%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL239-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n019.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 01:14:19 PM UTC 2026
% Result : Unsatisfiable 0.32s 0.72s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 3 RR)
% Number of literals : 29 ( 28 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-4 aty)
% Number of variables : 48 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
theorem(not(and(p,not(p)))) != true,
file('theBenchmark.p',prove_this) ).
cnf(c1,axiom,
implies(X,Y) = or(not(X),Y),
file('theBenchmark.p',implies_definition) ).
cnf(c2,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c3,axiom,
axiom(implies(X,or(Y,X))) = true,
file('theBenchmark.p',axiom_1_3) ).
cnf(c4,plain,
axiom(or(not(X),or(Y,X))) = true,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,axiom,
axiom(implies(or(X,X),X)) = true,
file('theBenchmark.p',axiom_1_2) ).
cnf(c6,plain,
axiom(or(not(or(X,X)),X)) = true,
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c7,axiom,
and(X,Y) = not(or(not(X),not(Y))),
file('theBenchmark.p',and_defn) ).
cnf(c8,axiom,
ifeq(axiom(X),true,theorem(X),true) = true,
file('theBenchmark.p',rule_1) ).
cnf(c9,plain,
theorem(or(not(or(X,X)),X)) = true,
inference(equational,[status(thm)],[c2,c6,c8]) ).
cnf(c10,plain,
theorem(or(not(X),or(Y,X))) = true,
inference(equational,[status(thm)],[c2,c4,c8]) ).
cnf(c11,axiom,
axiom(implies(or(X,Y),or(Y,X))) = true,
file('theBenchmark.p',axiom_1_4) ).
cnf(c12,plain,
axiom(or(not(or(X,Y)),or(Y,X))) = true,
inference(equational,[status(thm)],[c1,c11]) ).
cnf(c13,plain,
theorem(or(not(or(X,Y)),or(Y,X))) = true,
inference(equational,[status(thm)],[c2,c8,c12]) ).
cnf(c16,axiom,
axiom(implies(or(X,or(Y,Z)),or(Y,or(X,Z)))) = true,
file('theBenchmark.p',axiom_1_5) ).
cnf(c17,plain,
axiom(or(not(or(X,or(Y,Z))),or(Y,or(X,Z)))) = true,
inference(equational,[status(thm)],[c1,c16]) ).
cnf(c18,plain,
theorem(or(not(or(X,or(Y,Z))),or(Y,or(X,Z)))) = true,
inference(equational,[status(thm)],[c2,c8,c17]) ).
cnf(c19,axiom,
ifeq(theorem(implies(X,Y)),true,ifeq(theorem(X),true,theorem(Y),true),true) = true,
file('theBenchmark.p',rule_2) ).
cnf(c20,plain,
ifeq(theorem(or(not(X),Y)),true,ifeq(theorem(X),true,theorem(Y),true),true) = true,
inference(equational,[status(thm)],[c1,c19]) ).
cnf(c21,plain,
ifeq(theorem(or(X,X)),true,theorem(X),true) = true,
inference(equational,[status(thm)],[c2,c9,c20]) ).
cnf(c26,plain,
ifeq(theorem(or(X,Y)),true,theorem(or(Y,X)),true) = true,
inference(equational,[status(thm)],[c2,c13,c20]) ).
cnf(c70,plain,
ifeq(theorem(or(X,or(Y,Z))),true,theorem(or(Y,or(X,Z))),true) = true,
inference(equational,[status(thm)],[c2,c18,c20]) ).
cnf(c71,plain,
theorem(or(X,or(not(Y),Y))) = true,
inference(equational,[status(thm)],[c2,c10,c70]) ).
cnf(c72,plain,
theorem(or(not(X),X)) = true,
inference(equational,[status(thm)],[c2,c21,c71]) ).
cnf(c73,plain,
theorem(or(X,not(X))) = true,
inference(equational,[status(thm)],[c2,c26,c72]) ).
cnf(c98,plain,
ifeq(theorem(X),true,theorem(not(not(X))),true) = true,
inference(equational,[status(thm)],[c2,c20,c73]) ).
cnf(c99,plain,
theorem(not(not(or(X,not(X))))) = true,
inference(equational,[status(thm)],[c2,c73,c98]) ).
cnf(g1,plain,
theorem(not(and(p,not(p)))) = true,
inference(equational,[status(thm)],[c7,c99]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL239-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_Leo-III %s %d THM
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 10:45:53 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.32/0.72 % SZS status Unsatisfiable
% 0.32/0.72 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------