%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL439-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 12:42:42 PM UTC 2026
% Result : Unsatisfiable 2.27s 2.50s
% Output : CNFRefutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 12 unt; 0 nHn; 9 RR)
% Number of literals : 34 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 38 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_PropLog_Odeduction_0,axiom,
( ~ c_in(V_q,c_PropLog_Othms(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,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_PropLog_Othms__notE_0,axiom,
( ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ).
cnf(cls_PropLog_Oweaken__left__insert_0,axiom,
( ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(c_insert(V_a,V_G,tc_PropLog_Opl(T_a)),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(cls_conjecture_0,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ).
cnf(refute_0_0,plain,
( ~ c_in(X_2465,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_2465,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(subst,[],[cls_PropLog_Odeduction_0:[bind(T_a,$fot(t_a)),bind(V_H,$fot(v_H)),bind(V_p,$fot(v_p)),bind(V_q,$fot(X_2465))]]) ).
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)),
inference(subst,[],[cls_Set_OinsertCI_1:[bind(T_a,$fot(tc_PropLog_Opl(X_3))),bind(V_x,$fot(X_5))]]) ).
cnf(refute_0_2,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,$fot(X_5))]]) ).
cnf(refute_0_3,plain,
c_in(X_5,c_PropLog_Othms(c_insert(X_5,V_B,tc_PropLog_Opl(X_3)),X_3),tc_PropLog_Opl(X_3)),
inference(resolve,[$cnf( c_in(X_5,c_insert(X_5,V_B,tc_PropLog_Opl(X_3)),tc_PropLog_Opl(X_3)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
c_in(v_p,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[refute_0_3:[bind(V_B,$fot(v_H)),bind(X_3,$fot(t_a)),bind(X_5,$fot(v_p))]]) ).
cnf(refute_0_5,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_50,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(subst,[],[cls_PropLog_Oweaken__left__insert_0:[bind(T_a,$fot(t_a)),bind(V_G,$fot(v_H)),bind(V_a,$fot(X_50)),bind(V_p,$fot(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a)))]]) ).
cnf(refute_0_6,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_50,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[cls_conjecture_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_50,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_p,c_PropLog_Othms(c_insert(X_50,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(X_751,c_PropLog_Othms(c_insert(X_50,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(subst,[],[cls_PropLog_Othms__notE_0:[bind(T_a,$fot(t_a)),bind(V_H,$fot(c_insert(X_50,v_H,tc_PropLog_Opl(t_a)))),bind(V_p,$fot(v_p)),bind(V_q,$fot(X_751))]]) ).
cnf(refute_0_8,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_insert(X_50,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(X_751,c_PropLog_Othms(c_insert(X_50,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_50,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(X_2464,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(subst,[],[refute_0_8:[bind(X_50,$fot(v_p)),bind(X_751,$fot(X_2464))]]) ).
cnf(refute_0_10,plain,
c_in(X_2464,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[$cnf( c_in(v_p,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
c_in(X_2465,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[refute_0_10:[bind(X_2464,$fot(X_2465))]]) ).
cnf(refute_0_12,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_2465,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[$cnf( c_in(X_2465,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )],[refute_0_11,refute_0_0]) ).
cnf(refute_0_13,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[refute_0_12:[bind(X_2465,$fot(v_q))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[refute_0_13,cls_conjecture_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL439-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 6 01:31:14 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.27/2.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.27/2.50
% 2.27/2.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.27/2.51
%------------------------------------------------------------------------------