%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL218-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n028.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 01:14:16 PM UTC 2026
% Result : Unsatisfiable 107.90s 108.02s
% Output : CNFRefutation 107.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 3 RR)
% Number of literals : 19 ( 18 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 41 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
theorem(or(not(or(not(or(p,q)),q)),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(c9,axiom,
axiom(or(not(or(X,or(Y,Z))),or(Y,or(X,Z)))) = true,
file('theBenchmark.p',axiom_1_5) ).
cnf(c12,axiom,
ifeq(theorem(X),true,ifeq(axiom(or(not(X),Y)),true,theorem(Y),true),true) = true,
file('theBenchmark.p',rule_2) ).
cnf(c65,plain,
ifeq(theorem(or(X,or(Y,Z))),true,theorem(or(Y,or(X,Z))),true) = true,
inference(equational,[status(thm)],[c1,c9,c12]) ).
cnf(c71,plain,
theorem(or(X,or(not(or(Y,X)),Y))) = true,
inference(equational,[status(thm)],[c1,c8,c65]) ).
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(c2552,plain,
ifeq(theorem(or(not(or(X,Y)),Z)),true,theorem(or(not(or(Y,X)),Z)),true) = true,
inference(equational,[status(thm)],[c1,c7,c2065]) ).
cnf(c2658,plain,
theorem(or(not(or(X,Y)),or(not(or(Z,not(or(Y,X)))),Z))) = true,
inference(equational,[status(thm)],[c1,c71,c2552]) ).
cnf(c2659,plain,
theorem(or(not(X),or(not(or(Y,not(or(X,Z)))),Y))) = true,
inference(equational,[status(thm)],[c1,c2067,c2658]) ).
cnf(c2660,plain,
theorem(or(not(or(X,not(or(Y,Z)))),or(not(Y),X))) = true,
inference(equational,[status(thm)],[c1,c65,c2659]) ).
cnf(c2663,plain,
theorem(or(not(or(not(or(X,Y)),Z)),or(not(X),Z))) = true,
inference(equational,[status(thm)],[c1,c2552,c2660]) ).
cnf(g1,plain,
theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) = true,
inference(equational,[status(thm)],[c2663]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL218-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_Leo-III %s %d THM
% 0.08/0.37 % Computer : n028.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Fri Sep 4 12:45:29 UTC 2026
% 0.08/0.37 % CPUTime :
% 107.90/108.02 % SZS status Unsatisfiable
% 107.90/108.02 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------