%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET856-2 : 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 : n005.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 08:37:09 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.44s
% Output : CNFRefutation 0.16s
% 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 : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_5,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_1,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_3,axiom,
c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_2,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_3,plain,
$false,
inference(resolve,[status(thm)],[c_1,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET856-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 08:21:47 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1682236 was started by sandbox2 on n005,
% 0.16/0.43 % Sat Sep 26 08:21:47 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.44
% 0.16/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.44
% 0.16/0.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.44 % Length of proof is 3.
% 0.16/0.44 % Level of proof is 1.
% 0.16/0.44 % Maximum clause weight is 0.000.
% 0.16/0.44 % Given clauses 0.
% 0.16/0.44
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------