%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL441-2 : 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 : n007.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 07:58:56 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.36s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 5 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_3,axiom,
( ~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_1,plain,
( ~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_PropLog_Othms_OH_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_in(VAR_0,VAR_1,tc_PropLog_Opl(VAR_2)) ),
file('theBenchmark.p',cls_PropLog_Othms_OH_0) ).
cnf(c_2,plain,
( c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C))
| ~ c_in(A,B,tc_PropLog_Opl(C)) ),
inference(clausify,[status(thm)],[cls_PropLog_Othms_OH_0]) ).
fof(cls_Set_OinsertCI_1,axiom,
! [VAR_0,VAR_1,VAR_2] : c_in(VAR_0,c_insert(VAR_0,VAR_1,VAR_2),VAR_2),
file('theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(c_3,plain,
c_in(A,c_insert(A,B,C),C),
inference(clausify,[status(thm)],[cls_Set_OinsertCI_1]) ).
cnf(c_8,plain,
( ~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_5,plain,
~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_6,plain,
c_in(A,c_PropLog_Othms(c_insert(A,B,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C)),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_7,plain,
$false,
inference(resolve,[status(thm)],[c_6,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL441-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n007.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 22:31:39 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2084709 was started by sandbox on n007,
% 0.09/0.35 % Fri Sep 25 22:31:39 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.09/0.36
% 0.09/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.36
% 0.09/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.36 % Length of proof is 6.
% 0.09/0.36 % Level of proof is 2.
% 0.09/0.36 % Maximum clause weight is 36.000.
% 0.09/0.36 % Given clauses 3.
% 0.09/0.36
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------