%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET857-2 : 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 : n018.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 1.48s 0.70s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 22 unt; 0 def)
% Number of atoms : 223 ( 49 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 228 ( 80 ~; 148 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 76 ( 5 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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_2,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_3,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_OAbrial__axiom1_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_lessequals(VAR_0,c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),tc_set(tc_set(VAR_2))),
file('theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
cnf(c_4,plain,
c_lessequals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))),
inference(clausify,[status(thm)],[cls_Zorn_OAbrial__axiom1_0]) ).
fof(cls_Zorn_OTFin__linear__lemma1_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),VAR_3,tc_set(tc_set(VAR_2)))
| c_lessequals(VAR_3,VAR_0,tc_set(tc_set(VAR_2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(VAR_1,VAR_0,VAR_2),c_Zorn_OTFin(VAR_1,VAR_2),tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_3,c_Zorn_OTFin(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__linear__lemma1_0) ).
cnf(c_5,plain,
( c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| c_lessequals(D,A,tc_set(tc_set(C)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(B,A,C),c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| ~ c_in(D,c_Zorn_OTFin(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__linear__lemma1_0]) ).
fof(cls_Zorn_OTFin__linear__lemma1_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),VAR_3,tc_set(tc_set(VAR_2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(VAR_1,VAR_0,VAR_2),VAR_0,tc_set(tc_set(VAR_2)))
| c_lessequals(VAR_3,VAR_0,tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_3,c_Zorn_OTFin(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__linear__lemma1_1) ).
cnf(c_6,plain,
( c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(B,A,C),A,tc_set(tc_set(C)))
| c_lessequals(D,A,tc_set(tc_set(C)))
| ~ c_in(D,c_Zorn_OTFin(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__linear__lemma1_1]) ).
fof(cls_Zorn_OTFin__linear__lemma1_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),VAR_3,tc_set(tc_set(VAR_2)))
| c_lessequals(VAR_3,VAR_0,tc_set(tc_set(VAR_2)))
| c_Zorn_OTFin__linear__lemma1__1(VAR_1,VAR_0,VAR_2) != VAR_0
| ~ c_in(VAR_3,c_Zorn_OTFin(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__linear__lemma1_2) ).
cnf(c_7,plain,
( c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| c_lessequals(D,A,tc_set(tc_set(C)))
| c_Zorn_OTFin__linear__lemma1__1(B,A,C) != A
| ~ c_in(D,c_Zorn_OTFin(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__linear__lemma1_2]) ).
fof(cls_Zorn_OTFin__linear__lemma1_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Zorn_Osucc(VAR_1,VAR_0,VAR_2),VAR_3,tc_set(tc_set(VAR_2)))
| c_lessequals(VAR_3,VAR_0,tc_set(tc_set(VAR_2)))
| ~ c_lessequals(c_Zorn_Osucc(VAR_1,c_Zorn_OTFin__linear__lemma1__1(VAR_1,VAR_0,VAR_2),VAR_2),VAR_0,tc_set(tc_set(VAR_2)))
| ~ c_in(VAR_3,c_Zorn_OTFin(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__linear__lemma1_3) ).
cnf(c_8,plain,
( c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| c_lessequals(D,A,tc_set(tc_set(C)))
| ~ c_lessequals(c_Zorn_Osucc(B,c_Zorn_OTFin__linear__lemma1__1(B,A,C),C),A,tc_set(tc_set(C)))
| ~ c_in(D,c_Zorn_OTFin(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__linear__lemma1_3]) ).
fof(cls_conjecture_0,axiom,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_9,plain,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_10,plain,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_3,axiom,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_11,plain,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_12,plain,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_5,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_13,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_6,axiom,
! [VAR_0,VAR_1] :
( ~ c_in(VAR_1,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(VAR_0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(tc_set(t_a)))
| VAR_0 = VAR_1
| c_lessequals(c_Zorn_Osucc(v_S,VAR_0,t_a),VAR_1,tc_set(tc_set(t_a))) ),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_14,plain,
( ~ c_in(B,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(A,B,tc_set(tc_set(t_a)))
| A = B
| c_lessequals(c_Zorn_Osucc(v_S,A,t_a),B,tc_set(tc_set(t_a))) ),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
cnf(c_21,plain,
( c_in(A,c_Zorn_Osucc(D,B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_24,plain,
( c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(A,v_Y,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_9,c_1]) ).
cnf(c_25,plain,
( c_lessequals(c_Zorn_Osucc(v_S,A,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,A,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,A,t_a) != A
| ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_27,plain,
( c_lessequals(c_Zorn_Osucc(v_S,A,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,A,t_a),A,tc_set(tc_set(t_a)))
| c_lessequals(v_n,A,tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_29,plain,
( c_lessequals(c_Zorn_Osucc(v_S,A,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,A,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,A,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_10,c_5]) ).
cnf(c_32,plain,
c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_x,tc_set(t_a)),
inference(resolve,[status(thm)],[c_12,c_2]) ).
cnf(c_33,plain,
~ c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_n,tc_set(t_a)),
inference(resolve,[status(thm)],[c_3,c_12]) ).
cnf(c_44,plain,
c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),c_Zorn_Osucc(A,v_x,t_a),tc_set(t_a)),
inference(resolve,[status(thm)],[c_21,c_32]) ).
cnf(c_1274,plain,
( c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),B,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Osucc(A,v_x,t_a),B,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_1,c_44]) ).
cnf(c_51,plain,
~ c_lessequals(c_Zorn_Osucc(A,v_x,t_a),v_n,tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_1274,c_33]) ).
cnf(c_58,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[status(thm)],[c_24,c_11]) ).
cnf(c_1275,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x ),
inference(resolve,[status(thm)],[c_25,c_58]) ).
cnf(c_90,plain,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x ),
inference(resolve,[status(thm)],[c_51,c_1275]) ).
cnf(c_1276,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_27,c_58]) ).
cnf(c_100,plain,
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_51,c_1276]) ).
cnf(c_1277,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_100,c_14]) ).
cnf(c_101,plain,
( ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_11,c_1277]) ).
cnf(c_1278,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_29,c_58]) ).
cnf(c_126,plain,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_51,c_1278]) ).
cnf(c_1279,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_126,c_14]) ).
cnf(c_1280,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_n
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(copy,[status(thm)],[c_1279]) ).
cnf(c_1281,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_n
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_13,c_1280]) ).
cnf(c_1282,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| v_x = v_n
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_10,c_1281]) ).
cnf(c_133,plain,
( v_x = v_n
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_11,c_1282]) ).
cnf(c_698,plain,
( v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_101,c_133]) ).
cnf(c_1283,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),A,tc_set(tc_set(t_a)))
| c_lessequals(A,v_x,tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_698,c_8]) ).
cnf(c_881,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),A,tc_set(tc_set(t_a)))
| c_lessequals(A,v_x,tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_58,c_1283]) ).
cnf(c_1284,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(factor,[status(thm)],[c_881]) ).
cnf(c_1285,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_10,c_1284]) ).
cnf(c_883,plain,
( v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[status(thm)],[c_51,c_1285]) ).
cnf(c_1286,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(resolve,[status(thm)],[c_883,c_14]) ).
cnf(c_1287,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_n
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(copy,[status(thm)],[c_1286]) ).
cnf(c_1288,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(copy,[status(thm)],[c_1287]) ).
cnf(c_1289,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(resolve,[status(thm)],[c_13,c_1288]) ).
cnf(c_1290,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(resolve,[status(thm)],[c_10,c_1289]) ).
cnf(c_884,plain,
( v_x = v_n
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(resolve,[status(thm)],[c_11,c_1290]) ).
cnf(c_886,plain,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| v_x = v_n ),
inference(resolve,[status(thm)],[c_884,c_90]) ).
cnf(c_1291,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| v_x = v_n ),
inference(resolve,[status(thm)],[c_886,c_14]) ).
cnf(c_1292,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_n
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| v_x = v_n ),
inference(copy,[status(thm)],[c_1291]) ).
cnf(c_1293,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| v_x = v_n ),
inference(copy,[status(thm)],[c_1292]) ).
cnf(c_1294,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_n ),
inference(resolve,[status(thm)],[c_13,c_1293]) ).
cnf(c_1295,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| v_x = v_n ),
inference(resolve,[status(thm)],[c_10,c_1294]) ).
cnf(c_909,plain,
v_x = v_n,
inference(resolve,[status(thm)],[c_11,c_1295]) ).
cnf(c_1272,plain,
~ c_in(c_Main_OsubsetI__1(v_n,v_n,tc_set(t_a)),v_n,tc_set(t_a)),
inference(paramod,[status(thm)],[c_909,c_33]) ).
cnf(c_1296,plain,
c_in(c_Main_OsubsetI__1(v_n,v_n,tc_set(t_a)),v_x,tc_set(t_a)),
inference(paramod,[status(thm)],[c_909,c_32]) ).
cnf(c_1297,plain,
c_in(c_Main_OsubsetI__1(v_n,v_n,tc_set(t_a)),v_n,tc_set(t_a)),
inference(paramod,[status(thm)],[c_909,c_1296]) ).
cnf(c_1273,plain,
$false,
inference(resolve,[status(thm)],[c_1272,c_1297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 08:24:07 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 4181956 was started by sandbox2 on n018,
% 0.17/0.44 % Sat Sep 26 08:24:07 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 1.48/0.70
% 1.48/0.70 % SZS status Unsatisfiable for theBenchmark
% 1.48/0.70
% 1.48/0.70 % Proof 1 at 0.17 (+ 0.04) seconds.
% 1.48/0.70 % Length of proof is 37.
% 1.48/0.70 % Level of proof is 13.
% 1.48/0.70 % Maximum clause weight is 43.000.
% 1.48/0.70 % Given clauses 311.
% 1.48/0.70
% 1.48/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------