%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL438-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 8 unt; 0 nHn; 12 RR)
% Number of literals : 23 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 24 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(v_pa,v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ).
cnf(cls_conjecture_4,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(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_OS_0,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_r,T_a),T_a),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(V_p,V_r,T_a),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(v_p,v_pa,t_a),c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),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,v_pa,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,v_q,t_a),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,$fot(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a))),bind(V_q,$fot(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a)))]]) ).
cnf(refute_0_1,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_r,X_5),X_5),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_5),c_PropLog_Opl_Oop_A_N_62(V_p,V_r,X_5),X_5),X_5),c_PropLog_Othms(X_6,X_5),tc_PropLog_Opl(X_5)),
inference(subst,[],[cls_PropLog_Othms_OS_0:[bind(T_a,$fot(X_5)),bind(V_H,$fot(X_6))]]) ).
cnf(refute_0_2,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_r,X_5),X_5),c_PropLog_Othms(X_6,X_5),tc_PropLog_Opl(X_5))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_r,X_5),X_5),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_5),c_PropLog_Opl_Oop_A_N_62(V_p,V_r,X_5),X_5),X_5),c_PropLog_Othms(X_6,X_5),tc_PropLog_Opl(X_5))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_5),c_PropLog_Opl_Oop_A_N_62(V_p,V_r,X_5),X_5),c_PropLog_Othms(X_6,X_5),tc_PropLog_Opl(X_5)) ),
inference(subst,[],[cls_PropLog_Othms_OMP_0:[bind(T_a,$fot(X_5)),bind(V_H,$fot(X_6)),bind(V_p,$fot(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_r,X_5),X_5))),bind(V_q,$fot(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_5),c_PropLog_Opl_Oop_A_N_62(V_p,V_r,X_5),X_5)))]]) ).
cnf(refute_0_3,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_r,X_5),X_5),c_PropLog_Othms(X_6,X_5),tc_PropLog_Opl(X_5))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_5),c_PropLog_Opl_Oop_A_N_62(V_p,V_r,X_5),X_5),c_PropLog_Othms(X_6,X_5),tc_PropLog_Opl(X_5)) ),
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_r,X_5),X_5),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_5),c_PropLog_Opl_Oop_A_N_62(V_p,V_r,X_5),X_5),X_5),c_PropLog_Othms(X_6,X_5),tc_PropLog_Opl(X_5)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(v_pa,v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(subst,[],[refute_0_3:[bind(V_p,$fot(v_p)),bind(V_q,$fot(v_pa)),bind(V_r,$fot(v_q)),bind(X_5,$fot(t_a)),bind(X_6,$fot(v_H))]]) ).
cnf(refute_0_5,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(v_pa,v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[cls_conjecture_1,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[refute_0_5,refute_0_0]) ).
cnf(refute_0_7,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(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[cls_conjecture_3,refute_0_6]) ).
cnf(refute_0_8,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_7,cls_conjecture_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL438-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : metis --show proof --show saturation %s
% 0.17/0.44 % Computer : n028.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 5 00:32:14 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47
% 0.17/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.17/0.48
%------------------------------------------------------------------------------