%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET818-1 : 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 : n006.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 08:37:01 AM UTC 2026
% Result : Unsatisfiable 18.02s 2.78s
% Output : CNFRefutation 18.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 5 unt; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 6 ( 2 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Set_OemptyE_0,axiom,
! [VAR_0,VAR_1] : ~ c_in(VAR_0,c_emptyset,VAR_1),
file('theBenchmark.p',cls_Set_OemptyE_0) ).
cnf(c_1206,plain,
~ c_in(A,c_emptyset,B),
inference(clausify,[status(thm)],[cls_Set_OemptyE_0]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : c_in(v_x(VAR_0),VAR_0,tc_IntDef_Oint),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1699,plain,
c_in(v_x(A),A,tc_IntDef_Oint),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_1700,plain,
$false,
inference(resolve,[status(thm)],[c_1699,c_1206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET818-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:17:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 799365 was started by sandbox on n006,
% 0.10/0.37 % Sat Sep 26 08:17:55 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 18.02/2.78
% 18.02/2.78 % SZS status Unsatisfiable for theBenchmark
% 18.02/2.78
% 18.02/2.78 % Proof 1 at 2.33 (+ 0.01) seconds.
% 18.02/2.78 % Length of proof is 3.
% 18.02/2.78 % Level of proof is 1.
% 18.02/2.78 % Maximum clause weight is 15.000.
% 18.02/2.78 % Given clauses 0.
% 18.02/2.78
% 18.02/2.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------