%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET864-2 : 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 : n002.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 08:37:11 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 37 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Zorn_Omaxchain__Zorn_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_Union(VAR_3,VAR_2) = VAR_0
| ~ c_lessequals(c_Union(VAR_3,VAR_2),VAR_0,tc_set(VAR_2))
| ~ c_in(VAR_3,c_Zorn_Omaxchain(VAR_1,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Zorn_Omaxchain__Zorn_0) ).
cnf(c_1,plain,
( c_Union(D,C) = A
| ~ c_lessequals(c_Union(D,C),A,tc_set(C))
| ~ c_in(D,c_Zorn_Omaxchain(B,C),tc_set(tc_set(C)))
| ~ c_in(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Zorn_Omaxchain__Zorn_0]) ).
fof(cls_conjecture_0,axiom,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_2,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_2,axiom,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_3,plain,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,v_S,tc_set(t_a))
| c_in(v_x(VAR_0),v_S,tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_4,plain,
( ~ c_in(A,v_S,tc_set(t_a))
| c_in(v_x(A),v_S,tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,v_S,tc_set(t_a))
| c_lessequals(VAR_0,v_x(VAR_0),tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_5,plain,
( ~ c_in(A,v_S,tc_set(t_a))
| c_lessequals(A,v_x(A),tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_5,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,v_S,tc_set(t_a))
| VAR_0 != v_x(VAR_0) ),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_6,plain,
( ~ c_in(A,v_S,tc_set(t_a))
| A != v_x(A) ),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
cnf(c_7,plain,
( ~ c_in(A,v_S,tc_set(t_a))
| v_x(A) != A ),
inference(copy,[status(thm)],[c_6]) ).
cnf(c_8,plain,
c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_9,plain,
c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_10,plain,
v_x(c_Union(v_c,t_a)) != c_Union(v_c,t_a),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_15,plain,
( c_Union(A,t_a) = v_x(c_Union(v_c,t_a))
| ~ c_lessequals(c_Union(A,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a))
| ~ c_in(A,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_16,plain,
( c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a))
| ~ c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_15,c_2]) ).
cnf(c_17,plain,
c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)),
inference(copy,[status(thm)],[c_10]) ).
cnf(c_18,plain,
~ c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)),
inference(resolve,[status(thm)],[c_16,c_17]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_9,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET864-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 08:25:35 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 1248927 was started by sandbox on n002,
% 0.10/0.37 % Sat Sep 26 08:25:35 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 11.
% 0.14/0.39 % Level of proof is 3.
% 0.14/0.39 % Maximum clause weight is 25.000.
% 0.14/0.39 % Given clauses 8.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------