%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL445-2 : 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 : 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 : Sun Sep 27 07:58:57 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 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 : 26 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_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)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_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)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
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)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,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)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
~ c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_3,plain,
~ c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_PropLog_Odeduction_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(c_PropLog_Opl_Oop_A_N_62(VAR_1,VAR_0,VAR_3),c_PropLog_Othms(VAR_2,VAR_3),tc_PropLog_Opl(VAR_3))
| ~ c_in(VAR_0,c_PropLog_Othms(c_insert(VAR_1,VAR_2,tc_PropLog_Opl(VAR_3)),VAR_3),tc_PropLog_Opl(VAR_3)) ),
file('theBenchmark.p',cls_PropLog_Odeduction_0) ).
cnf(c_4,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(B,A,D),c_PropLog_Othms(C,D),tc_PropLog_Opl(D))
| ~ c_in(A,c_PropLog_Othms(c_insert(B,C,tc_PropLog_Opl(D)),D),tc_PropLog_Opl(D)) ),
inference(clausify,[status(thm)],[cls_PropLog_Odeduction_0]) ).
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_5,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__excluded__middle_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_1,VAR_2),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(VAR_0,c_PropLog_Opl_Ofalse,VAR_2),VAR_1,VAR_2),VAR_1,VAR_2),VAR_2),c_PropLog_Othms(VAR_3,VAR_2),tc_PropLog_Opl(VAR_2)),
file('theBenchmark.p',cls_PropLog_Othms__excluded__middle_0) ).
cnf(c_6,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,B,C),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Ofalse,C),B,C),B,C),C),c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),
inference(clausify,[status(thm)],[cls_PropLog_Othms__excluded__middle_0]) ).
cnf(c_7,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,[status(thm)],[c_4,c_2]) ).
cnf(c_8,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,[status(thm)],[c_4,c_1]) ).
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,v_q,t_a),A,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_5,c_8]) ).
cnf(c_12,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,[status(thm)],[c_15,c_6]) ).
cnf(c_16,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(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),A,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_13,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_16,c_12]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 22:37:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2441754 was started by sandbox on n015,
% 0.09/0.37 % Fri Sep 25 22:37:29 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 11.
% 0.09/0.38 % Level of proof is 4.
% 0.09/0.38 % Maximum clause weight is 24.000.
% 0.09/0.38 % Given clauses 9.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------