%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET865-2 : 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 08:37:11 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 51 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 27 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(VAR_0,t_a),v_S,tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
( ~ c_in(A,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(A,t_a),v_S,tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,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_1) ).
cnf(c_2,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_1]) ).
fof(cls_conjecture_2,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_2) ).
cnf(c_3,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_2]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,v_S,tc_set(t_a))
| VAR_0 != v_x(VAR_0) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_4,plain,
( ~ c_in(A,v_S,tc_set(t_a))
| A != v_x(A) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_5,plain,
( ~ c_in(A,v_S,tc_set(t_a))
| v_x(A) != A ),
inference(copy,[status(thm)],[c_4]) ).
fof(cls_Set_OsubsetD_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_3,VAR_2)
| ~ c_lessequals(VAR_1,VAR_3,tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(c_6,plain,
( c_in(A,D,C)
| ~ c_lessequals(B,D,tc_set(C))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetD_0]) ).
fof(cls_Zorn_OHausdorff_0,axiom,
! [VAR_0,VAR_1] : c_in(c_Zorn_OHausdorff__1(VAR_0,VAR_1),c_Zorn_Omaxchain(VAR_0,VAR_1),tc_set(tc_set(VAR_1))),
file('theBenchmark.p',cls_Zorn_OHausdorff_0) ).
cnf(c_7,plain,
c_in(c_Zorn_OHausdorff__1(A,B),c_Zorn_Omaxchain(A,B),tc_set(tc_set(B))),
inference(clausify,[status(thm)],[cls_Zorn_OHausdorff_0]) ).
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_8,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_Zorn_Omaxchain__subset__chain_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(c_Zorn_Omaxchain(VAR_0,VAR_1),c_Zorn_Ochain(VAR_0,VAR_1),tc_set(tc_set(tc_set(VAR_1)))),
file('theBenchmark.p',cls_Zorn_Omaxchain__subset__chain_0) ).
cnf(c_9,plain,
c_lessequals(c_Zorn_Omaxchain(A,B),c_Zorn_Ochain(A,B),tc_set(tc_set(tc_set(B)))),
inference(clausify,[status(thm)],[cls_Zorn_Omaxchain__subset__chain_0]) ).
cnf(c_25,plain,
( c_in(c_Zorn_OHausdorff__1(A,B),C,tc_set(tc_set(B)))
| ~ c_lessequals(c_Zorn_Omaxchain(A,B),C,tc_set(tc_set(tc_set(B)))) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_10,plain,
c_in(c_Zorn_OHausdorff__1(A,B),c_Zorn_Ochain(A,B),tc_set(tc_set(B))),
inference(resolve,[status(thm)],[c_25,c_9]) ).
cnf(c_11,plain,
c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_12,plain,
c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),tc_set(t_a)),
inference(resolve,[status(thm)],[c_3,c_11]) ).
cnf(c_13,plain,
c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),v_S,tc_set(t_a)),
inference(resolve,[status(thm)],[c_2,c_11]) ).
cnf(c_14,plain,
v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)) != c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),
inference(resolve,[status(thm)],[c_5,c_11]) ).
cnf(c_26,plain,
( c_Union(A,t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a))
| ~ c_lessequals(c_Union(A,t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),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_8,c_13]) ).
cnf(c_27,plain,
( c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a))
| ~ c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_26,c_7]) ).
cnf(c_28,plain,
c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),
inference(resolve,[status(thm)],[c_27,c_12]) ).
cnf(c_29,plain,
v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)) = c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_24,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET865-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n003.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 08:25:23 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 2434210 was started by sandbox2 on n003,
% 0.17/0.45 % Sat Sep 26 08:25:23 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.47
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47
% 0.17/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.47 % Length of proof is 15.
% 0.17/0.47 % Level of proof is 4.
% 0.17/0.47 % Maximum clause weight is 25.000.
% 0.17/0.47 % Given clauses 14.
% 0.17/0.47
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------