TSTP Solution File: GRP458-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP458-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% 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 01:15:03 EDT 2023
% Result : Unsatisfiable 0.77s 1.17s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP458-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.15 % Command : toma --casc %s
% 0.14/0.36 % Computer : n012.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 00:24:39 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.77/1.17 % SZS status Unsatisfiable
% 0.77/1.17 % SZS output start Proof
% 0.77/1.17 original problem:
% 0.77/1.17 axioms:
% 0.77/1.17 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(identity(), A), C)))), C) = B
% 0.77/1.17 multiply(A, B) = divide(A, divide(identity(), B))
% 0.77/1.17 inverse(A) = divide(identity(), A)
% 0.77/1.17 identity() = divide(A, A)
% 0.77/1.17 goal:
% 0.77/1.17 multiply(identity(), a2()) != a2()
% 0.77/1.17 To show the unsatisfiability of the original goal,
% 0.77/1.17 it suffices to show that multiply(identity(), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.77/1.17 Here is an equational proof:
% 0.77/1.17 0: divide(divide(divide(X0, X0), divide(X0, divide(X1, divide(divide(identity(), X0), X2)))), X2) = X1.
% 0.77/1.17 Proof: Axiom.
% 0.77/1.17
% 0.77/1.17 1: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.77/1.17 Proof: Axiom.
% 0.77/1.17
% 0.77/1.17 2: inverse(X0) = divide(identity(), X0).
% 0.77/1.17 Proof: Axiom.
% 0.77/1.17
% 0.77/1.17 3: identity() = divide(X0, X0).
% 0.77/1.17 Proof: Axiom.
% 0.77/1.17
% 0.77/1.17 4: divide(inverse(divide(X0, divide(X1, divide(inverse(X0), X2)))), X2) = X1.
% 0.77/1.17 Proof: Rewrite equation 0,
% 0.77/1.17 lhs with equations [3,2,2]
% 0.77/1.17 rhs with equations [].
% 0.77/1.17
% 0.77/1.17 5: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.77/1.17 Proof: Rewrite equation 1,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2].
% 0.77/1.17
% 0.77/1.17 6: inverse(identity()) = identity().
% 0.77/1.17 Proof: A critical pair between equations 2 and 3.
% 0.77/1.17
% 0.77/1.17 7: X1 = divide(inverse(divide(X0, divide(X1, identity()))), inverse(X0)).
% 0.77/1.17 Proof: A critical pair between equations 4 and 3.
% 0.77/1.17
% 0.77/1.17 8: divide(inverse(X0), X2) = divide(inverse(divide(X0, identity())), X2).
% 0.77/1.17 Proof: A critical pair between equations 4 and 3.
% 0.77/1.17
% 0.77/1.17 10: X1 = divide(inverse(inverse(divide(X1, divide(inverse(identity()), X2)))), X2).
% 0.77/1.17 Proof: A critical pair between equations 4 and 2.
% 0.77/1.17
% 0.77/1.17 11: X1 = divide(inverse(divide(divide(X3, divide(X4, divide(inverse(X3), X5))), divide(X1, X4))), X5).
% 0.77/1.17 Proof: A critical pair between equations 4 and 4.
% 0.77/1.17
% 0.77/1.17 12: inverse(divide(X3, divide(X4, divide(inverse(X3), divide(inverse(X0), X2))))) = divide(inverse(divide(X0, X4)), X2).
% 0.77/1.17 Proof: A critical pair between equations 4 and 4.
% 0.77/1.17
% 0.77/1.17 13: X1 = divide(divide(identity(), divide(divide(X3, divide(X4, divide(divide(identity(), X3), X5))), divide(X1, X4))), X5).
% 0.77/1.17 Proof: Rewrite equation 11,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2,2].
% 0.77/1.17
% 0.77/1.17 14: X1 = divide(divide(identity(), divide(identity(), divide(X1, divide(identity(), X2)))), X2).
% 0.77/1.17 Proof: Rewrite equation 10,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [6,2,2].
% 0.77/1.17
% 0.77/1.17 16: divide(divide(identity(), X0), X2) = divide(divide(identity(), divide(X0, identity())), X2).
% 0.77/1.17 Proof: Rewrite equation 8,
% 0.77/1.17 lhs with equations [2]
% 0.77/1.17 rhs with equations [2].
% 0.77/1.17
% 0.77/1.17 17: X1 = divide(divide(identity(), divide(X0, divide(X1, identity()))), divide(identity(), X0)).
% 0.77/1.17 Proof: Rewrite equation 7,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2,2].
% 0.77/1.17
% 0.77/1.17 18: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.77/1.17 Proof: Rewrite equation 5,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2].
% 0.77/1.17
% 0.77/1.17 19: divide(divide(identity(), divide(X0, divide(X1, divide(divide(identity(), X0), X2)))), X2) = X1.
% 0.77/1.17 Proof: Rewrite equation 4,
% 0.77/1.17 lhs with equations [2,2]
% 0.77/1.17 rhs with equations [].
% 0.77/1.17
% 0.77/1.17 20: divide(identity(), divide(X3, divide(X4, divide(divide(identity(), X3), divide(divide(identity(), X0), X2))))) = divide(divide(identity(), divide(X0, X4)), X2).
% 0.77/1.17 Proof: Rewrite equation 12,
% 0.77/1.17 lhs with equations [2,2,2]
% 0.77/1.17 rhs with equations [2].
% 0.77/1.17
% 0.77/1.17 21: X1 = divide(divide(identity(), divide(identity(), divide(X1, identity()))), identity()).
% 0.77/1.17 Proof: A critical pair between equations 14 and 3.
% 0.77/1.17
% 0.77/1.17 22: divide(divide(identity(), X0), divide(identity(), divide(X0, identity()))) = identity().
% 0.77/1.17 Proof: A critical pair between equations 16 and 3.
% 0.77/1.17
% 0.77/1.17 23: X1 = divide(divide(identity(), identity()), divide(identity(), divide(X1, identity()))).
% 0.77/1.17 Proof: A critical pair between equations 17 and 3.
% 0.77/1.17
% 0.77/1.17 24: X1 = divide(divide(identity(), divide(identity(), identity())), divide(identity(), divide(X1, identity()))).
% 0.77/1.17 Proof: A critical pair between equations 13 and 14.
% 0.77/1.17
% 0.77/1.17 26: divide(identity(), divide(X3, divide(X4, identity()))) = divide(divide(identity(), divide(identity(), X4)), X3).
% 0.77/1.17 Proof: A critical pair between equations 14 and 17.
% 0.77/1.17
% 0.77/1.17 28: X6 = divide(divide(divide(identity(), divide(X7, X6)), X8), divide(divide(identity(), X7), X8)).
% 0.77/1.17 Proof: A critical pair between equations 19 and 20.
% 0.77/1.17
% 0.77/1.17 37: X6 = divide(divide(inverse(divide(X7, X6)), X8), divide(inverse(X7), X8)).
% 0.77/1.17 Proof: Rewrite equation 28,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2,2].
% 0.77/1.17
% 0.77/1.17 40: X1 = divide(inverse(inverse(identity())), inverse(divide(X1, identity()))).
% 0.77/1.17 Proof: Rewrite equation 24,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2,2,2].
% 0.77/1.17
% 0.77/1.17 41: X1 = divide(inverse(identity()), inverse(divide(X1, identity()))).
% 0.77/1.17 Proof: Rewrite equation 23,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2,2].
% 0.77/1.17
% 0.77/1.17 42: divide(inverse(X0), inverse(divide(X0, identity()))) = identity().
% 0.77/1.17 Proof: Rewrite equation 22,
% 0.77/1.17 lhs with equations [2,2]
% 0.77/1.17 rhs with equations [].
% 0.77/1.17
% 0.77/1.17 43: X1 = divide(inverse(inverse(divide(X1, identity()))), identity()).
% 0.77/1.17 Proof: Rewrite equation 21,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2,2].
% 0.77/1.17
% 0.77/1.17 45: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.77/1.17 Proof: Rewrite equation 18,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2].
% 0.77/1.17
% 0.77/1.17 51: inverse(divide(X3, divide(X4, identity()))) = divide(inverse(inverse(X4)), X3).
% 0.77/1.17 Proof: Rewrite equation 26,
% 0.77/1.17 lhs with equations [2]
% 0.77/1.17 rhs with equations [2,2].
% 0.77/1.17
% 0.77/1.17 53: inverse(identity()) = identity().
% 0.77/1.17 Proof: A critical pair between equations 40 and 42.
% 0.77/1.17
% 0.77/1.17 62: inverse(divide(identity(), divide(divide(X5, identity()), identity()))) = X5.
% 0.77/1.17 Proof: A critical pair between equations 51 and 43.
% 0.77/1.17
% 0.77/1.17 64: divide(inverse(inverse(X4)), divide(X4, identity())) = inverse(identity()).
% 0.77/1.17 Proof: A critical pair between equations 51 and 3.
% 0.77/1.17
% 0.77/1.17 65: divide(divide(identity(), divide(identity(), X4)), divide(X4, identity())) = identity().
% 0.77/1.17 Proof: Rewrite equation 64,
% 0.77/1.17 lhs with equations [2,2]
% 0.77/1.17 rhs with equations [53].
% 0.77/1.17
% 0.77/1.17 66: divide(identity(), divide(identity(), divide(divide(X5, identity()), identity()))) = X5.
% 0.77/1.17 Proof: Rewrite equation 62,
% 0.77/1.17 lhs with equations [2]
% 0.77/1.17 rhs with equations [].
% 0.77/1.17
% 0.77/1.17 73: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.77/1.17 Proof: Rewrite equation 45,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2].
% 0.77/1.17
% 0.77/1.17 77: X1 = divide(identity(), divide(identity(), divide(X1, identity()))).
% 0.77/1.17 Proof: Rewrite equation 41,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2,3,2].
% 0.77/1.17
% 0.77/1.17 79: X6 = divide(divide(divide(identity(), divide(X7, X6)), X8), divide(divide(identity(), X7), X8)).
% 0.77/1.17 Proof: Rewrite equation 37,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2,2].
% 0.77/1.17
% 0.77/1.17 86: X5 = divide(X5, identity()).
% 0.77/1.17 Proof: A critical pair between equations 66 and 77.
% 0.77/1.17
% 0.77/1.17 97: X9 = divide(identity(), divide(divide(identity(), identity()), divide(X9, identity()))).
% 0.77/1.17 Proof: A critical pair between equations 79 and 65.
% 0.77/1.17
% 0.77/1.17 98: X9 = inverse(inverse(X9)).
% 0.77/1.17 Proof: Rewrite equation 97,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [86,86,2,2].
% 0.77/1.17
% 0.77/1.17 105: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.77/1.17 Proof: Rewrite equation 73,
% 0.77/1.17 lhs with equations []
% 0.77/1.17 rhs with equations [2].
% 0.77/1.17
% 0.77/1.17 112: multiply(identity(), a2()) = a2().
% 0.77/1.17 Proof: Rewrite lhs with equations [105,2,98]
% 0.77/1.17 rhs with equations [].
% 0.77/1.17
% 0.77/1.17 % SZS output end Proof
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