TSTP Solution File: GRP137-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP137-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n017.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 01:14:07 EDT 2023
% Result : Unsatisfiable 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP137-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:13:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.49 % SZS status Unsatisfiable
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 original problem:
% 0.19/0.49 axioms:
% 0.19/0.49 multiply(identity(), X) = X
% 0.19/0.49 multiply(inverse(X), X) = identity()
% 0.19/0.49 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.19/0.49 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.19/0.49 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.19/0.49 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.19/0.49 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.19/0.49 least_upper_bound(X, X) = X
% 0.19/0.49 greatest_lower_bound(X, X) = X
% 0.19/0.49 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.19/0.49 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.19/0.49 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.19/0.49 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.19/0.49 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.19/0.49 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.19/0.49 greatest_lower_bound(a(), b()) = a()
% 0.19/0.49 greatest_lower_bound(a(), b()) = b()
% 0.19/0.49 goal:
% 0.19/0.49 a() != b()
% 0.19/0.49 To show the unsatisfiability of the original goal,
% 0.19/0.49 it suffices to show that a() = b() (skolemized goal) is valid under the axioms.
% 0.19/0.49 Here is an equational proof:
% 0.19/0.49 15: greatest_lower_bound(a(), b()) = a().
% 0.19/0.49 Proof: Axiom.
% 0.19/0.49
% 0.19/0.49 16: greatest_lower_bound(a(), b()) = b().
% 0.19/0.49 Proof: Axiom.
% 0.19/0.49
% 0.19/0.49 17: b() = a().
% 0.19/0.49 Proof: Rewrite equation 15,
% 0.19/0.49 lhs with equations [16]
% 0.19/0.49 rhs with equations [].
% 0.19/0.49
% 0.19/0.49 18: a() = b().
% 0.19/0.49 Proof: Rewrite lhs with equations [17]
% 0.19/0.49 rhs with equations [].
% 0.19/0.49
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------