TSTP Solution File: GRP116-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP116-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n010.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 4.40s 4.70s
% Output : CNFRefutation 4.40s
% 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 : GRP116-1 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 22:16:19 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.40/4.70 % SZS status Unsatisfiable
% 4.40/4.70 % SZS output start Proof
% 4.40/4.70 original problem:
% 4.40/4.70 axioms:
% 4.40/4.70 multiply(X, multiply(multiply(X, multiply(multiply(X, Y), Z)), multiply(identity(), multiply(Z, Z)))) = Y
% 4.40/4.70 goal:
% 4.40/4.70 multiply(identity(), a()) != a()
% 4.40/4.70 To show the unsatisfiability of the original goal,
% 4.40/4.70 it suffices to show that multiply(identity(), a()) = a() (skolemized goal) is valid under the axioms.
% 4.40/4.70 Here is an equational proof:
% 4.40/4.70 0: multiply(X0, multiply(multiply(X0, multiply(multiply(X0, X1), X2)), multiply(identity(), multiply(X2, X2)))) = X1.
% 4.40/4.70 Proof: Axiom.
% 4.40/4.70
% 4.40/4.70 2: multiply(multiply(X3, X4), X5) = multiply(X3, multiply(X4, multiply(identity(), multiply(multiply(identity(), multiply(X5, X5)), multiply(identity(), multiply(X5, X5)))))).
% 4.40/4.70 Proof: A critical pair between equations 0 and 0.
% 4.40/4.70
% 4.40/4.70 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)))).
% 4.40/4.70 Proof: A critical pair between equations 0 and 0.
% 4.40/4.70
% 4.40/4.70 6: multiply(X0, multiply(X0, multiply(multiply(X0, multiply(X1, X2)), multiply(identity(), multiply(X2, X2))))) = X1.
% 4.40/4.70 Proof: Rewrite equation 0,
% 4.40/4.70 lhs with equations [3]
% 4.40/4.70 rhs with equations [].
% 4.40/4.70
% 4.40/4.70 7: multiply(multiply(X3, identity()), X8) = multiply(X3, X8).
% 4.40/4.70 Proof: A critical pair between equations 2 and 6.
% 4.40/4.70
% 4.40/4.70 8: X7 = multiply(X6, multiply(multiply(X6, multiply(multiply(X6, X7), X9)), multiply(identity(), multiply(X9, X9)))).
% 4.40/4.70 Proof: A critical pair between equations 6 and 3.
% 4.40/4.70
% 4.40/4.70 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))))))).
% 4.40/4.70 Proof: A critical pair between equations 2 and 3.
% 4.40/4.70
% 4.40/4.70 14: X1 = multiply(X0, multiply(X0, multiply(multiply(X0, multiply(X1, multiply(identity(), multiply(multiply(identity(), X7), multiply(identity(), X7))))), multiply(identity(), multiply(identity(), multiply(multiply(identity(), multiply(X7, X9)), multiply(identity(), multiply(X9, X9)))))))).
% 4.40/4.70 Proof: A critical pair between equations 6 and 3.
% 4.40/4.70
% 4.40/4.70 18: multiply(X6, multiply(multiply(X7, multiply(identity(), multiply(multiply(identity(), multiply(X8, X8)), multiply(identity(), multiply(X8, X8))))), multiply(identity(), multiply(multiply(identity(), multiply(X5, X5)), multiply(identity(), multiply(X5, X5)))))) = multiply(multiply(multiply(X6, X7), X8), X5).
% 4.40/4.70 Proof: A critical pair between equations 2 and 2.
% 4.40/4.70
% 4.40/4.70 19: X1 = multiply(X0, multiply(X0, multiply(X0, multiply(multiply(X1, multiply(identity(), multiply(multiply(identity(), X7), multiply(identity(), X7)))), multiply(identity(), multiply(multiply(identity(), multiply(X7, X7)), multiply(identity(), multiply(X7, X7)))))))).
% 4.40/4.70 Proof: Rewrite equation 14,
% 4.40/4.70 lhs with equations []
% 4.40/4.70 rhs with equations [6,2].
% 4.40/4.70
% 4.40/4.70 24: multiply(multiply(X3, X4), multiply(identity(), X7)) = multiply(X3, multiply(X4, X7)).
% 4.40/4.70 Proof: Rewrite equation 9,
% 4.40/4.70 lhs with equations []
% 4.40/4.70 rhs with equations [6].
% 4.40/4.70
% 4.40/4.70 25: multiply(multiply(X3, X4), X5) = multiply(X3, multiply(X4, multiply(identity(), multiply(identity(), multiply(multiply(X5, X5), multiply(X5, X5)))))).
% 4.40/4.70 Proof: Rewrite equation 2,
% 4.40/4.70 lhs with equations []
% 4.40/4.70 rhs with equations [24].
% 4.40/4.70
% 4.40/4.70 28: X10 = multiply(X9, multiply(X9, multiply(multiply(multiply(X9, X10), X11), multiply(X11, X11)))).
% 4.40/4.70 Proof: A critical pair between equations 19 and 18.
% 4.40/4.70
% 4.40/4.70 29: identity() = multiply(X10, multiply(multiply(X10, multiply(X10, X11)), multiply(identity(), multiply(X11, X11)))).
% 4.40/4.70 Proof: A critical pair between equations 8 and 7.
% 4.40/4.70
% 4.40/4.70 30: X1 = multiply(X8, multiply(X8, multiply(X8, multiply(multiply(X1, X2), multiply(X2, X2))))).
% 4.40/4.70 Proof: A critical pair between equations 6 and 24.
% 4.40/4.70
% 4.40/4.70 35: multiply(X9, identity()) = multiply(X0, multiply(X0, multiply(multiply(X0, multiply(X9, X10)), multiply(identity(), multiply(X10, X10))))).
% 4.40/4.70 Proof: A critical pair between equations 6 and 7.
% 4.40/4.70
% 4.40/4.70 39: multiply(X9, identity()) = X9.
% 4.40/4.70 Proof: Rewrite equation 35,
% 4.40/4.70 lhs with equations []
% 4.40/4.70 rhs with equations [24,30].
% 4.40/4.70
% 4.40/4.70 40: identity() = multiply(X10, multiply(X10, multiply(multiply(X10, X11), multiply(X11, X11)))).
% 4.40/4.70 Proof: Rewrite equation 29,
% 4.40/4.70 lhs with equations []
% 4.40/4.70 rhs with equations [24].
% 4.40/4.70
% 4.40/4.70 54: multiply(X6, multiply(X7, multiply(identity(), multiply(multiply(identity(), multiply(multiply(X8, X8), multiply(X8, X8))), multiply(multiply(X5, X5), multiply(X5, X5)))))) = multiply(multiply(multiply(X6, X7), X8), X5).
% 4.40/4.70 Proof: Rewrite equation 18,
% 4.40/4.70 lhs with equations [24,24,24,24]
% 4.40/4.70 rhs with equations [].
% 4.40/4.70
% 4.40/4.70 55: X1 = multiply(multiply(X1, multiply(X11, X11)), X11).
% 4.40/4.70 Proof: A critical pair between equations 30 and 30.
% 4.40/4.70
% 4.40/4.70 60: multiply(multiply(multiply(X6, identity()), X8), multiply(X8, X8)) = multiply(X6, identity()).
% 4.40/4.70 Proof: A critical pair between equations 54 and 40.
% 4.40/4.70
% 4.40/4.70 66: X10 = multiply(X9, multiply(X9, multiply(multiply(multiply(X9, X10), identity()), identity()))).
% 4.40/4.70 Proof: A critical pair between equations 28 and 39.
% 4.40/4.70
% 4.40/4.70 67: X10 = multiply(X9, multiply(X9, multiply(X9, X10))).
% 4.40/4.70 Proof: Rewrite equation 66,
% 4.40/4.70 lhs with equations []
% 4.40/4.70 rhs with equations [39,39].
% 4.40/4.70
% 4.40/4.70 69: multiply(multiply(X6, X8), multiply(X8, X8)) = X6.
% 4.40/4.70 Proof: Rewrite equation 60,
% 4.40/4.70 lhs with equations [39]
% 4.40/4.70 rhs with equations [39].
% 4.40/4.70
% 4.40/4.70 71: X1 = multiply(X1, multiply(X11, multiply(X11, multiply(identity(), X11)))).
% 4.40/4.70 Proof: Rewrite equation 55,
% 4.40/4.70 lhs with equations []
% 4.40/4.70 rhs with equations [25,69,24].
% 4.40/4.70
% 4.40/4.70 80: multiply(identity(), X13) = X13.
% 4.40/4.70 Proof: A critical pair between equations 67 and 71.
% 4.40/4.70
% 4.40/4.70 95: multiply(identity(), a()) = a().
% 4.40/4.70 Proof: Rewrite lhs with equations [80]
% 4.40/4.70 rhs with equations [].
% 4.40/4.70
% 4.40/4.70 % SZS output end Proof
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