TSTP Solution File: GRP115-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP115-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n017.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 01:13:52 EDT 2023
% Result : Unsatisfiable 3.88s 4.21s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : GRP115-1 : TPTP v8.1.2. Released v1.2.0.
% 0.09/0.15 % Command : toma --casc %s
% 0.16/0.37 % Computer : n017.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon Aug 28 20:12:58 EDT 2023
% 0.16/0.37 % CPUTime :
% 3.88/4.21 % SZS status Unsatisfiable
% 3.88/4.21 % SZS output start Proof
% 3.88/4.21 original problem:
% 3.88/4.21 axioms:
% 3.88/4.21 multiply(X, multiply(multiply(X, multiply(multiply(X, Y), Z)), multiply(identity(), multiply(Z, Z)))) = Y
% 3.88/4.21 goal:
% 3.88/4.21 multiply(a(), multiply(a(), a())) != identity()
% 3.88/4.21 To show the unsatisfiability of the original goal,
% 3.88/4.21 it suffices to show that multiply(a(), multiply(a(), a())) = identity() (skolemized goal) is valid under the axioms.
% 3.88/4.21 Here is an equational proof:
% 3.88/4.21 0: multiply(X0, multiply(multiply(X0, multiply(multiply(X0, X1), X2)), multiply(identity(), multiply(X2, X2)))) = X1.
% 3.88/4.21 Proof: Axiom.
% 3.88/4.21
% 3.88/4.21 2: multiply(multiply(X3, X4), X5) = multiply(X3, multiply(X4, multiply(identity(), multiply(multiply(identity(), multiply(X5, X5)), multiply(identity(), multiply(X5, X5)))))).
% 3.88/4.21 Proof: A critical pair between equations 0 and 0.
% 3.88/4.21
% 3.88/4.21 3: multiply(multiply(X3, multiply(multiply(X3, X4), X5)), multiply(identity(), multiply(X5, X5))) = multiply(X3, multiply(multiply(X3, multiply(X4, X2)), multiply(identity(), multiply(X2, X2)))).
% 3.88/4.21 Proof: A critical pair between equations 0 and 0.
% 3.88/4.22
% 3.88/4.22 6: multiply(X0, multiply(X0, multiply(multiply(X0, multiply(X1, X2)), multiply(identity(), multiply(X2, X2))))) = X1.
% 3.88/4.22 Proof: Rewrite equation 0,
% 3.88/4.22 lhs with equations [3]
% 3.88/4.22 rhs with equations [].
% 3.88/4.22
% 3.88/4.22 7: multiply(multiply(X3, identity()), X8) = multiply(X3, X8).
% 3.88/4.22 Proof: A critical pair between equations 2 and 6.
% 3.88/4.22
% 3.88/4.22 8: X7 = multiply(X6, multiply(multiply(X6, multiply(multiply(X6, X7), X9)), multiply(identity(), multiply(X9, X9)))).
% 3.88/4.22 Proof: A critical pair between equations 6 and 3.
% 3.88/4.22
% 3.88/4.22 9: multiply(multiply(X3, X4), multiply(identity(), X7)) = multiply(X3, multiply(X4, multiply(identity(), multiply(identity(), multiply(multiply(identity(), multiply(X7, X9)), multiply(identity(), multiply(X9, X9))))))).
% 3.88/4.22 Proof: A critical pair between equations 2 and 3.
% 3.88/4.22
% 3.88/4.22 24: multiply(multiply(X3, X4), multiply(identity(), X7)) = multiply(X3, multiply(X4, X7)).
% 3.88/4.22 Proof: Rewrite equation 9,
% 3.88/4.22 lhs with equations []
% 3.88/4.22 rhs with equations [6].
% 3.88/4.22
% 3.88/4.22 29: identity() = multiply(X10, multiply(multiply(X10, multiply(X10, X11)), multiply(identity(), multiply(X11, X11)))).
% 3.88/4.22 Proof: A critical pair between equations 8 and 7.
% 3.88/4.22
% 3.88/4.22 30: X1 = multiply(X8, multiply(X8, multiply(X8, multiply(multiply(X1, X2), multiply(X2, X2))))).
% 3.88/4.22 Proof: A critical pair between equations 6 and 24.
% 3.88/4.22
% 3.88/4.22 35: multiply(X9, identity()) = multiply(X0, multiply(X0, multiply(multiply(X0, multiply(X9, X10)), multiply(identity(), multiply(X10, X10))))).
% 3.88/4.22 Proof: A critical pair between equations 6 and 7.
% 3.88/4.22
% 3.88/4.22 39: multiply(X9, identity()) = X9.
% 3.88/4.22 Proof: Rewrite equation 35,
% 3.88/4.22 lhs with equations []
% 3.88/4.22 rhs with equations [24,30].
% 3.88/4.22
% 3.88/4.22 40: identity() = multiply(X10, multiply(X10, multiply(multiply(X10, X11), multiply(X11, X11)))).
% 3.88/4.22 Proof: Rewrite equation 29,
% 3.88/4.22 lhs with equations []
% 3.88/4.22 rhs with equations [24].
% 3.88/4.22
% 3.88/4.22 59: identity() = multiply(X12, multiply(X12, multiply(X12, multiply(identity(), identity())))).
% 3.88/4.22 Proof: A critical pair between equations 40 and 39.
% 3.88/4.22
% 3.88/4.22 70: identity() = multiply(X12, multiply(X12, X12)).
% 3.88/4.22 Proof: Rewrite equation 59,
% 3.88/4.22 lhs with equations []
% 3.88/4.22 rhs with equations [39,39].
% 3.88/4.22
% 3.88/4.22 80: multiply(a(), multiply(a(), a())) = identity().
% 3.88/4.22 Proof: Rewrite lhs with equations [70]
% 3.88/4.22 rhs with equations [].
% 3.88/4.22
% 3.88/4.22 % SZS output end Proof
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