%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL441-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 12:42:43 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.37s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of clauses : 10 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 13 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_3,negated_conjecture,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ) ).
cnf(cls_PropLog_Othms_OH_0,axiom,
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a),T_a) ).
cnf(refute_0_0,plain,
c_in(X_5,c_insert(X_5,V_B,tc_PropLog_Opl(X_3)),tc_PropLog_Opl(X_3)),
inference(subst,[],[cls_Set_OinsertCI_1:[bind(T_a,$fot(tc_PropLog_Opl(X_3))),bind(V_x,$fot(X_5))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(X_5,c_insert(X_5,V_B,tc_PropLog_Opl(X_3)),tc_PropLog_Opl(X_3))
| c_in(X_5,c_PropLog_Othms(c_insert(X_5,V_B,tc_PropLog_Opl(X_3)),X_3),tc_PropLog_Opl(X_3)) ),
inference(subst,[],[cls_PropLog_Othms_OH_0:[bind(T_a,$fot(X_3)),bind(V_H,$fot(c_insert(X_5,V_B,tc_PropLog_Opl(X_3)))),bind(V_p,$fot(X_5))]]) ).
cnf(refute_0_2,plain,
c_in(X_5,c_PropLog_Othms(c_insert(X_5,V_B,tc_PropLog_Opl(X_3)),X_3),tc_PropLog_Opl(X_3)),
inference(resolve,[$cnf( c_in(X_5,c_insert(X_5,V_B,tc_PropLog_Opl(X_3)),tc_PropLog_Opl(X_3)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[refute_0_2:[bind(V_B,$fot(c_emptyset)),bind(X_3,$fot(t_a)),bind(X_5,$fot(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a)))]]) ).
cnf(refute_0_4,plain,
~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )],[refute_0_3,cls_conjecture_3]) ).
cnf(refute_0_5,plain,
c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[refute_0_2:[bind(V_B,$fot(c_emptyset)),bind(X_3,$fot(t_a)),bind(X_5,$fot(c_PropLog_Opl_Ovar(v_a,t_a)))]]) ).
cnf(refute_0_6,plain,
$false,
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )],[refute_0_5,refute_0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL441-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 08:05:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.10/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37
% 0.10/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.10/0.37
%------------------------------------------------------------------------------