%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:58:53 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 5 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_PropLog_Osat(c_emptyset,v_p,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_PropLog_Osat(c_emptyset,v_p,t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_PropLog_Ocompleteness__0__lemma__dest_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(VAR_0,VAR_2,VAR_1),c_PropLog_Ohyps(VAR_0,VAR_3,VAR_1),tc_set(tc_PropLog_Opl(VAR_1))),VAR_1),tc_PropLog_Opl(VAR_1))
| ~ c_PropLog_Osat(c_emptyset,VAR_0,VAR_1) ),
file('theBenchmark.p',cls_PropLog_Ocompleteness__0__lemma__dest_0) ).
cnf(c_3,plain,
( c_in(A,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(A,C,B),c_PropLog_Ohyps(A,D,B),tc_set(tc_PropLog_Opl(B))),B),tc_PropLog_Opl(B))
| ~ c_PropLog_Osat(c_emptyset,A,B) ),
inference(clausify,[status(thm)],[cls_PropLog_Ocompleteness__0__lemma__dest_0]) ).
fof(cls_Set_ODiff__cancel_0,axiom,
! [VAR_0,VAR_1] : c_minus(VAR_0,VAR_0,tc_set(VAR_1)) = c_emptyset,
file('theBenchmark.p',cls_Set_ODiff__cancel_0) ).
cnf(c_4,plain,
c_minus(A,A,tc_set(B)) = c_emptyset,
inference(clausify,[status(thm)],[cls_Set_ODiff__cancel_0]) ).
cnf(c_5,plain,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,A,t_a),c_PropLog_Ohyps(v_p,B,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_6,plain,
c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_4,c_5]) ).
cnf(c_7,plain,
$false,
inference(resolve,[status(thm)],[c_6,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 22:34:23 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1297936 was started by sandbox2 on n003,
% 0.18/0.45 % Fri Sep 25 22:34:23 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.47 % Length of proof is 7.
% 0.18/0.47 % Level of proof is 3.
% 0.18/0.47 % Maximum clause weight is 22.000.
% 0.18/0.47 % Given clauses 5.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------