TSTP Solution File: GRP461-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP461-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n005.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 01:15:04 EDT 2023
% Result : Unsatisfiable 0.18s 0.58s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP461-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n005.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 20:39:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.58 % SZS status Unsatisfiable
% 0.18/0.58 % SZS output start Proof
% 0.18/0.58 original problem:
% 0.18/0.58 axioms:
% 0.18/0.58 divide(A, divide(divide(divide(identity(), B), C), divide(divide(divide(A, A), A), C))) = B
% 0.18/0.58 multiply(A, B) = divide(A, divide(identity(), B))
% 0.18/0.58 inverse(A) = divide(identity(), A)
% 0.18/0.58 identity() = divide(A, A)
% 0.18/0.58 goal:
% 0.18/0.58 multiply(identity(), a2()) != a2()
% 0.18/0.58 To show the unsatisfiability of the original goal,
% 0.18/0.58 it suffices to show that multiply(identity(), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.18/0.58 Here is an equational proof:
% 0.18/0.58 0: divide(X0, divide(divide(divide(identity(), X1), X2), divide(divide(divide(X0, X0), X0), X2))) = X1.
% 0.18/0.58 Proof: Axiom.
% 0.18/0.58
% 0.18/0.58 1: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.18/0.58 Proof: Axiom.
% 0.18/0.58
% 0.18/0.58 2: inverse(X0) = divide(identity(), X0).
% 0.18/0.58 Proof: Axiom.
% 0.18/0.58
% 0.18/0.58 3: identity() = divide(X0, X0).
% 0.18/0.58 Proof: Axiom.
% 0.18/0.58
% 0.18/0.58 4: divide(X0, divide(divide(inverse(X1), X2), divide(inverse(X0), X2))) = X1.
% 0.18/0.58 Proof: Rewrite equation 0,
% 0.18/0.58 lhs with equations [2,3,2]
% 0.18/0.58 rhs with equations [].
% 0.18/0.58
% 0.18/0.58 5: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.18/0.58 Proof: Rewrite equation 1,
% 0.18/0.58 lhs with equations []
% 0.18/0.58 rhs with equations [2].
% 0.18/0.58
% 0.18/0.58 6: inverse(identity()) = identity().
% 0.18/0.58 Proof: A critical pair between equations 2 and 3.
% 0.18/0.58
% 0.18/0.58 7: X1 = divide(X1, identity()).
% 0.18/0.58 Proof: A critical pair between equations 4 and 3.
% 0.18/0.58
% 0.18/0.58 10: X1 = inverse(divide(divide(inverse(X1), X2), divide(inverse(identity()), X2))).
% 0.18/0.58 Proof: A critical pair between equations 4 and 2.
% 0.18/0.58
% 0.18/0.58 15: X1 = divide(identity(), divide(divide(divide(identity(), X1), X2), divide(identity(), X2))).
% 0.18/0.58 Proof: Rewrite equation 10,
% 0.18/0.58 lhs with equations []
% 0.18/0.58 rhs with equations [2,6,2].
% 0.18/0.58
% 0.18/0.58 18: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.18/0.58 Proof: Rewrite equation 5,
% 0.18/0.58 lhs with equations []
% 0.18/0.58 rhs with equations [2].
% 0.18/0.58
% 0.18/0.58 22: X1 = divide(identity(), divide(divide(divide(identity(), X1), identity()), identity())).
% 0.18/0.58 Proof: A critical pair between equations 15 and 7.
% 0.18/0.58
% 0.18/0.58 40: X1 = inverse(inverse(X1)).
% 0.18/0.58 Proof: Rewrite equation 22,
% 0.18/0.58 lhs with equations []
% 0.18/0.58 rhs with equations [2,7,7,2].
% 0.18/0.58
% 0.18/0.58 42: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.18/0.58 Proof: Rewrite equation 18,
% 0.18/0.58 lhs with equations []
% 0.18/0.58 rhs with equations [2].
% 0.18/0.58
% 0.18/0.58 49: multiply(identity(), a2()) = a2().
% 0.18/0.58 Proof: Rewrite lhs with equations [42,2,40]
% 0.18/0.58 rhs with equations [].
% 0.18/0.58
% 0.18/0.58 % SZS output end Proof
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