%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL211-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n031.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 01:14:15 PM UTC 2026
% Result : Unsatisfiable 17.24s 17.54s
% Output : CNFRefutation 17.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 3 RR)
% Number of literals : 36 ( 35 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 67 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
theorem(implies(not(q),implies(or(p,q),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,
ifeq(axiom(X),true,theorem(X),true) = true,
file('theBenchmark.p',rule_1) ).
cnf(c8,plain,
theorem(or(not(or(X,X)),X)) = true,
inference(equational,[status(thm)],[c2,c6,c7]) ).
cnf(c9,plain,
theorem(or(not(X),or(Y,X))) = true,
inference(equational,[status(thm)],[c2,c4,c7]) ).
cnf(c10,axiom,
axiom(implies(or(X,Y),or(Y,X))) = true,
file('theBenchmark.p',axiom_1_4) ).
cnf(c11,plain,
axiom(or(not(or(X,Y)),or(Y,X))) = true,
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c12,plain,
theorem(or(not(or(X,Y)),or(Y,X))) = true,
inference(equational,[status(thm)],[c2,c7,c11]) ).
cnf(c13,axiom,
axiom(implies(implies(X,Y),implies(or(Z,X),or(Z,Y)))) = true,
file('theBenchmark.p',axiom_1_6) ).
cnf(c14,plain,
axiom(or(not(or(not(X),Y)),or(not(or(Z,X)),or(Z,Y)))) = true,
inference(equational,[status(thm)],[c1,c13]) ).
cnf(c15,axiom,
axiom(implies(or(X,or(Y,Z)),or(Y,or(X,Z)))) = true,
file('theBenchmark.p',axiom_1_5) ).
cnf(c16,plain,
axiom(or(not(or(X,or(Y,Z))),or(Y,or(X,Z)))) = true,
inference(equational,[status(thm)],[c1,c15]) ).
cnf(c17,plain,
theorem(or(not(or(X,or(Y,Z))),or(Y,or(X,Z)))) = true,
inference(equational,[status(thm)],[c2,c7,c16]) ).
cnf(c18,axiom,
ifeq(theorem(implies(X,Y)),true,ifeq(theorem(X),true,theorem(Y),true),true) = true,
file('theBenchmark.p',rule_2) ).
cnf(c19,plain,
ifeq(theorem(or(not(X),Y)),true,ifeq(theorem(X),true,theorem(Y),true),true) = true,
inference(equational,[status(thm)],[c1,c18]) ).
cnf(c20,plain,
ifeq(theorem(or(X,X)),true,theorem(X),true) = true,
inference(equational,[status(thm)],[c2,c8,c19]) ).
cnf(c25,plain,
ifeq(theorem(or(X,Y)),true,theorem(or(Y,X)),true) = true,
inference(equational,[status(thm)],[c2,c12,c19]) ).
cnf(c61,plain,
theorem(or(not(or(not(X),Y)),or(not(or(Z,X)),or(Z,Y)))) = true,
inference(equational,[status(thm)],[c2,c7,c14]) ).
cnf(c69,plain,
ifeq(theorem(or(X,or(Y,Z))),true,theorem(or(Y,or(X,Z))),true) = true,
inference(equational,[status(thm)],[c2,c17,c19]) ).
cnf(c70,plain,
theorem(or(X,or(not(Y),Y))) = true,
inference(equational,[status(thm)],[c2,c9,c69]) ).
cnf(c71,plain,
theorem(or(not(X),X)) = true,
inference(equational,[status(thm)],[c2,c20,c70]) ).
cnf(c72,plain,
theorem(or(X,not(X))) = true,
inference(equational,[status(thm)],[c2,c25,c71]) ).
cnf(c76,plain,
theorem(or(X,or(not(or(Y,X)),Y))) = true,
inference(equational,[status(thm)],[c2,c12,c69]) ).
cnf(c79,plain,
theorem(or(or(not(or(X,Y)),X),Y)) = true,
inference(equational,[status(thm)],[c2,c25,c76]) ).
cnf(c477,plain,
ifeq(theorem(or(not(or(X,not(X))),Y)),true,theorem(Y),true) = true,
inference(equational,[status(thm)],[c2,c19,c72]) ).
cnf(c478,plain,
theorem(or(not(or(X,Y)),or(X,not(not(Y))))) = true,
inference(equational,[status(thm)],[c2,c61,c477]) ).
cnf(c1218,plain,
ifeq(theorem(or(X,Y)),true,theorem(or(X,not(not(Y)))),true) = true,
inference(equational,[status(thm)],[c2,c19,c478]) ).
cnf(c1229,plain,
theorem(or(or(not(or(X,Y)),X),not(not(Y)))) = true,
inference(equational,[status(thm)],[c2,c79,c1218]) ).
cnf(c1242,plain,
theorem(or(not(not(X)),or(not(or(Y,X)),Y))) = true,
inference(equational,[status(thm)],[c2,c25,c1229]) ).
cnf(g1,plain,
theorem(implies(not(q),implies(or(p,q),p))) = true,
inference(equational,[status(thm)],[c1,c1242]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL211-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_Leo-III %s %d THM
% 0.08/0.35 % Computer : n031.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 05:08:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 17.24/17.54 % SZS status Unsatisfiable
% 17.24/17.54 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------