%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET862-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 12:42:11 PM UTC 2026
% Result : Unsatisfiable 0.79s 1.01s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 27
% Syntax : Number of formulae : 161 ( 17 unt; 12 def)
% Number of atoms : 555 ( 5 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 713 ( 319 ~; 382 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 208 ( 0 sgn 208 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f2,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2)
| c_in(X0,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f4,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(f5,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( c_in(c_union(c_insert(X0,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| c_in(c_Zorn_Ochain__extend__1(X3,X0,X2),X3,tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_in(c_union(c_insert(X0,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X3,X0,X2),X0,tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X3,tc_set(X2))
| ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| c_in(X0,X5,X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X5,tc_set(X2))
| ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,X2)
| c_in(X0,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
fof(f10,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f11,negated_conjecture,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f12,negated_conjecture,
c_in(v_y,v_S,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f13,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_c,tc_set(t_a))
| c_lessequals(X0,v_y,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f14,negated_conjecture,
! [X0] :
( c_in(v_x(X0),v_S,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f15,negated_conjecture,
! [X0] :
( c_lessequals(X0,v_x(X0),tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f16,negated_conjecture,
! [X0] :
( X0 != v_x(X0)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f17,plain,
! [X0] :
( v_x(X0) != X0
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0] :
( ~ c_lessequals(v_x(X0),X0,tc_set(t_a))
| v_x(X0) = X0
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(resolution,[],[f2,f15]) ).
fof(f21,plain,
! [X0] :
( ~ c_lessequals(v_x(X0),X0,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_subsumption_resolution,[],[f18,f17]) ).
fof(f22,plain,
! [X0] :
( c_in(c_Main_OsubsetI__1(v_x(X0),X0,t_a),v_x(X0),t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(resolution,[],[f21,f4]) ).
fof(f23,plain,
! [X0,X1] :
( ~ c_in(X0,X1,t_a)
| c_in(X0,v_x(X1),t_a)
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(resolution,[],[f3,f15]) ).
fof(f24,plain,
! [X2,X3,X0,X1] :
( c_in(c_Main_OsubsetI__1(X1,X3,X2),X1,X2)
| c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(resolution,[],[f3,f4]) ).
fof(f25,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(X0),X0,t_a),v_x(v_x(X0)),t_a)
| ~ c_in(v_x(X0),v_S,tc_set(t_a)) ),
inference(resolution,[],[f22,f23]) ).
fof(f26,plain,
! [X0] :
( c_in(c_Main_OsubsetI__1(v_x(X0),X0,t_a),v_x(v_x(X0)),t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_subsumption_resolution,[],[f25,f14]) ).
fof(f27,plain,
! [X0] :
( c_in(c_Main_OsubsetI__1(v_x(X0),X0,t_a),v_x(v_x(v_x(X0))),t_a)
| ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_in(v_x(v_x(X0)),v_S,tc_set(t_a)) ),
inference(resolution,[],[f26,f23]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( ~ c_in(v_c,c_Zorn_Omaxchain(X0,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(X0,t_a),tc_set(tc_set(t_a)))
| c_in(X2,X3,t_a)
| ~ c_in(X2,X1,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),v_y,tc_set(t_a)) ),
inference(resolution,[],[f8,f13]) ).
fof(f29,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_in(v_x(v_x(X0)),v_S,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(X0),X0,t_a),v_x(v_x(v_x(v_x(X0)))),t_a)
| ~ c_in(v_x(v_x(v_x(X0))),v_S,tc_set(t_a)) ),
inference(resolution,[],[f27,f23]) ).
fof(f30,plain,
! [X0] :
( c_in(c_Main_OsubsetI__1(v_x(X0),X0,t_a),v_x(v_x(v_x(v_x(X0)))),t_a)
| ~ c_in(v_x(v_x(X0)),v_S,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_subsumption_resolution,[],[f29,f14]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ c_in(c_union(c_insert(X0,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(X1,X2,t_a)
| ~ c_in(X1,X0,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_y,tc_set(t_a)) ),
inference(resolution,[],[f28,f10]) ).
fof(f34,plain,
! [X2,X0,X1] :
( c_in(X0,X1,t_a)
| ~ c_in(X0,X2,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X2,t_a),X2,tc_set(t_a))
| ~ c_in(X2,v_S,tc_set(t_a)) ),
inference(resolution,[],[f33,f7]) ).
fof(f35,plain,
! [X2,X0,X1] :
( c_in(X0,X1,t_a)
| ~ c_in(X0,X2,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,X2,t_a),v_c,tc_set(t_a))
| ~ c_in(X2,v_S,tc_set(t_a)) ),
inference(resolution,[],[f33,f6]) ).
fof(f36,plain,
! [X2,X0,X1] :
( c_in(c_Zorn_Ochain__extend__1(v_c,X2,t_a),v_c,tc_set(t_a))
| ~ c_in(X0,X2,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| c_in(X0,X1,t_a)
| ~ c_in(X2,v_S,tc_set(t_a)) ),
inference(forward_subsumption_resolution,[],[f35,f11]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X2,t_a),X2,tc_set(t_a))
| ~ c_in(X0,X2,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| c_in(X0,X1,t_a)
| ~ c_in(X2,v_S,tc_set(t_a)) ),
inference(forward_subsumption_resolution,[],[f34,f11]) ).
fof(f40,plain,
! [X2,X0,X1] :
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_y,tc_set(t_a))
| ~ c_in(X0,X1,t_a)
| c_in(X0,X2,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,tc_set(t_a)) ),
inference(resolution,[],[f36,f13]) ).
fof(f43,plain,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X2,X1,t_a),v_x(X2),t_a)
| ~ c_in(X0,X2,t_a)
| c_in(X0,X1,t_a)
| ~ c_in(X2,v_S,tc_set(t_a)) ),
inference(resolution,[],[f24,f23]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ c_in(X0,X1,t_a)
| c_in(X0,X2,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X2,t_a),v_x(v_x(X1)),t_a)
| ~ c_in(v_x(X1),v_S,tc_set(t_a)) ),
inference(resolution,[],[f43,f23]) ).
fof(f49,plain,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X1,X2,t_a),v_x(v_x(X1)),t_a)
| c_in(X0,X2,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X0,X1,t_a) ),
inference(forward_subsumption_resolution,[],[f48,f14]) ).
fof(f52,plain,
! [X0,X1] :
( c_in(X0,v_x(v_x(X1)),t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X0,X1,t_a)
| c_lessequals(X1,v_x(v_x(X1)),tc_set(t_a)) ),
inference(resolution,[],[f49,f5]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ c_in(v_x(v_x(X2)),v_S,tc_set(t_a))
| ~ c_in(X2,v_S,tc_set(t_a))
| ~ c_in(X0,X2,t_a)
| c_in(c_Main_OsubsetI__1(X2,X1,t_a),v_x(v_x(v_x(X2))),t_a)
| c_in(X0,X1,t_a) ),
inference(resolution,[],[f49,f23]) ).
fof(f54,plain,
! [X0,X1] :
( c_in(X0,v_x(v_x(X1)),t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X0,X1,t_a) ),
inference(forward_subsumption_resolution,[],[f52,f3]) ).
fof(f59,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X1,v_x(v_x(X0)),t_a),X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a))
| c_lessequals(X1,v_x(v_x(X0)),tc_set(t_a)) ),
inference(resolution,[],[f54,f5]) ).
fof(f86,plain,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,t_a),c_Zorn_Ochain__extend__1(v_c,X1,t_a),t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_y,tc_set(t_a))
| c_in(X0,X2,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[],[f37,f4]) ).
fof(f114,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,X1,t_a)
| c_in(X0,v_y,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(X2,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_union(c_insert(X3,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(X2,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X4,X3,t_a)
| c_in(X4,v_y,t_a) ),
inference(resolution,[],[f40,f9]) ).
fof(f119,definition,
( spl0_3
<=> ! [X2,X3,X4] :
( ~ c_in(v_c,c_Zorn_Omaxchain(X2,t_a),tc_set(tc_set(t_a)))
| c_in(X4,v_y,t_a)
| ~ c_in(X4,X3,t_a)
| ~ c_in(c_union(c_insert(X3,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(X2,t_a),tc_set(tc_set(t_a))) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f120,plain,
( ! [X2,X3,X4] :
( ~ c_in(v_c,c_Zorn_Omaxchain(X2,t_a),tc_set(tc_set(t_a)))
| c_in(X4,v_y,t_a)
| ~ c_in(X4,X3,t_a)
| ~ c_in(c_union(c_insert(X3,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(X2,t_a),tc_set(tc_set(t_a))) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,definition,
( spl0_4
<=> ! [X0,X1] :
( ~ c_in(X0,X1,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(X0,v_y,t_a) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f123,plain,
( ! [X0,X1] :
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,tc_set(t_a))
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(X0,v_y,t_a) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f114,f122,f119]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| c_in(c_Main_OsubsetI__1(X0,X2,t_a),v_x(v_x(v_x(X0))),t_a)
| c_in(X1,X2,t_a)
| ~ c_in(v_x(X0),v_S,tc_set(t_a)) ),
inference(resolution,[],[f53,f14]) ).
fof(f132,plain,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X0,X2,t_a),v_x(v_x(v_x(X0))),t_a)
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a))
| c_in(X1,X2,t_a) ),
inference(forward_subsumption_resolution,[],[f126,f14]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ c_in(v_x(v_x(v_x(X1))),v_S,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(X0,X2,t_a)
| c_in(c_Main_OsubsetI__1(X1,X2,t_a),v_x(v_x(v_x(v_x(X1)))),t_a)
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[],[f132,f23]) ).
fof(f215,plain,
( ! [X0,X1] :
( ~ c_in(c_union(c_insert(X1,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(X0,X1,t_a)
| c_in(X0,v_y,t_a) )
| ~ spl0_3 ),
inference(resolution,[],[f120,f10]) ).
fof(f227,definition,
( spl0_17
<=> c_in(v_x(v_y),v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f228,plain,
( c_in(v_x(v_y),v_S,tc_set(t_a))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f229,plain,
( ~ c_in(v_x(v_y),v_S,tc_set(t_a))
| spl0_17 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f234,plain,
( ~ c_in(v_y,v_S,tc_set(t_a))
| spl0_17 ),
inference(resolution,[],[f229,f14]) ).
fof(f236,plain,
( $false
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f234,f12]) ).
fof(f237,plain,
spl0_17,
inference(avatar_contradiction_clause,[],[f236]) ).
fof(f259,definition,
( spl0_19
<=> c_in(v_x(v_x(v_y)),v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f260,plain,
( c_in(v_x(v_x(v_y)),v_S,tc_set(t_a))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f261,plain,
( ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a))
| spl0_19 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f268,plain,
( ~ c_in(v_x(v_y),v_S,tc_set(t_a))
| spl0_19 ),
inference(resolution,[],[f261,f14]) ).
fof(f270,plain,
( $false
| ~ spl0_17
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f268,f228]) ).
fof(f271,plain,
( ~ spl0_17
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f274,plain,
( ! [X0,X1] :
( ~ c_in(X0,X1,t_a)
| c_in(X0,v_y,t_a)
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) )
| ~ spl0_3 ),
inference(resolution,[],[f215,f7]) ).
fof(f275,plain,
( ! [X0,X1] :
( ~ c_in(X0,X1,t_a)
| c_in(X0,v_y,t_a)
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) )
| ~ spl0_3 ),
inference(resolution,[],[f215,f6]) ).
fof(f276,plain,
( ! [X0,X1] :
( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_S,tc_set(t_a)) )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f275,f11]) ).
fof(f277,plain,
( ! [X0,X1] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f274,f11]) ).
fof(f381,plain,
( ! [X0,X1] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,tc_set(t_a)) )
| ~ spl0_3 ),
inference(resolution,[],[f276,f13]) ).
fof(f382,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f381,f119,f122]) ).
fof(f385,plain,
( ! [X2,X0,X1] :
( ~ c_in(X2,c_Zorn_Ochain__extend__1(v_c,X1,t_a),t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,t_a)
| c_in(X2,v_y,t_a) )
| ~ spl0_4 ),
inference(resolution,[],[f123,f3]) ).
fof(f390,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_y,t_a),X1,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(X0,v_y,tc_set(t_a)) )
| ~ spl0_3 ),
inference(resolution,[],[f277,f5]) ).
fof(f394,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,v_S,tc_set(t_a))
| c_in(X1,v_y,t_a)
| ~ c_in(X1,X0,t_a)
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,X0,t_a),X0,t_a),v_y,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_y,tc_set(t_a))
| c_in(X3,X2,t_a)
| ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_in(X3,X0,t_a) )
| ~ spl0_4 ),
inference(resolution,[],[f385,f86]) ).
fof(f396,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,X0,t_a),X2,t_a),v_y,t_a)
| c_in(X1,v_y,t_a)
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a))
| c_in(X3,X2,t_a)
| ~ c_in(X3,c_Zorn_Ochain__extend__1(v_c,X0,t_a),t_a) )
| ~ spl0_4 ),
inference(resolution,[],[f385,f24]) ).
fof(f397,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,X0,t_a),X0,t_a),v_y,t_a)
| c_in(X1,v_y,t_a)
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_y,tc_set(t_a))
| c_in(X3,X2,t_a)
| ~ c_in(X3,X0,t_a) )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f394]) ).
fof(f433,definition,
( spl0_26
<=> c_in(v_x(v_x(v_x(v_y))),v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f434,plain,
( c_in(v_x(v_x(v_x(v_y))),v_S,tc_set(t_a))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f435,plain,
( ~ c_in(v_x(v_x(v_x(v_y))),v_S,tc_set(t_a))
| spl0_26 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f450,plain,
( ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a))
| spl0_26 ),
inference(resolution,[],[f435,f14]) ).
fof(f453,plain,
( $false
| ~ spl0_19
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f450,f260]) ).
fof(f454,plain,
( ~ spl0_19
| spl0_26 ),
inference(avatar_contradiction_clause,[],[f453]) ).
fof(f457,plain,
( ! [X0,X1] :
( ~ c_in(v_y,v_S,tc_set(t_a))
| c_in(X0,X1,t_a)
| c_in(c_Main_OsubsetI__1(v_y,X1,t_a),v_x(v_x(v_x(v_x(v_y)))),t_a)
| ~ c_in(X0,v_y,t_a) )
| ~ spl0_26 ),
inference(resolution,[],[f434,f135]) ).
fof(f463,plain,
( ! [X0,X1] :
( c_in(c_Main_OsubsetI__1(v_y,X1,t_a),v_x(v_x(v_x(v_x(v_y)))),t_a)
| c_in(X0,X1,t_a)
| ~ c_in(X0,v_y,t_a) )
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f457,f12]) ).
fof(f577,definition,
( spl0_39
<=> c_in(v_x(v_x(v_x(v_x(v_y)))),v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f578,plain,
( c_in(v_x(v_x(v_x(v_x(v_y)))),v_S,tc_set(t_a))
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f579,plain,
( ~ c_in(v_x(v_x(v_x(v_x(v_y)))),v_S,tc_set(t_a))
| spl0_39 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f586,plain,
( ~ c_in(v_x(v_x(v_x(v_y))),v_S,tc_set(t_a))
| spl0_39 ),
inference(resolution,[],[f579,f14]) ).
fof(f589,plain,
( $false
| ~ spl0_26
| spl0_39 ),
inference(forward_subsumption_resolution,[],[f586,f434]) ).
fof(f590,plain,
( ~ spl0_26
| spl0_39 ),
inference(avatar_contradiction_clause,[],[f589]) ).
fof(f591,plain,
( ! [X2,X0,X1] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(X2,v_x(v_x(v_y)),t_a)
| ~ c_in(X2,c_Zorn_Ochain__extend__1(v_c,X1,t_a),t_a)
| ~ c_in(v_y,v_S,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_x(v_x(v_y)),tc_set(t_a)) )
| ~ spl0_4 ),
inference(resolution,[],[f396,f59]) ).
fof(f595,plain,
( ! [X2,X0,X1] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(X2,v_x(v_x(v_y)),t_a)
| ~ c_in(X2,c_Zorn_Ochain__extend__1(v_c,X1,t_a),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_x(v_x(v_y)),tc_set(t_a)) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f591,f12]) ).
fof(f596,plain,
( ! [X2,X0,X1] :
( c_in(X2,v_x(v_x(v_y)),t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X2,c_Zorn_Ochain__extend__1(v_c,X1,t_a),t_a) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f595,f3]) ).
fof(f714,definition,
( spl0_50
<=> ! [X0] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_y)),t_a) ) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f715,plain,
( ! [X0] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_y)),t_a) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f808,plain,
( ! [X0] :
( c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a)
| ~ c_in(X0,v_y,t_a)
| c_lessequals(v_y,v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)) )
| ~ spl0_26 ),
inference(resolution,[],[f463,f5]) ).
fof(f811,plain,
( ! [X0] :
( c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a)
| ~ c_in(X0,v_y,t_a) )
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f808,f3]) ).
fof(f816,plain,
( ! [X0] :
( c_lessequals(X0,v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_y)))),t_a),v_y,t_a) )
| ~ spl0_26 ),
inference(resolution,[],[f811,f5]) ).
fof(f876,plain,
( ! [X0,X1] :
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,t_a),c_Zorn_Ochain__extend__1(v_c,X1,t_a),t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(X0,v_y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_y,t_a),X1,t_a) )
| ~ spl0_3 ),
inference(resolution,[],[f390,f4]) ).
fof(f898,plain,
( ! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_x(v_x(v_x(v_y)))),t_a),v_x(v_x(v_x(v_x(v_y)))),t_a),v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| c_in(X0,X1,t_a)
| ~ c_in(v_x(v_x(v_x(v_x(v_y)))),v_S,tc_set(t_a)) )
| ~ spl0_26 ),
inference(resolution,[],[f816,f37]) ).
fof(f902,plain,
( ! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_x(v_x(v_x(v_y)))),t_a),v_x(v_x(v_x(v_x(v_y)))),t_a),v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| c_in(X0,X1,t_a) )
| ~ spl0_26
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[],[f898,f578]) ).
fof(f906,definition,
( spl0_59
<=> ! [X0,X1] :
( ~ c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a)
| c_in(X0,X1,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a)) ) ),
introduced(definition,[new_symbols(definition,[spl0_59])],[avatar_definition]) ).
fof(f907,plain,
( ! [X0,X1] :
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| c_in(X0,X1,t_a)
| ~ c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f906]) ).
fof(f909,definition,
( spl0_60
<=> c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_x(v_x(v_x(v_y)))),t_a),v_x(v_x(v_x(v_x(v_y)))),t_a),v_y,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_60])],[avatar_definition]) ).
fof(f911,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_x(v_x(v_x(v_y)))),t_a),v_x(v_x(v_x(v_x(v_y)))),t_a),v_y,t_a)
| spl0_60 ),
inference(avatar_component_clause,[],[f909]) ).
fof(f912,plain,
( spl0_59
| ~ spl0_60
| ~ spl0_26
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f902,f577,f433,f909,f906]) ).
fof(f919,definition,
( spl0_62
<=> ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_y,t_a),v_x(v_x(v_x(v_x(v_y)))),t_a)
| c_lessequals(X0,v_y,tc_set(t_a)) ) ),
introduced(definition,[new_symbols(definition,[spl0_62])],[avatar_definition]) ).
fof(f920,plain,
( ! [X0] :
( c_lessequals(X0,v_y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_y,t_a),v_x(v_x(v_x(v_x(v_y)))),t_a) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f924,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X2,v_x(v_x(v_y)),t_a),c_Zorn_Ochain__extend__1(v_c,X1,t_a),t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,t_a)
| c_lessequals(X2,v_x(v_x(v_y)),tc_set(t_a)) )
| ~ spl0_4 ),
inference(resolution,[],[f596,f5]) ).
fof(f974,definition,
( spl0_63
<=> ! [X0] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a) ) ),
introduced(definition,[new_symbols(definition,[spl0_63])],[avatar_definition]) ).
fof(f975,plain,
( ! [X0] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f1029,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_y,t_a),v_x(v_x(v_x(v_x(v_y)))),t_a)
| c_lessequals(X0,v_y,tc_set(t_a)) )
| ~ spl0_63 ),
inference(resolution,[],[f975,f5]) ).
fof(f1033,plain,
( spl0_62
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f1029,f974,f919]) ).
fof(f1049,plain,
( ~ c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_x(v_x(v_x(v_y)))),t_a)
| ~ c_in(v_y,v_S,tc_set(t_a))
| ~ spl0_62 ),
inference(resolution,[],[f920,f21]) ).
fof(f1051,plain,
( ~ c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_x(v_x(v_x(v_y)))),t_a)
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[],[f1049,f12]) ).
fof(f1071,plain,
( ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a))
| ~ c_in(v_y,v_S,tc_set(t_a))
| ~ spl0_62 ),
inference(resolution,[],[f1051,f30]) ).
fof(f1085,plain,
( ~ c_in(v_y,v_S,tc_set(t_a))
| ~ spl0_19
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[],[f1071,f260]) ).
fof(f1095,plain,
( $false
| ~ spl0_19
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[],[f1085,f12]) ).
fof(f1096,plain,
( ~ spl0_19
| ~ spl0_62 ),
inference(avatar_contradiction_clause,[],[f1095]) ).
fof(f1139,plain,
( ! [X2,X0,X1] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a)
| ~ c_in(v_x(v_x(v_x(v_x(v_y)))),v_S,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| c_in(X2,X1,t_a)
| ~ c_in(X2,v_x(v_x(v_x(v_x(v_y)))),t_a) )
| ~ spl0_4
| spl0_60 ),
inference(resolution,[],[f911,f397]) ).
fof(f1142,plain,
( ! [X2,X0,X1] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| c_in(X2,X1,t_a)
| ~ c_in(X2,v_x(v_x(v_x(v_x(v_y)))),t_a) )
| ~ spl0_4
| ~ spl0_39
| spl0_60 ),
inference(forward_subsumption_resolution,[],[f1139,f578]) ).
fof(f1145,plain,
( spl0_59
| spl0_63
| ~ spl0_4
| ~ spl0_39
| spl0_60 ),
inference(avatar_split_clause,[],[f1142,f909,f577,f122,f974,f906]) ).
fof(f1182,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_x(v_x(v_y)))),t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(X1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(X1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X3,X2,t_a)
| c_in(X3,v_y,t_a) )
| ~ spl0_59 ),
inference(resolution,[],[f907,f9]) ).
fof(f2069,plain,
( ! [X0,X1] :
( ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_y)),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_x(v_y)),t_a),v_x(v_x(v_y)),tc_set(t_a))
| ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a))
| c_lessequals(X1,v_y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,v_y,t_a),v_x(v_x(v_y)),t_a) )
| ~ spl0_3
| ~ spl0_4 ),
inference(resolution,[],[f924,f876]) ).
fof(f2074,plain,
( ! [X0,X1] :
( ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_y)),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_x(v_y)),t_a),v_x(v_x(v_y)),tc_set(t_a))
| c_lessequals(X1,v_y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,v_y,t_a),v_x(v_x(v_y)),t_a) )
| ~ spl0_3
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f2069]) ).
fof(f2076,plain,
( ! [X0,X1] :
( ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_y)),t_a)
| c_lessequals(X1,v_y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,v_y,t_a),v_x(v_x(v_y)),t_a) )
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f2074,f277]) ).
fof(f2077,plain,
( ! [X0,X1] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_x(v_y)),t_a)
| c_lessequals(X1,v_y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,v_y,t_a),v_x(v_x(v_y)),t_a) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f2076,f260]) ).
fof(f2079,definition,
( spl0_100
<=> ! [X1] :
( c_lessequals(X1,v_y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,v_y,t_a),v_x(v_x(v_y)),t_a) ) ),
introduced(definition,[new_symbols(definition,[spl0_100])],[avatar_definition]) ).
fof(f2080,plain,
( ! [X1] :
( c_lessequals(X1,v_y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,v_y,t_a),v_x(v_x(v_y)),t_a) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f2079]) ).
fof(f2081,plain,
( spl0_100
| spl0_50
| ~ spl0_3
| ~ spl0_4
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f2077,f259,f122,f119,f714,f2079]) ).
fof(f2090,plain,
( ~ c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_x(v_y)),t_a)
| ~ c_in(v_y,v_S,tc_set(t_a))
| ~ spl0_100 ),
inference(resolution,[],[f2080,f21]) ).
fof(f2094,plain,
( ~ c_in(v_y,v_S,tc_set(t_a))
| ~ spl0_100 ),
inference(forward_subsumption_resolution,[],[f2090,f26]) ).
fof(f2095,plain,
( $false
| ~ spl0_100 ),
inference(forward_subsumption_resolution,[],[f2094,f12]) ).
fof(f2096,plain,
~ spl0_100,
inference(avatar_contradiction_clause,[],[f2095]) ).
fof(f2102,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_y,t_a),v_x(v_x(v_y)),t_a)
| c_lessequals(X0,v_y,tc_set(t_a)) )
| ~ spl0_50 ),
inference(resolution,[],[f715,f5]) ).
fof(f2110,plain,
( spl0_100
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f2102,f714,f2079]) ).
fof(f2114,plain,
( spl0_3
| spl0_63
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f1182,f906,f974,f119]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f124]) ).
cnf(s15,plain,
spl0_17,
inference(sat_conversion,[],[f237]) ).
cnf(s17,plain,
( ~ spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f271]) ).
cnf(s33,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f382]) ).
cnf(s36,plain,
( ~ spl0_19
| spl0_26 ),
inference(sat_conversion,[],[f454]) ).
cnf(s49,plain,
( ~ spl0_26
| spl0_39 ),
inference(sat_conversion,[],[f590]) ).
cnf(s69,plain,
( ~ spl0_26
| ~ spl0_39
| spl0_59
| ~ spl0_60 ),
inference(sat_conversion,[],[f912]) ).
cnf(s76,plain,
( spl0_62
| ~ spl0_63 ),
inference(sat_conversion,[],[f1033]) ).
cnf(s80,plain,
( ~ spl0_19
| ~ spl0_62 ),
inference(sat_conversion,[],[f1096]) ).
cnf(s81,plain,
( ~ spl0_4
| ~ spl0_39
| spl0_59
| spl0_60
| spl0_63 ),
inference(sat_conversion,[],[f1145]) ).
cnf(s119,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_19
| spl0_50
| spl0_100 ),
inference(sat_conversion,[],[f2081]) ).
cnf(s120,plain,
~ spl0_100,
inference(sat_conversion,[],[f2096]) ).
cnf(s121,plain,
( ~ spl0_50
| spl0_100 ),
inference(sat_conversion,[],[f2110]) ).
cnf(s123,plain,
( spl0_3
| ~ spl0_59
| spl0_63 ),
inference(sat_conversion,[],[f2114]) ).
cnf(s129,plain,
~ spl0_50,
inference(rat,[],[s121,s120]) ).
cnf(s130,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_19 ),
inference(rat,[],[s119,s120,s129]) ).
cnf(s133,plain,
spl0_19,
inference(rat,[],[s17,s15]) ).
cnf(s135,plain,
~ spl0_62,
inference(rat,[],[s80,s133]) ).
cnf(s136,plain,
spl0_26,
inference(rat,[],[s36,s133]) ).
cnf(s137,plain,
~ spl0_63,
inference(rat,[],[s76,s135]) ).
cnf(s138,plain,
spl0_39,
inference(rat,[],[s49,s136]) ).
cnf(s172,plain,
spl0_3,
inference(rat,[],[s81,s69,s2,s123,s138,s137,s136]) ).
cnf(s173,plain,
~ spl0_4,
inference(rat,[],[s130,s133,s172]) ).
cnf(s179,plain,
$false,
inference(rat,[],[s33,s173,s172]) ).
fof(f2134,plain,
$false,
inference(avatar_sat_refutation,[],[s179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET862-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:03:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.79/1.01 % (391943)Input is clausal, will run a generic CNF schedule.
% 0.79/1.01 % (391949)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3004453564:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.79/1.01 % (391952)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3230193330:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.79/1.01 % (391953)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2071475110:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.79/1.01 % (391948)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2532273523:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.79/1.01 % (391954)dis-21_1_sil=8000:lcm=predicate:random_seed=164228679:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.79/1.01 % (391951)lrs+10_1_sil=8000:sp=occurrence:random_seed=485954196:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.79/1.01 % (391950)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2626094411:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.79/1.01 % (391952)Refutation not found, incomplete strategy
% 0.79/1.01 % (391952)------------------------------
% 0.79/1.01 % (391952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.79/1.01 % (391952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/1.01 % (391952)CaDiCaL version: 2.1.3
% 0.79/1.01 % (391952)Termination reason: Refutation not found, incomplete strategy
% 0.79/1.01 % (391952)Time elapsed: 0.002 s
% 0.79/1.01 % (391952)Peak memory usage: 87 MB
% 0.79/1.01 % (391952)Instructions burned: 1 (million)
% 0.79/1.01 % (391951)Instruction limit reached!
% 0.79/1.01 % (391951)------------------------------
% 0.79/1.01 % (391951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.79/1.01 % (391951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/1.01 % (391951)CaDiCaL version: 2.1.3
% 0.79/1.01 % (391951)Termination reason: Instruction limit
% 0.79/1.01 % (391951)Termination phase: Saturation
% 0.79/1.01 % (391951)Time elapsed: 0.068 s
% 0.79/1.01 % (391951)Peak memory usage: 88 MB
% 0.79/1.01 % (391951)Instructions burned: 108 (million)
% 0.79/1.01 % (391954)Instruction limit reached!
% 0.79/1.01 % (391954)------------------------------
% 0.79/1.01 % (391954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.79/1.01 % (391954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/1.01 % (391954)CaDiCaL version: 2.1.3
% 0.79/1.01 % (391954)Termination reason: Instruction limit
% 0.79/1.01 % (391954)Termination phase: Saturation
% 0.79/1.01 % (391954)Time elapsed: 0.069 s
% 0.79/1.01 % (391954)Peak memory usage: 88 MB
% 0.79/1.01 % (391954)Instructions burned: 119 (million)
% 0.79/1.01 % (391953)First to succeed.
% 0.79/1.01 % (391953)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-391943"
% 0.79/1.01 % (391953)Refutation found. Thanks to Tanya!
% 0.79/1.01 % SZS status Unsatisfiable for theBenchmark
% 0.79/1.01 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/1.21 % (391953)------------------------------
% 0.13/1.21 % (391953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.13/1.21 % (391953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/1.21 % (391953)CaDiCaL version: 2.1.3
% 0.13/1.21 % (391953)Termination reason: Refutation
% 0.13/1.21 % (391953)Time elapsed: 0.076 s
% 0.13/1.21 % (391953)Peak memory usage: 90 MB
% 0.13/1.21 % (391953)Instructions burned: 173 (million)
% 0.13/1.21 % (391953)------------------------------
% 0.13/1.21 % (391953)------------------------------
% 0.13/1.21 % (391943)Success in time 0.405 s
% 0.13/1.21 % Vampire exiting
%------------------------------------------------------------------------------