
% 0.22/0.52 divide(X, multiply(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), multiply(S, Y2)))), multiply(inverse(divide(multiply(divide(Y, Y), Z), W)), X2))), Y2))
% 0.22/0.52 = { by lemma 4 }
% 0.22/0.52 divide(X, inverse(divide(multiply(divide(Y, Y), Z), W)))
% 0.22/0.52 = { by axiom 1 (multiply) R->L }
% 0.22/0.52 multiply(X, divide(multiply(divide(Y, Y), Z), W))
% 0.22/0.52
% 0.22/0.52 Lemma 9: multiply(multiply(inverse(X), X), Y) = multiply(divide(Z, Z), Y).
% 0.22/0.52 Proof:
% 0.22/0.52 multiply(multiply(inverse(X), X), Y)
% 0.22/0.52 = { by lemma 7 R->L }
% 0.22/0.52 multiply(divide(W, W), divide(multiply(multiply(inverse(X), X), Y), divide(divide(V, V), divide(U, U))))
% 0.22/0.52 = { by axiom 1 (multiply) }
% 0.22/0.52 multiply(divide(W, W), divide(multiply(divide(inverse(X), inverse(X)), Y), divide(divide(V, V), divide(U, U))))
% 0.22/0.52 = { by lemma 8 R->L }
% 0.22/0.52 multiply(divide(W, W), divide(multiply(divide(Z, Z), Y), divide(divide(V, V), divide(U, U))))
% 0.22/0.52 = { by lemma 7 }
% 0.22/0.52 multiply(divide(Z, Z), Y)
% 0.22/0.52
% 0.22/0.52 Lemma 10: multiply(X, divide(Y, Y)) = X.
% 0.22/0.52 Proof:
% 0.22/0.52 multiply(X, divide(Y, Y))
% 0.22/0.52 = { by lemma 4 R->L }
% 0.22/0.52 multiply(X, multiply(inverse(divide(multiply(divide(Z, Z), divide(divide(divide(W, W), V), divide(inverse(U), multiply(V, T)))), multiply(divide(Y, Y), U))), T))
% 0.22/0.52 = { by lemma 7 R->L }
% 0.22/0.52 multiply(X, multiply(inverse(divide(multiply(divide(Z, Z), divide(divide(divide(W, W), V), divide(inverse(U), multiply(V, T)))), multiply(divide(S, S), divide(multiply(divide(Y, Y), U), divide(divide(X2, X2), divide(Y2, Y2)))))), T))
% 0.22/0.52 = { by lemma 8 }
% 0.22/0.52 multiply(X, multiply(inverse(divide(multiply(divide(Z, Z), divide(divide(divide(W, W), V), divide(inverse(U), multiply(V, T)))), multiply(divide(S, S), divide(multiply(divide(divide(divide(Z2, Z2), X), divide(divide(Z2, Z2), X)), U), divide(divide(X2, X2), divide(Y2, Y2)))))), T))
% 0.22/0.52 = { by lemma 7 }
% 0.22/0.52 multiply(X, multiply(inverse(divide(multiply(divide(Z, Z), divide(divide(divide(W, W), V), divide(inverse(U), multiply(V, T)))), multiply(divide(divide(divide(Z2, Z2), X), divide(divide(Z2, Z2), X)), U))), T))
% 0.22/0.52 = { by lemma 4 }
% 0.22/0.52 multiply(X, divide(divide(divide(Z2, Z2), X), divide(divide(Z2, Z2), X)))
% 0.22/0.52 = { by lemma 6 }
% 0.22/0.52 X
% 0.22/0.52
% 0.22/0.52 Lemma 11: divide(X, divide(Y, Y)) = X.
% 0.22/0.52 Proof:
% 0.22/0.53 divide(X, divide(Y, Y))
% 0.22/0.53 = { by lemma 4 R->L }
% 0.22/0.53 divide(X, multiply(inverse(divide(multiply(divide(Z, Z), divide(divide(divide(W, W), V), divide(inverse(U), multiply(V, T)))), multiply(divide(Y, Y), U))), T))
% 0.22/0.53 = { by lemma 9 R->L }
% 0.22/0.53 divide(X, multiply(inverse(divide(multiply(divide(Z, Z), divide(divide(divide(W, W), V), divide(inverse(U), multiply(V, T)))), multiply(multiply(inverse(divide(S, S)), divide(S, S)), U))), T))
% 0.22/0.53 = { by lemma 4 }
% 0.22/0.53 divide(X, multiply(inverse(divide(S, S)), divide(S, S)))
% 0.22/0.53 = { by lemma 10 }
% 0.22/0.53 divide(X, inverse(divide(S, S)))
% 0.22/0.53 = { by axiom 1 (multiply) R->L }
% 0.22/0.53 multiply(X, divide(S, S))
% 0.22/0.53 = { by lemma 10 }
% 0.22/0.53 X
% 0.22/0.53
% 0.22/0.53 Lemma 12: multiply(divide(X, X), Y) = Y.
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(divide(X, X), Y)
% 0.22/0.53 = { by lemma 11 R->L }
% 0.22/0.53 multiply(divide(X, X), divide(Y, divide(divide(Z, Z), divide(Z, Z))))
% 0.22/0.53 = { by lemma 7 }
% 0.22/0.53 Y
% 0.22/0.53
% 0.22/0.53 Lemma 13: divide(multiply(inverse(multiply(multiply(divide(X, X), Y), Z)), W), multiply(inverse(Y), W)) = inverse(Z).
% 0.22/0.53 Proof:
% 0.22/0.53 divide(multiply(inverse(multiply(multiply(divide(X, X), Y), Z)), W), multiply(inverse(Y), W))
% 0.22/0.53 = { by axiom 1 (multiply) }
% 0.22/0.53 divide(multiply(inverse(divide(multiply(divide(X, X), Y), inverse(Z))), W), multiply(inverse(Y), W))
% 0.22/0.53 = { by axiom 1 (multiply) }
% 0.22/0.53 divide(multiply(inverse(divide(divide(divide(X, X), inverse(Y)), inverse(Z))), W), multiply(inverse(Y), W))
% 0.22/0.53 = { by lemma 5 }
% 0.22/0.53 inverse(Z)
% 0.22/0.53
% 0.22/0.53 Lemma 14: multiply(inverse(multiply(X, Y)), X) = inverse(Y).
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(inverse(multiply(X, Y)), X)
% 0.22/0.53 = { by lemma 12 R->L }
% 0.22/0.53 multiply(inverse(multiply(X, Y)), multiply(divide(Z, Z), X))
% 0.22/0.53 = { by axiom 1 (multiply) }
% 0.22/0.53 multiply(inverse(multiply(X, Y)), divide(divide(Z, Z), inverse(X)))
% 0.22/0.53 = { by lemma 12 R->L }
% 0.22/0.53 multiply(inverse(multiply(multiply(divide(W, W), X), Y)), divide(divide(Z, Z), inverse(X)))
% 0.22/0.53 = { by lemma 11 R->L }
% 0.22/0.53 divide(multiply(inverse(multiply(multiply(divide(W, W), X), Y)), divide(divide(Z, Z), inverse(X))), divide(V, V))
% 0.22/0.53 = { by lemma 6 R->L }
% 0.22/0.53 divide(multiply(inverse(multiply(multiply(divide(W, W), X), Y)), divide(divide(Z, Z), inverse(X))), multiply(inverse(X), divide(divide(divide(Z, Z), inverse(X)), divide(divide(U, U), divide(V, V)))))
% 0.22/0.53 = { by lemma 11 }
% 0.22/0.53 divide(multiply(inverse(multiply(multiply(divide(W, W), X), Y)), divide(divide(Z, Z), inverse(X))), multiply(inverse(X), divide(divide(divide(Z, Z), inverse(X)), divide(U, U))))
% 0.22/0.53 = { by lemma 11 }
% 0.22/0.53 divide(multiply(inverse(multiply(multiply(divide(W, W), X), Y)), divide(divide(Z, Z), inverse(X))), multiply(inverse(X), divide(divide(Z, Z), inverse(X))))
% 0.22/0.53 = { by lemma 13 }
% 0.22/0.53 inverse(Y)
% 0.22/0.53
% 0.22/0.53 Lemma 15: multiply(multiply(inverse(multiply(multiply(X, Y), Z)), X), Y) = inverse(Z).
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(multiply(inverse(multiply(multiply(X, Y), Z)), X), Y)
% 0.22/0.53 = { by lemma 12 R->L }
% 0.22/0.53 multiply(multiply(inverse(multiply(multiply(divide(W, W), multiply(X, Y)), Z)), X), Y)
% 0.22/0.53 = { by axiom 1 (multiply) }
% 0.22/0.53 divide(multiply(inverse(multiply(multiply(divide(W, W), multiply(X, Y)), Z)), X), inverse(Y))
% 0.22/0.53 = { by lemma 14 R->L }
% 0.22/0.53 divide(multiply(inverse(multiply(multiply(divide(W, W), multiply(X, Y)), Z)), X), multiply(inverse(multiply(X, Y)), X))
% 0.22/0.53 = { by lemma 13 }
% 0.22/0.53 inverse(Z)
% 0.22/0.53
% 0.22/0.53 Lemma 16: multiply(multiply(inverse(X), inverse(Y)), Y) = inverse(X).
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(multiply(inverse(X), inverse(Y)), Y)
% 0.22/0.53 = { by lemma 12 R->L }
% 0.22/0.53 multiply(multiply(inverse(multiply(divide(Z, Z), X)), inverse(Y)), Y)
% 0.22/0.53 = { by lemma 9 R->L }
% 0.22/0.53 multiply(multiply(inverse(multiply(multiply(inverse(Y), Y), X)), inverse(Y)), Y)
% 0.22/0.53 = { by lemma 15 }
% 0.22/0.53 inverse(X)
% 0.22/0.53
% 0.22/0.53 Lemma 17: inverse(inverse(X)) = X.
% 0.22/0.53 Proof:
% 0.22/0.53 inverse(inverse(X))
% 0.22/0.53 = { by lemma 16 R->L }
% 0.22/0.53 multiply(multiply(inverse(inverse(X)), inverse(X)), X)
% 0.22/0.53 = { by lemma 9 }
% 0.22/0.53 multiply(divide(Y, Y), X)
% 0.22/0.53 = { by lemma 12 }
% 0.22/0.53 X
% 0.22/0.53
% 0.22/0.53 Lemma 18: multiply(multiply(X, Y), inverse(Y)) = X.
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(multiply(X, Y), inverse(Y))
% 0.22/0.53 = { by lemma 17 R->L }
% 0.22/0.53 multiply(multiply(X, inverse(inverse(Y))), inverse(Y))
% 0.22/0.53 = { by lemma 17 R->L }
% 0.22/0.53 multiply(multiply(inverse(inverse(X)), inverse(inverse(Y))), inverse(Y))
% 0.22/0.53 = { by lemma 16 }
% 0.22/0.53 inverse(inverse(X))
% 0.22/0.53 = { by lemma 17 }
% 0.22/0.53 X
% 0.22/0.53
% 0.22/0.53 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(multiply(a3, b3), c3)
% 0.22/0.53 = { by lemma 17 R->L }
% 0.22/0.53 multiply(multiply(inverse(inverse(a3)), b3), c3)
% 0.22/0.53 = { by lemma 18 R->L }
% 0.22/0.53 multiply(multiply(inverse(multiply(multiply(inverse(a3), multiply(a3, multiply(b3, c3))), inverse(multiply(a3, multiply(b3, c3))))), b3), c3)
% 0.22/0.53 = { by lemma 18 R->L }
% 0.22/0.53 multiply(multiply(inverse(multiply(multiply(inverse(multiply(multiply(a3, multiply(b3, c3)), inverse(multiply(b3, c3)))), multiply(a3, multiply(b3, c3))), inverse(multiply(a3, multiply(b3, c3))))), b3), c3)
% 0.22/0.53 = { by lemma 14 }
% 0.22/0.53 multiply(multiply(inverse(multiply(inverse(inverse(multiply(b3, c3))), inverse(multiply(a3, multiply(b3, c3))))), b3), c3)
% 0.22/0.53 = { by lemma 17 }
% 0.22/0.53 multiply(multiply(inverse(multiply(multiply(b3, c3), inverse(multiply(a3, multiply(b3, c3))))), b3), c3)
% 0.22/0.53 = { by lemma 15 }
% 0.22/0.53 inverse(inverse(multiply(a3, multiply(b3, c3))))
% 0.22/0.53 = { by lemma 17 }
% 0.22/0.53 multiply(a3, multiply(b3, c3))
% 0.22/0.53 % SZS output end Proof
% 0.22/0.53
% 0.22/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------