TSTP Solution File: GRP118-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP118-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n013.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 4.64s 4.97s
% Output : CNFRefutation 4.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP118-1 : TPTP v8.1.2. Released v1.2.0.
% 0.06/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 20:15:46 EDT 2023
% 0.12/0.34 % CPUTime :
% 4.64/4.97 % SZS status Unsatisfiable
% 4.64/4.97 % SZS output start Proof
% 4.64/4.97 original problem:
% 4.64/4.97 axioms:
% 4.64/4.97 multiply(X, multiply(multiply(X, multiply(multiply(X, Y), Z)), multiply(identity(), multiply(Z, Z)))) = Y
% 4.64/4.97 goal:
% 4.64/4.97 multiply(multiply(a(), b()), c()) != multiply(a(), multiply(b(), c()))
% 4.64/4.97 To show the unsatisfiability of the original goal,
% 4.64/4.97 it suffices to show that multiply(multiply(a(), b()), c()) = multiply(a(), multiply(b(), c())) (skolemized goal) is valid under the axioms.
% 4.64/4.97 Here is an equational proof:
% 4.64/4.97 0: multiply(X0, multiply(multiply(X0, multiply(multiply(X0, X1), X2)), multiply(identity(), multiply(X2, X2)))) = X1.
% 4.64/4.97 Proof: Axiom.
% 4.64/4.97
% 4.64/4.97 2: multiply(multiply(X3, X4), X5) = multiply(X3, multiply(X4, multiply(identity(), multiply(multiply(identity(), multiply(X5, X5)), multiply(identity(), multiply(X5, X5)))))).
% 4.64/4.97 Proof: A critical pair between equations 0 and 0.
% 4.64/4.97
% 4.64/4.97 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)))).
% 4.64/4.97 Proof: A critical pair between equations 0 and 0.
% 4.64/4.97
% 4.64/4.97 6: multiply(X0, multiply(X0, multiply(multiply(X0, multiply(X1, X2)), multiply(identity(), multiply(X2, X2))))) = X1.
% 4.64/4.97 Proof: Rewrite equation 0,
% 4.64/4.97 lhs with equations [3]
% 4.64/4.97 rhs with equations [].
% 4.64/4.97
% 4.64/4.97 7: multiply(multiply(X3, identity()), X8) = multiply(X3, X8).
% 4.64/4.97 Proof: A critical pair between equations 2 and 6.
% 4.64/4.97
% 4.64/4.97 8: X7 = multiply(X6, multiply(multiply(X6, multiply(multiply(X6, X7), X9)), multiply(identity(), multiply(X9, X9)))).
% 4.64/4.97 Proof: A critical pair between equations 6 and 3.
% 4.64/4.97
% 4.64/4.97 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))))))).
% 4.64/4.97 Proof: A critical pair between equations 2 and 3.
% 4.64/4.97
% 4.64/4.97 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)))))))).
% 4.64/4.97 Proof: A critical pair between equations 6 and 3.
% 4.64/4.97
% 4.64/4.97 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).
% 4.64/4.97 Proof: A critical pair between equations 2 and 2.
% 4.64/4.97
% 4.64/4.97 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)))))))).
% 4.64/4.97 Proof: Rewrite equation 14,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [6,2].
% 4.64/4.97
% 4.64/4.97 24: multiply(multiply(X3, X4), multiply(identity(), X7)) = multiply(X3, multiply(X4, X7)).
% 4.64/4.97 Proof: Rewrite equation 9,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [6].
% 4.64/4.97
% 4.64/4.97 25: multiply(multiply(X3, X4), X5) = multiply(X3, multiply(X4, multiply(identity(), multiply(identity(), multiply(multiply(X5, X5), multiply(X5, X5)))))).
% 4.64/4.97 Proof: Rewrite equation 2,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [24].
% 4.64/4.97
% 4.64/4.97 28: X10 = multiply(X9, multiply(X9, multiply(multiply(multiply(X9, X10), X11), multiply(X11, X11)))).
% 4.64/4.97 Proof: A critical pair between equations 19 and 18.
% 4.64/4.97
% 4.64/4.97 29: identity() = multiply(X10, multiply(multiply(X10, multiply(X10, X11)), multiply(identity(), multiply(X11, X11)))).
% 4.64/4.97 Proof: A critical pair between equations 8 and 7.
% 4.64/4.97
% 4.64/4.97 30: X1 = multiply(X8, multiply(X8, multiply(X8, multiply(multiply(X1, X2), multiply(X2, X2))))).
% 4.64/4.97 Proof: A critical pair between equations 6 and 24.
% 4.64/4.97
% 4.64/4.97 35: multiply(X9, identity()) = multiply(X0, multiply(X0, multiply(multiply(X0, multiply(X9, X10)), multiply(identity(), multiply(X10, X10))))).
% 4.64/4.97 Proof: A critical pair between equations 6 and 7.
% 4.64/4.97
% 4.64/4.97 39: multiply(X9, identity()) = X9.
% 4.64/4.97 Proof: Rewrite equation 35,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [24,30].
% 4.64/4.97
% 4.64/4.97 40: identity() = multiply(X10, multiply(X10, multiply(multiply(X10, X11), multiply(X11, X11)))).
% 4.64/4.97 Proof: Rewrite equation 29,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [24].
% 4.64/4.97
% 4.64/4.97 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).
% 4.64/4.97 Proof: Rewrite equation 18,
% 4.64/4.97 lhs with equations [24,24,24,24]
% 4.64/4.97 rhs with equations [].
% 4.64/4.97
% 4.64/4.97 55: X1 = multiply(multiply(X1, multiply(X11, X11)), X11).
% 4.64/4.97 Proof: A critical pair between equations 30 and 30.
% 4.64/4.97
% 4.64/4.97 60: multiply(multiply(multiply(X6, identity()), X8), multiply(X8, X8)) = multiply(X6, identity()).
% 4.64/4.97 Proof: A critical pair between equations 54 and 40.
% 4.64/4.97
% 4.64/4.97 66: X10 = multiply(X9, multiply(X9, multiply(multiply(multiply(X9, X10), identity()), identity()))).
% 4.64/4.97 Proof: A critical pair between equations 28 and 39.
% 4.64/4.97
% 4.64/4.97 67: X10 = multiply(X9, multiply(X9, multiply(X9, X10))).
% 4.64/4.97 Proof: Rewrite equation 66,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [39,39].
% 4.64/4.97
% 4.64/4.97 69: multiply(multiply(X6, X8), multiply(X8, X8)) = X6.
% 4.64/4.97 Proof: Rewrite equation 60,
% 4.64/4.97 lhs with equations [39]
% 4.64/4.97 rhs with equations [39].
% 4.64/4.97
% 4.64/4.97 71: X1 = multiply(X1, multiply(X11, multiply(X11, multiply(identity(), X11)))).
% 4.64/4.97 Proof: Rewrite equation 55,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [25,69,24].
% 4.64/4.97
% 4.64/4.97 76: multiply(multiply(X3, X4), X5) = multiply(X3, multiply(X4, multiply(identity(), multiply(identity(), X5)))).
% 4.64/4.97 Proof: Rewrite equation 25,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [69].
% 4.64/4.97
% 4.64/4.97 80: multiply(identity(), X13) = X13.
% 4.64/4.97 Proof: A critical pair between equations 67 and 71.
% 4.64/4.97
% 4.64/4.97 93: multiply(multiply(X3, X4), X5) = multiply(X3, multiply(X4, X5)).
% 4.64/4.97 Proof: Rewrite equation 76,
% 4.64/4.97 lhs with equations []
% 4.64/4.97 rhs with equations [80,80].
% 4.64/4.97
% 4.64/4.97 95: multiply(multiply(a(), b()), c()) = multiply(a(), multiply(b(), c())).
% 4.64/4.97 Proof: Rewrite lhs with equations [93]
% 4.64/4.97 rhs with equations [].
% 4.64/4.97
% 4.64/4.97 % SZS output end Proof
%------------------------------------------------------------------------------