%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 10 unt; 0 nHn; 17 RR)
% Number of literals : 31 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 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 : 24 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
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)) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ).
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_OMP_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,V_q,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_Othms__excluded__middle_0,axiom,
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_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),V_q,T_a),V_q,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ).
cnf(refute_0_0,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,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)) ),
inference(subst,[],[cls_PropLog_Othms_OMP_0:[bind(T_a,$fot(t_a)),bind(V_H,$fot(v_H)),bind(V_p,$fot(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a))),bind(V_q,$fot(v_q))]]) ).
cnf(refute_0_1,plain,
( ~ 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)) ),
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(v_q))]]) ).
cnf(refute_0_2,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(resolve,[$cnf( c_in(v_q,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )],[cls_conjecture_0,refute_0_1]) ).
cnf(refute_0_3,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26),X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26)),
inference(subst,[],[cls_PropLog_Othms__excluded__middle_0:[bind(T_a,$fot(X_26)),bind(V_H,$fot(X_27))]]) ).
cnf(refute_0_4,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26),X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26)) ),
inference(subst,[],[cls_PropLog_Othms_OMP_0:[bind(T_a,$fot(X_26)),bind(V_H,$fot(X_27)),bind(V_p,$fot(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26))),bind(V_q,$fot(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26)))]]) ).
cnf(refute_0_5,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26)) ),
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26),X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,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))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(subst,[],[refute_0_5:[bind(V_p,$fot(v_p)),bind(V_q,$fot(v_q)),bind(X_26,$fot(t_a)),bind(X_27,$fot(v_H))]]) ).
cnf(refute_0_7,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[refute_0_7,refute_0_0]) ).
cnf(refute_0_9,plain,
( ~ c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,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,$fot(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a))),bind(V_q,$fot(v_q))]]) ).
cnf(refute_0_10,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[$cnf( c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )],[cls_conjecture_1,refute_0_9]) ).
cnf(refute_0_11,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[refute_0_10,refute_0_8]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[refute_0_11,cls_conjecture_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 4 21:53:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.10/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.10/0.40
%------------------------------------------------------------------------------