%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET847-2 : 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 : n017.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 08:37:07 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 16 unt; 0 def)
% Number of atoms : 59 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 27 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 73 ( 6 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Set_ODiffI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_minus(VAR_1,VAR_3,tc_set(VAR_2)),VAR_2)
| c_in(VAR_0,VAR_3,VAR_2)
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_ODiffI_0) ).
cnf(c_1,plain,
( c_in(A,c_minus(B,D,tc_set(C)),C)
| c_in(A,D,C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_ODiffI_0]) ).
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_2,plain,
~ c_in(A,c_emptyset,B),
inference(clausify,[status(thm)],[cls_Set_OemptyE_0]) ).
fof(cls_Set_Oempty__subsetI_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(c_emptyset,VAR_0,tc_set(VAR_1)),
file('theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
cnf(c_3,plain,
c_lessequals(c_emptyset,A,tc_set(B)),
inference(clausify,[status(thm)],[cls_Set_Oempty__subsetI_0]) ).
fof(cls_Set_OsubsetI_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,VAR_1,tc_set(VAR_2))
| c_in(c_Main_OsubsetI__1(VAR_0,VAR_1,VAR_2),VAR_0,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(c_4,plain,
( c_lessequals(A,B,tc_set(C))
| c_in(c_Main_OsubsetI__1(A,B,C),A,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetI_0]) ).
fof(cls_Set_Osubset__antisym_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_0
| ~ c_lessequals(VAR_1,VAR_0,tc_set(VAR_2))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(c_5,plain,
( B = A
| ~ c_lessequals(B,A,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_Osubset__antisym_0]) ).
fof(cls_Set_Osubset__refl_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(VAR_0,VAR_0,tc_set(VAR_1)),
file('theBenchmark.p',cls_Set_Osubset__refl_0) ).
cnf(c_6,plain,
c_lessequals(A,A,tc_set(B)),
inference(clausify,[status(thm)],[cls_Set_Osubset__refl_0]) ).
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_7,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]) ).
fof(cls_Zorn_OTFin__chain__lemma4_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_Zorn_Ochain(VAR_1,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_0,c_Zorn_OTFin(VAR_1,VAR_2),tc_set(tc_set(VAR_2))) ),
file('theBenchmark.p',cls_Zorn_OTFin__chain__lemma4_0) ).
cnf(c_8,plain,
( c_in(A,c_Zorn_Ochain(B,C),tc_set(tc_set(C)))
| ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) ),
inference(clausify,[status(thm)],[cls_Zorn_OTFin__chain__lemma4_0]) ).
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_9,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_10,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_9]) ).
fof(cls_Zorn_Osucc__not__equals_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_Zorn_Osucc(VAR_1,VAR_0,VAR_2) != VAR_0
| ~ c_in(VAR_0,c_minus(c_Zorn_Ochain(VAR_1,VAR_2),c_Zorn_Omaxchain(VAR_1,VAR_2),tc_set(tc_set(tc_set(VAR_2)))),tc_set(tc_set(VAR_2))) ),
file('theBenchmark.p',cls_Zorn_Osucc__not__equals_0) ).
cnf(c_11,plain,
( c_Zorn_Osucc(B,A,C) != A
| ~ c_in(A,c_minus(c_Zorn_Ochain(B,C),c_Zorn_Omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C))) ),
inference(clausify,[status(thm)],[cls_Zorn_Osucc__not__equals_0]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : ~ c_in(VAR_0,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_12,plain,
~ c_in(A,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_13,plain,
( c_in(c_Main_OsubsetI__1(B,A,C),B,C)
| A = B
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_16,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_7,c_6]) ).
cnf(c_19,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_16,c_10]) ).
cnf(c_21,plain,
( c_in(c_Main_OsubsetI__1(A,c_emptyset,B),A,B)
| c_emptyset = A ),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_41,plain,
c_emptyset = c_Zorn_Omaxchain(v_S,t_a),
inference(resolve,[status(thm)],[c_21,c_12]) ).
cnf(c_22,plain,
c_Zorn_Omaxchain(v_S,t_a) = c_emptyset,
inference(copy,[status(thm)],[c_41]) ).
cnf(c_26,plain,
( c_Zorn_Osucc(v_S,A,t_a) != A
| ~ c_in(A,c_minus(c_Zorn_Ochain(v_S,t_a),c_emptyset,tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a))) ),
inference(paramod,[status(thm)],[c_22,c_11]) ).
cnf(c_31,plain,
c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_Ochain(A,B),tc_set(tc_set(B))),
inference(resolve,[status(thm)],[c_16,c_8]) ).
cnf(c_34,plain,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_minus(c_Zorn_Ochain(v_S,t_a),c_emptyset,tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_26,c_19]) ).
cnf(c_42,plain,
( c_in(A,c_minus(B,c_emptyset,tc_set(C)),C)
| ~ c_in(A,B,C) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_43,plain,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_42,c_34]) ).
cnf(c_40,plain,
$false,
inference(resolve,[status(thm)],[c_31,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET847-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.45 % Computer : n017.cluster.edu
% 0.16/5.45 % Model : x86_64 x86_64
% 0.16/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.45 % Memory : 8046.5625MB
% 0.16/5.45 % OS : Linux 6.8.0-71-generic
% 0.16/5.45 % CPULimit : 300
% 0.16/5.45 % WCLimit : 300
% 0.16/5.45 % DateTime : Sat Sep 26 08:16:25 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 251009 was started by sandbox on n017,
% 0.16/5.45 % Sat Sep 26 08:16:25 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.46
% 0.16/5.46 % From the command line: assign(max_seconds, 300).
% 0.16/5.47
% 0.16/5.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.47
% 0.16/5.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/5.47 % Length of proof is 21.
% 0.16/5.47 % Level of proof is 6.
% 0.16/5.47 % Maximum clause weight is 29.000.
% 0.16/5.47 % Given clauses 23.
% 0.16/5.47
% 0.16/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------