%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 : Fri Sep 25 02:48:49 PM UTC 2026
% Result : Unsatisfiable 14.72s 2.80s
% Output : CNFRefutation 14.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 70 ( 20 unt; 0 def)
% Number of atoms : 216 ( 29 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 260 ( 114 ~; 146 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 103 ( 0 sgn 103 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f4,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) != X0
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Osucc(X1,c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X2),X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
fof(f9,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f10,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f11,negated_conjecture,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f12,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f13,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f14,negated_conjecture,
! [X0,X1] :
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| X0 = X1
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X3,X1,X2)
| ~ c_in(X3,X0,X2)
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ( c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Osucc(X0,c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2),X2),X1,tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,negated_conjecture,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,negated_conjecture,
! [X0: $i,X1: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a)))
| ( X0 = X1 )
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_169,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_lessequals(X0,X2,X4)
| ~ c_lessequals(X1,X3,X5)
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_428,plain,
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_n,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_429,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(X2,X1,X0)
| ( v_x != X2 )
| ( v_n != X1 )
| ( tc_set(tc_set(t_a)) != X0 ) ),
inference(instantiation,[status(thm)],[c_174]) ).
tcf(c_437,plain,
! [X0: $i] :
( c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_n,tc_set(t_a))
| ~ c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),X0,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(X2,X1,tc_set(X0))
| ( v_x != X2 )
| ( v_n != X1 )
| ( tc_set(tc_set(t_a)) != tc_set(X0) ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_457,plain,
! [X0: $i] :
( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_491,plain,
! [X0: $i,X1: $i] :
( c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_n,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Osucc(X0,X1,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),c_Zorn_Osucc(X0,X1,t_a),tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_437]) ).
tcf(c_494,plain,
! [X0: $i] :
( c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x,tc_set(t_a)),v_x,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_499,plain,
( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))) ),
inference(instantiation,[status(thm)],[c_457]) ).
tcf(c_502,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,X1,tc_set(X0))
| ( v_x != v_x )
| ( v_n != X1 )
| ( tc_set(tc_set(t_a)) != tc_set(X0) ) ),
inference(instantiation,[status(thm)],[c_446]) ).
tcf(c_520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Main_OsubsetI__1(X0,X1,X2),X3,X2)
| ~ c_lessequals(X0,X3,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_546,plain,
v_x = v_x,
inference(instantiation,[status(thm)],[c_169]) ).
tcf(c_570,plain,
( ( v_n = v_x )
| ~ c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| ~ 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))) ),
inference(superposition,[status(thm)],[c_76,c_75]) ).
tcf(c_571,plain,
( ( v_n = v_x )
| ~ c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(global_subsumption_just,[status(thm)],[c_570,c_73,c_72,c_570]) ).
tcf(c_577,plain,
( c_lessequals(v_x,v_x,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_x,v_x,tc_set(t_a)),v_x,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_494]) ).
tcf(c_579,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_n,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X1,X0,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(X1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(X1,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_581,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X0,X1,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(X0,c_Zorn_OTFin__linear__lemma1__1(X0,X1,t_a),t_a),X1,tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_582,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X0,X1,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(X0,X1,t_a) != X1 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_682,plain,
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_x,tc_set(tc_set(t_a)))
| ( v_x != v_x )
| ( v_n != v_x )
| ( tc_set(tc_set(t_a)) != tc_set(tc_set(t_a)) ) ),
inference(instantiation,[status(thm)],[c_502]) ).
tcf(c_794,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_x,X0,tc_set(X1))
| c_in(c_Main_OsubsetI__1(v_x,X0,X1),v_x,X1) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_809,plain,
! [X0: $i,X1: $i] : c_lessequals(v_x,c_Zorn_Osucc(X0,v_x,X1),tc_set(tc_set(X1))),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_815,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_x,tc_set(tc_set(t_a)))
| ( X0 = v_x )
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_982,plain,
! [X0: $i] :
( c_lessequals(v_n,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_n,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_991,plain,
! [X0: $i] :
( c_lessequals(v_n,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_579]) ).
tcf(c_996,plain,
! [X0: $i] :
( c_lessequals(v_n,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X0,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)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),t_a),X0,tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_581]) ).
tcf(c_1002,plain,
! [X0: $i] :
( c_lessequals(v_n,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X0,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)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a) != X0 ) ),
inference(instantiation,[status(thm)],[c_582]) ).
tcf(c_1050,plain,
tc_set(tc_set(t_a)) = tc_set(tc_set(t_a)),
inference(instantiation,[status(thm)],[c_169]) ).
tcf(c_1106,plain,
! [X0: $i] : c_lessequals(v_x,c_Zorn_Osucc(X0,v_x,t_a),tc_set(tc_set(t_a))),
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_1498,plain,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,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_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_982]) ).
tcf(c_1526,plain,
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_x,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_794]) ).
tcf(c_1531,plain,
( c_lessequals(v_x,v_x,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(v_x,v_x,tc_set(t_a)),v_x,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_794]) ).
tcf(c_1539,plain,
( c_lessequals(v_n,v_x,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(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_991]) ).
tcf(c_1564,plain,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),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,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_996]) ).
tcf(c_1804,plain,
! [X0: $i] :
( c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),X0,tc_set(t_a))
| ~ c_lessequals(v_x,X0,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_x,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_520]) ).
tcf(c_2284,plain,
~ c_lessequals(v_n,v_x,tc_set(tc_set(t_a))),
inference(global_subsumption_just,[status(thm)],[c_571,c_74,c_546,c_571,c_577,c_682,c_1050,c_1531]) ).
tcf(c_2643,plain,
( c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_n,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_491]) ).
tcf(c_3171,plain,
( c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a))
| ~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_x,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_1804]) ).
tcf(c_5157,plain,
c_lessequals(v_x,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(instantiation,[status(thm)],[c_1106]) ).
tcf(c_8647,plain,
( 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_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x )
| ~ c_in(v_x,v_Y,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_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(instantiation,[status(thm)],[c_815]) ).
tcf(c_18128,plain,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,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 ) ),
inference(instantiation,[status(thm)],[c_1002]) ).
tcf(c_18129,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18128,c_8647,c_5157,c_3171,c_2643,c_2284,c_1564,c_1539,c_1526,c_1498,c_499,c_428,c_71,c_72,c_74,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:15:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 14.72/2.80 % SZS status Started for theBenchmark.p
% 14.72/2.80 % SZS status Unsatisfiable for theBenchmark.p
% 14.72/2.80
% 14.72/2.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.72/2.80
% 14.72/2.80 % ------ iProver source info
% 14.72/2.80
% 14.72/2.80 % git: date: 2026-07-19 20:42:38 +0200
% 14.72/2.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.72/2.80 % git: non_committed_changes: false
% 14.72/2.80
% 14.72/2.80 % ------ Parsing...% successful
% 14.72/2.80
% 14.72/2.80
% 14.72/2.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.72/2.80
% 14.72/2.80 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 14.72/2.80
% 14.72/2.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.72/2.80
% 14.72/2.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 14.72/2.80 % ------ Proving...
% 14.72/2.80 % ------ Problem Properties
% 14.72/2.80
% 14.72/2.80 %
% 14.72/2.80 % clauses 14
% 14.72/2.80 % conjectures 6
% 14.72/2.80 % EPR 0
% 14.72/2.80 % Horn 8
% 14.72/2.80 % unary 6
% 14.72/2.80 % binary 2
% 14.72/2.80 % lits 38
% 14.72/2.80 % lits eq 2
% 14.72/2.80 % fd_pure 0
% 14.72/2.80 % fd_pseudo 0
% 14.72/2.80 % fd_cond 0
% 14.72/2.80 % fd_pseudo_cond 1
% 14.72/2.80 % AC symbols 0
% 14.72/2.80
% 14.72/2.80 % ------ Input Options Time Limit: Unbounded
% 14.72/2.80
% 14.72/2.80
% 14.72/2.80 % ------
% 14.72/2.80 % Current options:
% 14.72/2.80 % ------
% 14.72/2.80
% 14.72/2.80
% 14.72/2.80 %
% 14.72/2.80
% 14.72/2.80 % ------ Proving...
% 14.72/2.80 %
% 14.72/2.80
% 14.72/2.80 % SZS status Unsatisfiable for theBenchmark.p
% 14.72/2.80
% 14.72/2.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.72/2.81
% 14.72/2.81
%------------------------------------------------------------------------------