%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 01:14:12 PM UTC 2026
% Result : Unsatisfiable 74.76s 74.82s
% Output : CNFRefutation 74.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 3 RR)
% Number of literals : 11 ( 10 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 : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 18 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
theorem(or(not(not(p)),or(not(p),q))) != true,
file('theBenchmark.p',prove_this) ).
cnf(c1,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c3,axiom,
axiom(or(not(X),or(Y,X))) = true,
file('theBenchmark.p',axiom_1_3) ).
cnf(c4,axiom,
ifeq(axiom(X),true,theorem(X),true) = true,
file('theBenchmark.p',rule_1) ).
cnf(c7,axiom,
axiom(or(not(or(X,Y)),or(Y,X))) = true,
file('theBenchmark.p',axiom_1_4) ).
cnf(c8,plain,
theorem(or(not(or(X,Y)),or(Y,X))) = true,
inference(equational,[status(thm)],[c1,c4,c7]) ).
cnf(c2065,axiom,
ifeq(theorem(or(not(X),Y)),true,ifeq(axiom(or(not(Z),X)),true,theorem(or(not(Z),Y)),true),true) = true,
file('theBenchmark.p',rule_3) ).
cnf(c2067,plain,
ifeq(theorem(or(not(or(X,Y)),Z)),true,theorem(or(not(Y),Z)),true) = true,
inference(equational,[status(thm)],[c1,c3,c2065]) ).
cnf(c2068,plain,
theorem(or(not(X),or(X,Y))) = true,
inference(equational,[status(thm)],[c1,c8,c2067]) ).
cnf(g1,plain,
theorem(or(not(not(p)),or(not(p),q))) = true,
inference(equational,[status(thm)],[c2068]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_Leo-III %s %d THM
% 0.07/0.33 % Computer : n002.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 5 11:51:35 UTC 2026
% 0.07/0.34 % CPUTime :
% 74.76/74.82 % SZS status Unsatisfiable
% 74.76/74.82 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------