%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n018.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 01:14:38 PM UTC 2026
% Result : Unsatisfiable 10.33s 10.73s
% Output : CNFRefutation 10.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 7 RR)
% Number of literals : 19 ( 18 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 : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 30 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true,
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c1,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c2,axiom,
c_in(X,c_insert(X,Y,Z),Z) = true,
file('theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(c3,axiom,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c4,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c5,axiom,
ifeq(c_in(X,Y,tc_PropLog_Opl(Z)),true,c_in(X,c_PropLog_Othms(Y,Z),tc_PropLog_Opl(Z)),true) = true,
file('theBenchmark.p',cls_PropLog_Othms_OH_0) ).
cnf(c8,plain,
c_in(X,c_PropLog_Othms(c_insert(X,Y,tc_PropLog_Opl(Z)),Z),tc_PropLog_Opl(Z)) = true,
inference(equational,[status(thm)],[c1,c2,c5]) ).
cnf(c19,axiom,
ifeq(c_in(X,c_PropLog_Othms(Y,Z),tc_PropLog_Opl(Z)),true,c_in(X,c_PropLog_Othms(c_insert(W,Y,tc_PropLog_Opl(Z)),Z),tc_PropLog_Opl(Z)),true) = true,
file('theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
cnf(c20,plain,
c_in(v_p,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(equational,[status(thm)],[c1,c3,c19]) ).
cnf(c25,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(equational,[status(thm)],[c1,c4,c19]) ).
cnf(c89,axiom,
ifeq(c_in(X,c_PropLog_Othms(c_insert(Y,Z,tc_PropLog_Opl(W)),W),tc_PropLog_Opl(W)),true,c_in(c_PropLog_Opl_Oop_A_N_62(Y,X,W),c_PropLog_Othms(Z,W),tc_PropLog_Opl(W)),true) = true,
file('theBenchmark.p',cls_PropLog_Odeduction_0) ).
cnf(c486,axiom,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X,Y,Z),c_PropLog_Othms(W,Z),tc_PropLog_Opl(Z)),true,ifeq(c_in(X,c_PropLog_Othms(W,Z),tc_PropLog_Opl(Z)),true,c_in(Y,c_PropLog_Othms(W,Z),tc_PropLog_Opl(Z)),true),true) = true,
file('theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
cnf(c527,plain,
ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(equational,[status(thm)],[c1,c25,c486]) ).
cnf(c1427,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),c_PropLog_Othms(c_insert(Y,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X,c_PropLog_Othms(c_insert(Y,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(equational,[status(thm)],[c1,c20,c486]) ).
cnf(c1428,plain,
c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(equational,[status(thm)],[c1,c8,c1427]) ).
cnf(c1430,plain,
c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(equational,[status(thm)],[c1,c527,c1428]) ).
cnf(c1431,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(equational,[status(thm)],[c1,c89,c1430]) ).
cnf(g1,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(equational,[status(thm)],[c1431]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_Leo-III %s %d THM
% 0.09/0.34 % Computer : n018.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 5 18:48:34 UTC 2026
% 0.09/0.34 % CPUTime :
% 10.33/10.73 % SZS status Unsatisfiable
% 10.33/10.73 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------