%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL133-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:14:07 PM UTC 2026
% Result : Unsatisfiable 0.32s 0.58s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 3 RR)
% Number of literals : 14 ( 13 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
x != y,
file('theBenchmark.p',prove_wajsberg_lemma) ).
cnf(c1,axiom,
implies(truth,X) = X,
file('LCL001-0.ax',wajsberg_1) ).
cnf(c2,axiom,
implies(X,Y) = implies(Y,X),
file('theBenchmark.p',lemma_antecedent) ).
cnf(c3,plain,
implies(X,truth) = X,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('LCL001-0.ax',wajsberg_3) ).
cnf(c5,plain,
implies(X,implies(Y,X)) = implies(Y,implies(X,Y)),
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
implies(X,X) = X,
inference(equational,[status(thm)],[c1,c3,c5]) ).
cnf(c7,plain,
implies(X,implies(X,Y)) = implies(Y,implies(X,Y)),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c9,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('LCL001-0.ax',wajsberg_4) ).
cnf(c10,plain,
implies(X,not(X)) = truth,
inference(equational,[status(thm)],[c2,c6,c9]) ).
cnf(c11,plain,
not(X) = X,
inference(equational,[status(thm)],[c3,c7,c10]) ).
cnf(c12,plain,
X = truth,
inference(equational,[status(thm)],[c6,c10,c11]) ).
cnf(g1,plain,
x = y,
inference(equational,[status(thm)],[c12]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL133-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_Leo-III %s %d THM
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 08:09:11 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.32/0.58 % SZS status Unsatisfiable
% 0.32/0.58 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------