TSTP Solution File: GRP550-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP550-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n023.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 01:15:19 EDT 2023
% Result : Unsatisfiable 0.44s 0.71s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP550-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n023.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 : Mon Aug 28 23:08:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.44/0.71 % SZS status Unsatisfiable
% 0.44/0.71 % SZS output start Proof
% 0.44/0.71 original problem:
% 0.44/0.71 axioms:
% 0.44/0.71 divide(divide(identity(), A), divide(divide(divide(B, A), C), B)) = C
% 0.44/0.71 multiply(A, B) = divide(A, divide(identity(), B))
% 0.44/0.71 inverse(A) = divide(identity(), A)
% 0.44/0.71 identity() = divide(A, A)
% 0.44/0.71 goal:
% 0.44/0.71 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 0.44/0.71 To show the unsatisfiability of the original goal,
% 0.44/0.71 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.44/0.71 Here is an equational proof:
% 0.44/0.71 0: divide(divide(identity(), X0), divide(divide(divide(X1, X0), X2), X1)) = X2.
% 0.44/0.71 Proof: Axiom.
% 0.44/0.71
% 0.44/0.71 1: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.44/0.71 Proof: Axiom.
% 0.44/0.71
% 0.44/0.71 2: inverse(X0) = divide(identity(), X0).
% 0.44/0.71 Proof: Axiom.
% 0.44/0.71
% 0.44/0.71 3: identity() = divide(X0, X0).
% 0.44/0.71 Proof: Axiom.
% 0.44/0.71
% 0.44/0.71 4: divide(inverse(X0), divide(divide(divide(X1, X0), X2), X1)) = X2.
% 0.44/0.71 Proof: Rewrite equation 0,
% 0.44/0.71 lhs with equations [2]
% 0.44/0.71 rhs with equations [].
% 0.44/0.71
% 0.44/0.71 5: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.44/0.71 Proof: Rewrite equation 1,
% 0.44/0.71 lhs with equations []
% 0.44/0.71 rhs with equations [2].
% 0.44/0.71
% 0.44/0.71 7: X2 = divide(inverse(X3), divide(divide(identity(), X2), X3)).
% 0.44/0.71 Proof: A critical pair between equations 4 and 3.
% 0.44/0.71
% 0.44/0.71 8: divide(X1, X0) = divide(inverse(X0), divide(identity(), X1)).
% 0.44/0.71 Proof: A critical pair between equations 4 and 3.
% 0.44/0.71
% 0.44/0.71 9: X2 = divide(inverse(X3), divide(divide(inverse(X3), X2), identity())).
% 0.44/0.71 Proof: A critical pair between equations 4 and 2.
% 0.44/0.71
% 0.44/0.71 12: X2 = divide(divide(identity(), X3), divide(divide(divide(identity(), X3), X2), identity())).
% 0.44/0.71 Proof: Rewrite equation 9,
% 0.44/0.71 lhs with equations []
% 0.44/0.71 rhs with equations [2,2].
% 0.44/0.71
% 0.44/0.71 13: X2 = divide(divide(identity(), X3), divide(divide(identity(), X2), X3)).
% 0.44/0.71 Proof: Rewrite equation 7,
% 0.44/0.71 lhs with equations []
% 0.44/0.71 rhs with equations [2].
% 0.44/0.71
% 0.44/0.71 14: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.44/0.71 Proof: Rewrite equation 5,
% 0.44/0.71 lhs with equations []
% 0.44/0.71 rhs with equations [2].
% 0.44/0.71
% 0.44/0.71 16: divide(X1, X0) = divide(divide(identity(), X0), divide(identity(), X1)).
% 0.44/0.71 Proof: Rewrite equation 8,
% 0.44/0.71 lhs with equations []
% 0.44/0.71 rhs with equations [2].
% 0.44/0.71
% 0.44/0.71 18: divide(X1, identity()) = divide(identity(), divide(identity(), X1)).
% 0.44/0.71 Proof: A critical pair between equations 16 and 3.
% 0.44/0.71
% 0.44/0.71 22: divide(identity(), X3) = divide(divide(identity(), X3), divide(identity(), identity())).
% 0.44/0.71 Proof: A critical pair between equations 12 and 3.
% 0.44/0.71
% 0.44/0.71 24: X4 = divide(divide(identity(), divide(identity(), X5)), divide(X5, X4)).
% 0.44/0.71 Proof: A critical pair between equations 13 and 16.
% 0.44/0.71
% 0.44/0.71 28: divide(identity(), X5) = divide(divide(identity(), X4), divide(divide(X5, X4), identity())).
% 0.44/0.71 Proof: A critical pair between equations 12 and 16.
% 0.44/0.71
% 0.44/0.71 29: inverse(X5) = divide(inverse(X4), inverse(inverse(divide(X5, X4)))).
% 0.44/0.71 Proof: Rewrite equation 28,
% 0.44/0.71 lhs with equations [2]
% 0.44/0.71 rhs with equations [2,18,2,2].
% 0.44/0.71
% 0.44/0.71 33: X4 = divide(inverse(inverse(X5)), divide(X5, X4)).
% 0.44/0.71 Proof: Rewrite equation 24,
% 0.44/0.71 lhs with equations []
% 0.44/0.71 rhs with equations [2,2].
% 0.44/0.71
% 0.44/0.71 35: inverse(X3) = divide(inverse(X3), inverse(identity())).
% 0.44/0.71 Proof: Rewrite equation 22,
% 0.44/0.71 lhs with equations [2]
% 0.44/0.71 rhs with equations [2,2].
% 0.44/0.71
% 0.44/0.71 40: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.44/0.71 Proof: Rewrite equation 14,
% 0.44/0.71 lhs with equations []
% 0.44/0.71 rhs with equations [2].
% 0.44/0.71
% 0.44/0.71 45: inverse(identity()) = identity().
% 0.44/0.71 Proof: A critical pair between equations 35 and 3.
% 0.44/0.71
% 0.44/0.71 53: X6 = divide(inverse(inverse(identity())), inverse(X6)).
% 0.44/0.71 Proof: A critical pair between equations 33 and 2.
% 0.44/0.71
% 0.44/0.71 58: X6 = divide(identity(), divide(identity(), X6)).
% 0.44/0.71 Proof: Rewrite equation 53,
% 0.44/0.71 lhs with equations []
% 0.44/0.71 rhs with equations [45,45,2].
% 0.44/0.71
% 0.44/0.71 62: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.44/0.71 Proof: Rewrite equation 40,
% 0.44/0.71 lhs with equations []
% 0.44/0.71 rhs with equations [2].
% 0.44/0.71
% 0.44/0.71 64: X4 = divide(X5, divide(X5, X4)).
% 0.44/0.71 Proof: Rewrite equation 33,
% 0.44/0.71 lhs with equations []
% 0.44/0.71 rhs with equations [2,2,58].
% 0.44/0.71
% 0.44/0.71 67: divide(identity(), X5) = divide(divide(identity(), X4), divide(X5, X4)).
% 0.44/0.71 Proof: Rewrite equation 29,
% 0.44/0.71 lhs with equations [2]
% 0.44/0.71 rhs with equations [2,2,2,64].
% 0.44/0.71
% 0.44/0.71 69: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 0.44/0.71 Proof: Rewrite lhs with equations [2,62,67,3,62,64]
% 0.44/0.71 rhs with equations [].
% 0.44/0.71
% 0.44/0.71 % SZS output end Proof
%------------------------------------------------------------------------------