%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL433-2 : 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 : n004.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 07:58:54 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.37s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 46 ( 4 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,axiom,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1,plain,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_2,plain,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
! [VAR_0] :
( ~ c_PropLog_Osat(v_F,VAR_0,t_a)
| c_in(VAR_0,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_3,plain,
( ~ c_PropLog_Osat(v_F,A,t_a)
| c_in(A,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_PropLog_Osat__imp_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_PropLog_Osat(VAR_1,c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_3,VAR_2),VAR_2)
| ~ c_PropLog_Osat(c_insert(VAR_0,VAR_1,tc_PropLog_Opl(VAR_2)),VAR_3,VAR_2) ),
file('theBenchmark.p',cls_PropLog_Osat__imp_0) ).
cnf(c_4,plain,
( c_PropLog_Osat(B,c_PropLog_Opl_Oop_A_N_62(A,D,C),C)
| ~ c_PropLog_Osat(c_insert(A,B,tc_PropLog_Opl(C)),D,C) ),
inference(clausify,[status(thm)],[cls_PropLog_Osat__imp_0]) ).
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_5,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_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_6,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_Oweaken__left__insert_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_PropLog_Othms(c_insert(VAR_3,VAR_1,tc_PropLog_Opl(VAR_2)),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_Oweaken__left__insert_0) ).
cnf(c_7,plain,
( c_in(A,c_PropLog_Othms(c_insert(D,B,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C))
| ~ c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)) ),
inference(clausify,[status(thm)],[cls_PropLog_Oweaken__left__insert_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_8,plain,
c_in(A,c_insert(A,B,C),C),
inference(clausify,[status(thm)],[cls_Set_OinsertCI_1]) ).
cnf(c_9,plain,
c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_13,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_5,c_8]) ).
cnf(c_14,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_3,c_9]) ).
cnf(c_18,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(A,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_7,c_14]) ).
cnf(c_26,plain,
( c_in(B,c_PropLog_Othms(c_insert(A,D,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(A,B,C),c_PropLog_Othms(c_insert(A,D,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C)) ),
inference(resolve,[status(thm)],[c_6,c_13]) ).
cnf(c_24,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_26,c_2]) ).
cnf(c_25,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL433-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 22:32:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 161486 was started by sandbox on n004,
% 0.10/0.36 % Fri Sep 25 22:32:53 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.10/0.37
% 0.10/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.37
% 0.10/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.37 % Length of proof is 14.
% 0.10/0.37 % Level of proof is 4.
% 0.10/0.37 % Maximum clause weight is 24.000.
% 0.10/0.37 % Given clauses 15.
% 0.10/0.37
% 0.10/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------