%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL438-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Sun Sep 27 07:58:55 AM UTC 2026
% Result : Unsatisfiable 0.14s 25.51s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 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 : 20 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_1,axiom,
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)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1,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)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_3,axiom,
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)),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_2,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)),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
~ 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)),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_3,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(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_PropLog_Othms_OMP_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_3,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_3,VAR_2),c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_in(VAR_0,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2)) ),
file('theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
cnf(c_4,plain,
( c_in(D,c_PropLog_Othms(B,C),tc_PropLog_Opl(C))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(A,D,C),c_PropLog_Othms(B,C),tc_PropLog_Opl(C))
| ~ c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)) ),
inference(clausify,[status(thm)],[cls_PropLog_Othms_OMP_0]) ).
fof(cls_PropLog_Othms_OS_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(VAR_0,c_PropLog_Opl_Oop_A_N_62(VAR_1,VAR_2,VAR_3),VAR_3),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_1,VAR_3),c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_2,VAR_3),VAR_3),VAR_3),c_PropLog_Othms(VAR_4,VAR_3),tc_PropLog_Opl(VAR_3)),
file('theBenchmark.p',cls_PropLog_Othms_OS_0) ).
cnf(c_5,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Oop_A_N_62(B,C,D),D),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,B,D),c_PropLog_Opl_Oop_A_N_62(A,C,D),D),D),c_PropLog_Othms(E,D),tc_PropLog_Opl(D)),
inference(clausify,[status(thm)],[cls_PropLog_Othms_OS_0]) ).
cnf(c_14,plain,
( c_in(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),A,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_9,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,[status(thm)],[c_14,c_3]) ).
cnf(c_15,plain,
( c_in(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_Oop_A_N_62(v_pa,v_q,t_a),t_a),A,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_16,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,[status(thm)],[c_15,c_5]) ).
cnf(c_13,plain,
$false,
inference(resolve,[status(thm)],[c_9,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL438-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.14/25.50 % CPULimit : 300
% 0.14/25.50 % WCLimit : 300
% 0.14/25.50 % DateTime : Fri Sep 25 22:33:37 UTC 2026
% 0.14/25.50 % CPUTime :
% 0.14/25.51 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/25.51 % Process 3917909 was started by sandbox on n006,
% 0.14/25.51 % Fri Sep 25 22:33:37 2026
% 0.14/25.51 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/25.51
% 0.14/25.51 % From the command line: assign(max_seconds, 300).
% 0.14/25.51
% 0.14/25.51 % Assigning unary symbol tc_PropLog_Opl kb_weight 0 and highest precedence (9).
% 0.14/25.51
% 0.14/25.51 % SZS status Unsatisfiable for theBenchmark
% 0.14/25.51
% 0.14/25.51 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/25.51 % Length of proof is 7.
% 0.14/25.51 % Level of proof is 2.
% 0.14/25.51 % Maximum clause weight is 45.000.
% 0.14/25.51 % Given clauses 5.
% 0.14/25.51
% 0.14/25.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------