%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET849-1 : 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 : 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 08:37:08 AM UTC 2026
% Result : Unsatisfiable 17.72s 2.75s
% Output : CNFRefutation 17.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 22 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 24 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_1,VAR_1,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
cnf(c_2,plain,
( c_lessequals(B,B,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__class_Oaxioms__1_0]) ).
fof(clsarity_set_2,axiom,
! [VAR_0] : class_Orderings_Oorder(tc_set(VAR_0)),
file('theBenchmark.p',clsarity_set_2) ).
cnf(c_9,plain,
class_Orderings_Oorder(tc_set(A)),
inference(clausify,[status(thm)],[clsarity_set_2]) ).
cnf(c_962,plain,
c_lessequals(A,A,tc_set(B)),
inference(resolve,[status(thm)],[c_9,c_2]) ).
fof(cls_conjecture_1,axiom,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_975,plain,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_Zorn_Oequal__succ__Union_1,axiom,
! [VAR_0,VAR_1] :
( c_Union(c_Zorn_OTFin(VAR_0,VAR_1),tc_set(VAR_1)) = c_Zorn_Osucc(VAR_0,c_Union(c_Zorn_OTFin(VAR_0,VAR_1),tc_set(VAR_1)),VAR_1)
| ~ c_in(c_Union(c_Zorn_OTFin(VAR_0,VAR_1),tc_set(VAR_1)),c_Zorn_OTFin(VAR_0,VAR_1),tc_set(tc_set(VAR_1))) ),
file('theBenchmark.p',cls_Zorn_Oequal__succ__Union_1) ).
cnf(c_978,plain,
( c_Union(c_Zorn_OTFin(A,B),tc_set(B)) = c_Zorn_Osucc(A,c_Union(c_Zorn_OTFin(A,B),tc_set(B)),B)
| ~ c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B))) ),
inference(clausify,[status(thm)],[cls_Zorn_Oequal__succ__Union_1]) ).
cnf(c_979,plain,
( c_Zorn_Osucc(A,c_Union(c_Zorn_OTFin(A,B),tc_set(B)),B) = c_Union(c_Zorn_OTFin(A,B),tc_set(B))
| ~ c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B))) ),
inference(copy,[status(thm)],[c_978]) ).
fof(cls_Zorn_OTFin__UnionI_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Union(VAR_0,tc_set(VAR_2)),c_Zorn_OTFin(VAR_1,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_lessequals(VAR_0,c_Zorn_OTFin(VAR_1,VAR_2),tc_set(tc_set(tc_set(VAR_2)))) ),
file('theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
cnf(c_983,plain,
( c_in(c_Union(A,tc_set(C)),c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| ~ c_lessequals(A,c_Zorn_OTFin(B,C),tc_set(tc_set(tc_set(C)))) ),
inference(clausify,[status(thm)],[cls_Zorn_OTFin__UnionI_0]) ).
cnf(c_2029,plain,
c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B))),
inference(resolve,[status(thm)],[c_983,c_962]) ).
cnf(c_2030,plain,
c_Zorn_Osucc(A,c_Union(c_Zorn_OTFin(A,B),tc_set(B)),B) = c_Union(c_Zorn_OTFin(A,B),tc_set(B)),
inference(resolve,[status(thm)],[c_2029,c_979]) ).
cnf(c_2031,plain,
$false,
inference(resolve,[status(thm)],[c_2030,c_975]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET849-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n005.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 08:21:01 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 1680505 was started by sandbox on n005,
% 0.15/0.42 % Sat Sep 26 08:21:01 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.47
% 0.15/0.47 % From the command line: assign(max_seconds, 300).
% 17.72/2.75
% 17.72/2.75 % SZS status Unsatisfiable for theBenchmark
% 17.72/2.75
% 17.72/2.75 % Proof 1 at 2.19 (+ 0.04) seconds.
% 17.72/2.75 % Length of proof is 10.
% 17.72/2.75 % Level of proof is 4.
% 17.72/2.75 % Maximum clause weight is 49.000.
% 17.72/2.75 % Given clauses 179.
% 17.72/2.75
% 17.72/2.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------