TSTP Solution File: GRP185-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP185-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n001.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 01:14:21 EDT 2023
% Result : Unsatisfiable 0.15s 0.62s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP185-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.11 % Command : toma --casc %s
% 0.10/0.31 % Computer : n001.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 29 02:00:06 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.62 % SZS status Unsatisfiable
% 0.15/0.62 % SZS output start Proof
% 0.15/0.62 original problem:
% 0.15/0.62 axioms:
% 0.15/0.62 multiply(identity(), X) = X
% 0.15/0.62 multiply(inverse(X), X) = identity()
% 0.15/0.62 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.15/0.62 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.15/0.62 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.15/0.62 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.15/0.62 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.15/0.62 least_upper_bound(X, X) = X
% 0.15/0.62 greatest_lower_bound(X, X) = X
% 0.15/0.62 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.15/0.62 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.15/0.62 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.15/0.62 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.15/0.62 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.15/0.62 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.15/0.62 goal:
% 0.15/0.62 least_upper_bound(least_upper_bound(multiply(a(), b()), identity()), multiply(least_upper_bound(a(), identity()), least_upper_bound(b(), identity()))) != multiply(least_upper_bound(a(), identity()), least_upper_bound(b(), identity()))
% 0.15/0.62 To show the unsatisfiability of the original goal,
% 0.15/0.62 it suffices to show that least_upper_bound(least_upper_bound(multiply(a(), b()), identity()), multiply(least_upper_bound(a(), identity()), least_upper_bound(b(), identity()))) = multiply(least_upper_bound(a(), identity()), least_upper_bound(b(), identity())) (skolemized goal) is valid under the axioms.
% 0.15/0.62 Here is an equational proof:
% 0.15/0.62 0: multiply(identity(), X0) = X0.
% 0.15/0.62 Proof: Axiom.
% 0.15/0.62
% 0.15/0.62 4: least_upper_bound(X0, X1) = least_upper_bound(X1, X0).
% 0.15/0.62 Proof: Axiom.
% 0.15/0.62
% 0.15/0.62 6: least_upper_bound(X0, least_upper_bound(X1, X2)) = least_upper_bound(least_upper_bound(X0, X1), X2).
% 0.15/0.62 Proof: Axiom.
% 0.15/0.62
% 0.15/0.62 7: least_upper_bound(X0, X0) = X0.
% 0.15/0.62 Proof: Axiom.
% 0.15/0.62
% 0.15/0.62 11: multiply(X0, least_upper_bound(X1, X2)) = least_upper_bound(multiply(X0, X1), multiply(X0, X2)).
% 0.15/0.62 Proof: Axiom.
% 0.15/0.62
% 0.15/0.62 13: multiply(least_upper_bound(X1, X2), X0) = least_upper_bound(multiply(X1, X0), multiply(X2, X0)).
% 0.15/0.62 Proof: Axiom.
% 0.15/0.62
% 0.15/0.62 18: least_upper_bound(X3, least_upper_bound(X3, X2)) = least_upper_bound(X3, X2).
% 0.15/0.62 Proof: A critical pair between equations 6 and 7.
% 0.15/0.62
% 0.15/0.62 21: least_upper_bound(X5, least_upper_bound(X3, X4)) = least_upper_bound(X3, least_upper_bound(X4, X5)).
% 0.15/0.62 Proof: A critical pair between equations 4 and 6.
% 0.15/0.62
% 0.15/0.62 25: least_upper_bound(X3, least_upper_bound(X4, X2)) = least_upper_bound(least_upper_bound(X4, X3), X2).
% 0.15/0.62 Proof: A critical pair between equations 6 and 4.
% 0.15/0.62
% 0.15/0.62 27: least_upper_bound(X3, least_upper_bound(X4, X2)) = least_upper_bound(X4, least_upper_bound(X3, X2)).
% 0.15/0.62 Proof: Rewrite equation 25,
% 0.15/0.62 lhs with equations []
% 0.15/0.62 rhs with equations [6].
% 0.15/0.62
% 0.15/0.62 30: least_upper_bound(least_upper_bound(multiply(a(), b()), identity()), multiply(least_upper_bound(a(), identity()), least_upper_bound(b(), identity()))) = multiply(least_upper_bound(a(), identity()), least_upper_bound(b(), identity())).
% 0.15/0.62 Proof: Rewrite lhs with equations [4,4,4,11,13,0,13,0,6,6,27,27,21,7,18]
% 0.15/0.62 rhs with equations [4,4,11,13,0,13,0,6].
% 0.15/0.62
% 0.15/0.62 % SZS output end Proof
%------------------------------------------------------------------------------