%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET862-2 : 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 08:37:10 AM UTC 2026
% Result : Unsatisfiable 107.94s 15.21s
% Output : CNFRefutation 107.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 15
% Syntax : Number of formulae : 79 ( 20 unt; 0 def)
% Number of atoms : 189 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 188 ( 78 ~; 110 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 118 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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_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_2,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_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_3,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_OsubsetI_1,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_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(c_4,plain,
( c_lessequals(A,B,tc_set(C))
| ~ c_in(c_Main_OsubsetI__1(A,B,C),B,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetI_1]) ).
fof(cls_Zorn_Ochain__extend_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(c_union(c_insert(VAR_0,c_emptyset,tc_set(VAR_2)),VAR_3,tc_set(VAR_2)),c_Zorn_Ochain(VAR_1,VAR_2),tc_set(tc_set(VAR_2)))
| c_in(c_Zorn_Ochain__extend__1(VAR_3,VAR_0,VAR_2),VAR_3,tc_set(VAR_2))
| ~ c_in(VAR_3,c_Zorn_Ochain(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_Ochain__extend_0) ).
cnf(c_5,plain,
( c_in(c_union(c_insert(A,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(B,C),tc_set(tc_set(C)))
| c_in(c_Zorn_Ochain__extend__1(D,A,C),D,tc_set(C))
| ~ c_in(D,c_Zorn_Ochain(B,C),tc_set(tc_set(C)))
| ~ c_in(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Zorn_Ochain__extend_0]) ).
fof(cls_Zorn_Ochain__extend_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(c_union(c_insert(VAR_0,c_emptyset,tc_set(VAR_2)),VAR_3,tc_set(VAR_2)),c_Zorn_Ochain(VAR_1,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(VAR_3,VAR_0,VAR_2),VAR_0,tc_set(VAR_2))
| ~ c_in(VAR_3,c_Zorn_Ochain(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_Ochain__extend_1) ).
cnf(c_6,plain,
( c_in(c_union(c_insert(A,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(B,C),tc_set(tc_set(C)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(D,A,C),A,tc_set(C))
| ~ c_in(D,c_Zorn_Ochain(B,C),tc_set(tc_set(C)))
| ~ c_in(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Zorn_Ochain__extend_1]) ).
fof(cls_Zorn_Omaxchain__super__lemma_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(VAR_3,VAR_5,VAR_2),VAR_3,tc_set(VAR_2))
| c_in(VAR_0,VAR_5,VAR_2)
| ~ c_in(c_union(c_insert(VAR_1,c_emptyset,tc_set(VAR_2)),VAR_3,tc_set(VAR_2)),c_Zorn_Ochain(VAR_4,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_3,c_Zorn_Omaxchain(VAR_4,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
cnf(c_7,plain,
( c_in(c_Zorn_Omaxchain__super__lemma__1(D,F,C),D,tc_set(C))
| c_in(A,F,C)
| ~ c_in(c_union(c_insert(B,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(E,C),tc_set(tc_set(C)))
| ~ c_in(D,c_Zorn_Omaxchain(E,C),tc_set(tc_set(C)))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Zorn_Omaxchain__super__lemma_0]) ).
fof(cls_Zorn_Omaxchain__super__lemma_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( c_in(VAR_0,VAR_5,VAR_2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(VAR_3,VAR_5,VAR_2),VAR_5,tc_set(VAR_2))
| ~ c_in(c_union(c_insert(VAR_1,c_emptyset,tc_set(VAR_2)),VAR_3,tc_set(VAR_2)),c_Zorn_Ochain(VAR_4,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_3,c_Zorn_Omaxchain(VAR_4,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
cnf(c_8,plain,
( c_in(A,F,C)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(D,F,C),F,tc_set(C))
| ~ c_in(c_union(c_insert(B,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(E,C),tc_set(tc_set(C)))
| ~ c_in(D,c_Zorn_Omaxchain(E,C),tc_set(tc_set(C)))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Zorn_Omaxchain__super__lemma_1]) ).
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_9,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_1,axiom,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_10,plain,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
c_in(v_y,v_S,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_11,plain,
c_in(v_y,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_c,tc_set(t_a))
| c_lessequals(VAR_0,v_y,tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_12,plain,
( ~ c_in(A,v_c,tc_set(t_a))
| c_lessequals(A,v_y,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_in(v_x(VAR_0),v_S,tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_13,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_4]) ).
fof(cls_conjecture_5,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_5) ).
cnf(c_14,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_5]) ).
fof(cls_conjecture_6,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,v_S,tc_set(t_a))
| VAR_0 != v_x(VAR_0) ),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_15,plain,
( ~ c_in(A,v_S,tc_set(t_a))
| A != v_x(A) ),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
cnf(c_16,plain,
( ~ c_in(A,v_S,tc_set(t_a))
| v_x(A) != A ),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_17,plain,
( c_in(D,B,C)
| ~ c_in(D,A,C)
| c_in(c_Main_OsubsetI__1(A,B,C),A,C) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_47,plain,
c_in(v_x(v_y),v_S,tc_set(t_a)),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_49,plain,
c_lessequals(v_y,v_x(v_y),tc_set(t_a)),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_51,plain,
v_x(v_y) != v_y,
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_7646,plain,
( c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),A,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(A,v_x(v_y),t_a),A,tc_set(t_a))
| ~ c_in(A,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_5,c_47]) ).
cnf(c_61,plain,
( c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_7646,c_10]) ).
cnf(c_63,plain,
( c_in(A,v_x(v_y),t_a)
| ~ c_in(A,v_y,t_a) ),
inference(resolve,[status(thm)],[c_49,c_2]) ).
cnf(c_7647,plain,
( v_y = v_x(v_y)
| ~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_49,c_1]) ).
cnf(c_7648,plain,
( v_x(v_y) = v_y
| ~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_7647]) ).
cnf(c_64,plain,
~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)),
inference(resolve,[status(thm)],[c_51,c_7648]) ).
cnf(c_7649,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_1,c_3]) ).
cnf(c_7650,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a)
| v_y = v_x(v_y) ),
inference(resolve,[status(thm)],[c_7649,c_49]) ).
cnf(c_7651,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a)
| v_x(v_y) = v_y ),
inference(copy,[status(thm)],[c_7650]) ).
cnf(c_66,plain,
c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a),
inference(resolve,[status(thm)],[c_51,c_7651]) ).
cnf(c_78,plain,
~ c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a),
inference(resolve,[status(thm)],[c_4,c_64]) ).
cnf(c_82,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),A,t_a)
| c_in(c_Main_OsubsetI__1(v_x(v_y),A,t_a),v_x(v_y),t_a) ),
inference(resolve,[status(thm)],[c_66,c_17]) ).
cnf(c_7652,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),C,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(A,D,t_a),A,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),C,t_a),D,t_a)
| ~ c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),A,tc_set(t_a)),c_Zorn_Ochain(B,t_a),tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_Omaxchain(B,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_7,c_82]) ).
cnf(c_7653,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),A,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,B,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),A,t_a),B,t_a)
| ~ c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_7652,c_9]) ).
cnf(c_5192,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),A,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,B,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),A,t_a),B,t_a) ),
inference(resolve,[status(thm)],[c_7653,c_61]) ).
cnf(c_7654,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a) ),
inference(factor,[status(thm)],[c_5192]) ).
cnf(c_5334,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_78,c_7654]) ).
cnf(c_5341,plain,
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_5334,c_12]) ).
cnf(c_7655,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),C,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(A,C,t_a),C,tc_set(t_a))
| ~ c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),A,tc_set(t_a)),c_Zorn_Ochain(B,t_a),tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_Omaxchain(B,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_8,c_66]) ).
cnf(c_7656,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),A,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,A,t_a),A,tc_set(t_a))
| ~ c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_7655,c_9]) ).
cnf(c_7657,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),A,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,A,t_a),A,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_7656,c_61]) ).
cnf(c_7658,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a) ),
inference(resolve,[status(thm)],[c_7657,c_5341]) ).
cnf(c_7659,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a) ),
inference(copy,[status(thm)],[c_7658]) ).
cnf(c_5568,plain,
c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a)),
inference(resolve,[status(thm)],[c_78,c_7659]) ).
cnf(c_5575,plain,
c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_y,tc_set(t_a)),
inference(resolve,[status(thm)],[c_5568,c_12]) ).
cnf(c_7660,plain,
( c_lessequals(A,D,tc_set(C))
| c_in(c_Main_OsubsetI__1(A,D,C),B,C)
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_5625,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),A,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),A,t_a),v_y,t_a) ),
inference(resolve,[status(thm)],[c_7660,c_5575]) ).
cnf(c_6051,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),A,t_a),v_x(v_y),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),A,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_5625,c_63]) ).
cnf(c_7661,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_6051,c_4]) ).
cnf(c_6877,plain,
c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a)),
inference(copy,[status(thm)],[c_7661]) ).
cnf(c_7662,plain,
( c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),A,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(A,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))
| ~ c_in(A,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_6,c_47]) ).
cnf(c_7663,plain,
( c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_7662,c_10]) ).
cnf(c_6926,plain,
c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_7663,c_6877]) ).
cnf(c_7664,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),C,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(A,D,t_a),A,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),C,t_a),D,t_a)
| ~ c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),A,tc_set(t_a)),c_Zorn_Ochain(B,t_a),tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_Omaxchain(B,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_7,c_82]) ).
cnf(c_7665,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),A,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,B,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),A,t_a),B,t_a)
| ~ c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_7664,c_9]) ).
cnf(c_7463,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),A,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,B,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),A,t_a),B,t_a) ),
inference(resolve,[status(thm)],[c_7665,c_6926]) ).
cnf(c_7666,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),C,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(A,C,t_a),C,tc_set(t_a))
| ~ c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),A,tc_set(t_a)),c_Zorn_Ochain(B,t_a),tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_Omaxchain(B,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_8,c_66]) ).
cnf(c_7667,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),A,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,A,t_a),A,tc_set(t_a))
| ~ c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_7666,c_9]) ).
cnf(c_7668,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),A,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,A,t_a),A,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_7667,c_6926]) ).
cnf(c_7578,plain,
~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)),
inference(resolve,[status(thm)],[c_7668,c_78]) ).
cnf(c_7669,plain,
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a) ),
inference(factor,[status(thm)],[c_7463]) ).
cnf(c_7638,plain,
c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a)),
inference(resolve,[status(thm)],[c_78,c_7669]) ).
cnf(c_7670,plain,
c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)),
inference(resolve,[status(thm)],[c_7638,c_12]) ).
cnf(c_7645,plain,
$false,
inference(resolve,[status(thm)],[c_7578,c_7670]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET862-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 08:25:50 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 1249320 was started by sandbox on n002,
% 0.12/0.38 % Sat Sep 26 08:25:50 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 107.94/15.21
% 107.94/15.21 % SZS status Unsatisfiable for theBenchmark
% 107.94/15.21
% 107.94/15.21 % Proof 1 at 5.92 (+ 0.75) seconds.
% 107.94/15.21 % Length of proof is 39.
% 107.94/15.21 % Level of proof is 16.
% 107.94/15.21 % Maximum clause weight is 44.000.
% 107.94/15.21 % Given clauses 293.
% 107.94/15.21
% 107.94/15.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------