TSTP Solution File: GRP450-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP450-1 : 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 : n011.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 01:18:29 EDT 2023
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP450-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:14:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.40 Command-line arguments: --ground-connectedness --complete-subsets
% 0.13/0.40
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.20/0.42 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.20/0.42 Axiom 3 (single_axiom): divide(X, divide(divide(divide(divide(Y, Y), Y), Z), divide(divide(divide(Y, Y), X), Z))) = Y.
% 0.20/0.42
% 0.20/0.42 Lemma 4: divide(inverse(divide(X, X)), Y) = inverse(Y).
% 0.20/0.42 Proof:
% 0.20/0.42 divide(inverse(divide(X, X)), Y)
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 divide(divide(divide(X, X), divide(X, X)), Y)
% 0.20/0.42 = { by axiom 1 (inverse) R->L }
% 0.20/0.42 inverse(Y)
% 0.20/0.42
% 0.20/0.42 Lemma 5: divide(X, inverse(Y)) = multiply(X, Y).
% 0.20/0.42 Proof:
% 0.20/0.42 divide(X, inverse(Y))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 divide(X, divide(divide(Z, Z), Y))
% 0.20/0.42 = { by axiom 2 (multiply) R->L }
% 0.20/0.42 multiply(X, Y)
% 0.20/0.42
% 0.20/0.42 Lemma 6: divide(X, divide(divide(inverse(Y), Z), divide(inverse(X), Z))) = Y.
% 0.20/0.42 Proof:
% 0.20/0.42 divide(X, divide(divide(inverse(Y), Z), divide(inverse(X), Z)))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 divide(X, divide(divide(inverse(Y), Z), divide(divide(divide(Y, Y), X), Z)))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 divide(X, divide(divide(divide(divide(Y, Y), Y), Z), divide(divide(divide(Y, Y), X), Z)))
% 0.20/0.42 = { by axiom 3 (single_axiom) }
% 0.20/0.42 Y
% 0.20/0.42
% 0.20/0.42 Lemma 7: inverse(multiply(divide(inverse(X), Y), Y)) = X.
% 0.20/0.42 Proof:
% 0.20/0.42 inverse(multiply(divide(inverse(X), Y), Y))
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 inverse(divide(divide(inverse(X), Y), inverse(Y)))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 divide(divide(Z, Z), divide(divide(inverse(X), Y), inverse(Y)))
% 0.20/0.42 = { by lemma 4 R->L }
% 0.20/0.42 divide(divide(Z, Z), divide(divide(inverse(X), Y), divide(inverse(divide(Z, Z)), Y)))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 X
% 0.20/0.42
% 0.20/0.42 Lemma 8: inverse(multiply(inverse(X), X)) = divide(Y, Y).
% 0.20/0.42 Proof:
% 0.20/0.42 inverse(multiply(inverse(X), X))
% 0.20/0.42 = { by lemma 4 R->L }
% 0.20/0.42 inverse(multiply(divide(inverse(divide(Y, Y)), X), X))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 divide(Y, Y)
% 0.20/0.42
% 0.20/0.42 Lemma 9: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, multiply(inverse(X), Y))
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 multiply(X, divide(inverse(X), inverse(Y)))
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 divide(X, inverse(divide(inverse(X), inverse(Y))))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 divide(X, divide(divide(inverse(Y), inverse(Y)), divide(inverse(X), inverse(Y))))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 Y
% 0.20/0.42
% 0.20/0.42 Lemma 10: multiply(X, divide(Y, Y)) = X.
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, divide(Y, Y))
% 0.20/0.42 = { by lemma 8 R->L }
% 0.20/0.42 multiply(X, inverse(multiply(inverse(Z), Z)))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 multiply(X, inverse(multiply(divide(divide(W, W), Z), Z)))
% 0.20/0.42 = { by lemma 8 R->L }
% 0.20/0.42 multiply(X, inverse(multiply(divide(inverse(multiply(inverse(X), X)), Z), Z)))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 multiply(X, multiply(inverse(X), X))
% 0.20/0.42 = { by lemma 9 }
% 0.20/0.42 X
% 0.20/0.42
% 0.20/0.42 Lemma 11: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(inverse(inverse(X)), Y)
% 0.20/0.42 = { by lemma 9 R->L }
% 0.20/0.42 multiply(X, multiply(inverse(X), multiply(inverse(inverse(X)), Y)))
% 0.20/0.42 = { by lemma 9 }
% 0.20/0.42 multiply(X, Y)
% 0.20/0.42
% 0.20/0.42 Lemma 12: inverse(inverse(X)) = X.
% 0.20/0.42 Proof:
% 0.20/0.42 inverse(inverse(X))
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 multiply(inverse(inverse(X)), divide(Y, Y))
% 0.20/0.42 = { by lemma 11 }
% 0.20/0.42 multiply(X, divide(Y, Y))
% 0.20/0.42 = { by lemma 10 }
% 0.20/0.42 X
% 0.20/0.42
% 0.20/0.42 Lemma 13: divide(X, divide(Y, Y)) = X.
% 0.20/0.42 Proof:
% 0.20/0.42 divide(X, divide(Y, Y))
% 0.20/0.42 = { by lemma 7 R->L }
% 0.20/0.42 divide(X, inverse(multiply(divide(inverse(divide(Y, Y)), Z), Z)))
% 0.20/0.42 = { by lemma 4 }
% 0.20/0.42 divide(X, inverse(multiply(inverse(Z), Z)))
% 0.20/0.42 = { by lemma 4 R->L }
% 0.20/0.42 divide(X, inverse(multiply(divide(inverse(divide(divide(inverse(X), W), divide(inverse(X), W))), Z), Z)))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 divide(X, divide(divide(inverse(X), W), divide(inverse(X), W)))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 X
% 0.20/0.42
% 0.20/0.42 Lemma 14: multiply(divide(X, X), Y) = inverse(inverse(Y)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(divide(X, X), Y)
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 divide(divide(X, X), inverse(Y))
% 0.20/0.43 = { by axiom 1 (inverse) R->L }
% 0.20/0.43 inverse(inverse(Y))
% 0.20/0.43
% 0.20/0.43 Lemma 15: inverse(divide(X, Y)) = divide(Y, X).
% 0.20/0.43 Proof:
% 0.20/0.43 inverse(divide(X, Y))
% 0.20/0.43 = { by lemma 6 R->L }
% 0.20/0.43 divide(Y, divide(divide(inverse(inverse(divide(X, Y))), divide(Z, Z)), divide(inverse(Y), divide(Z, Z))))
% 0.20/0.43 = { by lemma 13 }
% 0.20/0.43 divide(Y, divide(inverse(inverse(divide(X, Y))), divide(inverse(Y), divide(Z, Z))))
% 0.20/0.43 = { by lemma 13 }
% 0.20/0.43 divide(Y, divide(inverse(inverse(divide(X, Y))), inverse(Y)))
% 0.20/0.43 = { by lemma 5 }
% 0.20/0.43 divide(Y, multiply(inverse(inverse(divide(X, Y))), Y))
% 0.20/0.43 = { by lemma 11 }
% 0.20/0.43 divide(Y, multiply(divide(X, Y), Y))
% 0.20/0.43 = { by lemma 9 R->L }
% 0.20/0.43 divide(Y, multiply(divide(multiply(inverse(divide(W, W)), multiply(inverse(inverse(divide(W, W))), X)), Y), Y))
% 0.20/0.43 = { by axiom 1 (inverse) }
% 0.20/0.43 divide(Y, multiply(divide(multiply(divide(divide(W, W), divide(W, W)), multiply(inverse(inverse(divide(W, W))), X)), Y), Y))
% 0.20/0.43 = { by lemma 14 }
% 0.20/0.43 divide(Y, multiply(divide(inverse(inverse(multiply(inverse(inverse(divide(W, W))), X))), Y), Y))
% 0.20/0.43 = { by lemma 11 }
% 0.20/0.43 divide(Y, multiply(divide(inverse(inverse(multiply(divide(W, W), X))), Y), Y))
% 0.20/0.43 = { by lemma 14 }
% 0.20/0.43 divide(Y, multiply(divide(inverse(inverse(inverse(inverse(X)))), Y), Y))
% 0.20/0.43 = { by lemma 7 R->L }
% 0.20/0.43 divide(Y, inverse(multiply(divide(inverse(multiply(divide(inverse(inverse(inverse(inverse(X)))), Y), Y)), V), V)))
% 0.20/0.43 = { by lemma 7 }
% 0.20/0.43 divide(Y, inverse(multiply(divide(inverse(inverse(inverse(X))), V), V)))
% 0.20/0.43 = { by lemma 7 }
% 0.20/0.43 divide(Y, inverse(inverse(X)))
% 0.20/0.43 = { by lemma 12 }
% 0.20/0.43 divide(Y, X)
% 0.20/0.43
% 0.20/0.43 Lemma 16: divide(inverse(X), Y) = inverse(multiply(Y, X)).
% 0.20/0.43 Proof:
% 0.20/0.43 divide(inverse(X), Y)
% 0.20/0.43 = { by lemma 15 R->L }
% 0.20/0.43 inverse(divide(Y, inverse(X)))
% 0.20/0.43 = { by lemma 5 }
% 0.20/0.43 inverse(multiply(Y, X))
% 0.20/0.43
% 0.20/0.43 Lemma 17: multiply(X, inverse(Y)) = divide(X, Y).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, inverse(Y))
% 0.20/0.43 = { by lemma 5 R->L }
% 0.20/0.43 divide(X, inverse(inverse(Y)))
% 0.20/0.43 = { by lemma 12 }
% 0.20/0.43 divide(X, Y)
% 0.20/0.43
% 0.20/0.43 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(multiply(a3, b3), c3)
% 0.20/0.43 = { by lemma 6 R->L }
% 0.20/0.43 divide(X, divide(divide(inverse(multiply(multiply(a3, b3), c3)), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 16 R->L }
% 0.20/0.43 divide(X, divide(divide(divide(inverse(c3), multiply(a3, b3)), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 17 R->L }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), inverse(multiply(a3, b3))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 16 R->L }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(inverse(b3), a3)), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 6 R->L }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(c3, divide(divide(inverse(divide(inverse(b3), a3)), inverse(multiply(inverse(inverse(divide(inverse(b3), a3))), a3))), divide(inverse(c3), inverse(multiply(inverse(inverse(divide(inverse(b3), a3))), a3)))))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 5 }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(c3, divide(multiply(inverse(divide(inverse(b3), a3)), multiply(inverse(inverse(divide(inverse(b3), a3))), a3)), divide(inverse(c3), inverse(multiply(inverse(inverse(divide(inverse(b3), a3))), a3)))))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 15 R->L }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(c3, inverse(divide(divide(inverse(c3), inverse(multiply(inverse(inverse(divide(inverse(b3), a3))), a3))), multiply(inverse(divide(inverse(b3), a3)), multiply(inverse(inverse(divide(inverse(b3), a3))), a3)))))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 5 }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), multiply(c3, divide(divide(inverse(c3), inverse(multiply(inverse(inverse(divide(inverse(b3), a3))), a3))), multiply(inverse(divide(inverse(b3), a3)), multiply(inverse(inverse(divide(inverse(b3), a3))), a3))))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 16 }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), multiply(c3, divide(inverse(multiply(inverse(multiply(inverse(inverse(divide(inverse(b3), a3))), a3)), c3)), multiply(inverse(divide(inverse(b3), a3)), multiply(inverse(inverse(divide(inverse(b3), a3))), a3))))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 16 }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), multiply(c3, inverse(multiply(multiply(inverse(divide(inverse(b3), a3)), multiply(inverse(inverse(divide(inverse(b3), a3))), a3)), multiply(inverse(multiply(inverse(inverse(divide(inverse(b3), a3))), a3)), c3))))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 17 }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(c3, multiply(multiply(inverse(divide(inverse(b3), a3)), multiply(inverse(inverse(divide(inverse(b3), a3))), a3)), multiply(inverse(multiply(inverse(inverse(divide(inverse(b3), a3))), a3)), c3)))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 9 }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(c3, multiply(a3, multiply(inverse(multiply(inverse(inverse(divide(inverse(b3), a3))), a3)), c3)))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 16 R->L }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(c3, multiply(a3, multiply(divide(inverse(a3), inverse(inverse(divide(inverse(b3), a3)))), c3)))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 5 }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(c3, multiply(a3, multiply(multiply(inverse(a3), inverse(divide(inverse(b3), a3))), c3)))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 17 }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(c3, multiply(a3, multiply(divide(inverse(a3), divide(inverse(b3), a3)), c3)))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 16 }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(c3, multiply(a3, multiply(inverse(multiply(divide(inverse(b3), a3), a3)), c3)))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 7 }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), divide(c3, multiply(a3, multiply(b3, c3)))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 17 R->L }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), multiply(c3, inverse(multiply(a3, multiply(b3, c3))))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 11 R->L }
% 0.20/0.43 divide(X, divide(divide(multiply(inverse(c3), multiply(inverse(inverse(c3)), inverse(multiply(a3, multiply(b3, c3))))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 9 }
% 0.20/0.43 divide(X, divide(divide(inverse(multiply(a3, multiply(b3, c3))), Y), divide(inverse(X), Y)))
% 0.20/0.43 = { by lemma 6 }
% 0.20/0.43 multiply(a3, multiply(b3, c3))
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------