TSTP Solution File: GRP159-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP159-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n027.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 01:14:11 EDT 2023
% Result : Unsatisfiable 0.20s 0.70s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP159-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.14 % Command : toma --casc %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 23:39:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.70 % SZS status Unsatisfiable
% 0.20/0.70 % SZS output start Proof
% 0.20/0.70 original problem:
% 0.20/0.70 axioms:
% 0.20/0.70 multiply(identity(), X) = X
% 0.20/0.70 multiply(inverse(X), X) = identity()
% 0.20/0.70 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.20/0.70 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.20/0.70 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.20/0.70 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.20/0.70 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.20/0.70 least_upper_bound(X, X) = X
% 0.20/0.70 greatest_lower_bound(X, X) = X
% 0.20/0.70 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.20/0.70 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.20/0.70 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.20/0.70 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.20/0.70 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.20/0.70 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.20/0.70 greatest_lower_bound(a(), b()) = a()
% 0.20/0.70 goal:
% 0.20/0.70 least_upper_bound(multiply(c(), a()), multiply(c(), b())) != multiply(c(), b())
% 0.20/0.70 To show the unsatisfiability of the original goal,
% 0.20/0.70 it suffices to show that least_upper_bound(multiply(c(), a()), multiply(c(), b())) = multiply(c(), b()) (skolemized goal) is valid under the axioms.
% 0.20/0.70 Here is an equational proof:
% 0.20/0.70 3: greatest_lower_bound(X0, X1) = greatest_lower_bound(X1, X0).
% 0.20/0.70 Proof: Axiom.
% 0.20/0.70
% 0.20/0.70 4: least_upper_bound(X0, X1) = least_upper_bound(X1, X0).
% 0.20/0.70 Proof: Axiom.
% 0.20/0.70
% 0.20/0.70 9: least_upper_bound(X0, greatest_lower_bound(X0, X1)) = X0.
% 0.20/0.70 Proof: Axiom.
% 0.20/0.70
% 0.20/0.70 11: multiply(X0, least_upper_bound(X1, X2)) = least_upper_bound(multiply(X0, X1), multiply(X0, X2)).
% 0.20/0.70 Proof: Axiom.
% 0.20/0.70
% 0.20/0.70 15: greatest_lower_bound(a(), b()) = a().
% 0.20/0.70 Proof: Axiom.
% 0.20/0.70
% 0.20/0.70 16: greatest_lower_bound(b(), a()) = a().
% 0.20/0.70 Proof: Rewrite equation 15,
% 0.20/0.70 lhs with equations [3]
% 0.20/0.70 rhs with equations [].
% 0.20/0.70
% 0.20/0.70 17: b() = least_upper_bound(b(), a()).
% 0.20/0.70 Proof: A critical pair between equations 9 and 16.
% 0.20/0.70
% 0.20/0.70 31: least_upper_bound(multiply(c(), a()), multiply(c(), b())) = multiply(c(), b()).
% 0.20/0.70 Proof: Rewrite lhs with equations [11,4,17]
% 0.20/0.70 rhs with equations [].
% 0.20/0.70
% 0.20/0.70 % SZS output end Proof
%------------------------------------------------------------------------------