TSTP Solution File: GRP001-2 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP001-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n023.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 01:13:30 EDT 2023
% Result : Unsatisfiable 0.45s 0.78s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP001-2 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n023.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 22:46:40 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.45/0.78 % SZS status Unsatisfiable
% 0.45/0.78 % SZS output start Proof
% 0.45/0.78 original problem:
% 0.45/0.78 axioms:
% 0.45/0.78 multiply(identity(), X) = X
% 0.45/0.78 multiply(inverse(X), X) = identity()
% 0.45/0.78 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.45/0.78 multiply(X, identity()) = X
% 0.45/0.78 multiply(X, inverse(X)) = identity()
% 0.45/0.78 multiply(X, X) = identity()
% 0.45/0.78 multiply(a(), b()) = c()
% 0.45/0.78 goal:
% 0.45/0.78 multiply(b(), a()) != c()
% 0.45/0.78 To show the unsatisfiability of the original goal,
% 0.45/0.78 it suffices to show that multiply(b(), a()) = c() (skolemized goal) is valid under the axioms.
% 0.45/0.78 Here is an equational proof:
% 0.45/0.78 0: multiply(identity(), X0) = X0.
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 1: multiply(inverse(X0), X0) = identity().
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 2: multiply(multiply(X0, X1), X2) = multiply(X0, multiply(X1, X2)).
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 3: multiply(X0, identity()) = X0.
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 4: multiply(X0, inverse(X0)) = identity().
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 5: multiply(X0, X0) = identity().
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 6: multiply(a(), b()) = c().
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 8: multiply(X3, multiply(X3, X2)) = multiply(identity(), X2).
% 0.45/0.78 Proof: A critical pair between equations 2 and 5.
% 0.45/0.78
% 0.45/0.78 11: multiply(inverse(X3), multiply(X3, X2)) = multiply(identity(), X2).
% 0.45/0.78 Proof: A critical pair between equations 2 and 1.
% 0.45/0.78
% 0.45/0.78 12: multiply(X3, multiply(inverse(X3), X2)) = multiply(identity(), X2).
% 0.45/0.78 Proof: A critical pair between equations 2 and 4.
% 0.45/0.78
% 0.45/0.78 13: multiply(X0, multiply(X1, inverse(multiply(X0, X1)))) = identity().
% 0.45/0.78 Proof: A critical pair between equations 2 and 4.
% 0.45/0.78
% 0.45/0.78 14: multiply(X3, multiply(inverse(X3), X2)) = X2.
% 0.45/0.78 Proof: Rewrite equation 12,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [0].
% 0.45/0.78
% 0.45/0.78 15: multiply(inverse(X3), multiply(X3, X2)) = X2.
% 0.45/0.78 Proof: Rewrite equation 11,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [0].
% 0.45/0.78
% 0.45/0.78 16: multiply(X3, multiply(X3, X2)) = X2.
% 0.45/0.78 Proof: Rewrite equation 8,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [0].
% 0.45/0.78
% 0.45/0.78 17: inverse(X3) = multiply(X3, identity()).
% 0.45/0.78 Proof: A critical pair between equations 14 and 5.
% 0.45/0.78
% 0.45/0.78 28: multiply(X5, inverse(multiply(X4, X5))) = multiply(inverse(X4), identity()).
% 0.45/0.78 Proof: A critical pair between equations 15 and 13.
% 0.45/0.78
% 0.45/0.78 29: multiply(X5, multiply(X4, X5)) = X4.
% 0.45/0.78 Proof: Rewrite equation 28,
% 0.45/0.78 lhs with equations [17,2,3]
% 0.45/0.78 rhs with equations [17,3,3].
% 0.45/0.78
% 0.45/0.78 32: b() = multiply(a(), c()).
% 0.45/0.78 Proof: A critical pair between equations 16 and 6.
% 0.45/0.78
% 0.45/0.78 33: multiply(X7, X6) = multiply(X6, X7).
% 0.45/0.78 Proof: A critical pair between equations 16 and 29.
% 0.45/0.78
% 0.45/0.78 41: b() = multiply(c(), a()).
% 0.45/0.78 Proof: Rewrite equation 32,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [33].
% 0.45/0.78
% 0.45/0.78 42: multiply(b(), a()) = c().
% 0.45/0.78 Proof: Rewrite lhs with equations [41,2,5,3]
% 0.45/0.78 rhs with equations [].
% 0.45/0.78
% 0.45/0.78 % SZS output end Proof
%------------------------------------------------------------------------------