TSTP Solution File: SET862-2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET862-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:13:49 EDT 2024
% Result : Unsatisfiable 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 61
% Syntax : Number of formulae : 255 ( 12 unt; 0 def)
% Number of atoms : 733 ( 43 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 815 ( 337 ~; 432 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 50 ( 48 usr; 47 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 165 ( 165 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1181,plain,
$false,
inference(avatar_sat_refutation,[],[f66,f104,f160,f217,f239,f242,f288,f317,f339,f365,f385,f398,f413,f419,f469,f488,f628,f661,f748,f756,f760,f873,f888,f950,f969,f983,f1092,f1134,f1148,f1180]) ).
fof(f1180,plain,
( ~ spl0_9
| spl0_37
| ~ spl0_38 ),
inference(avatar_contradiction_clause,[],[f1179]) ).
fof(f1179,plain,
( $false
| ~ spl0_9
| spl0_37
| ~ spl0_38 ),
inference(subsumption_resolution,[],[f1172,f37]) ).
fof(f37,plain,
~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)),
inference(subsumption_resolution,[],[f36,f16]) ).
fof(f16,plain,
v_y != v_x(v_y),
inference(resolution,[],[f15,f11]) ).
fof(f11,axiom,
c_in(v_y,v_S,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f15,axiom,
! [X8] :
( ~ c_in(X8,v_S,tc_set(t_a))
| v_x(X8) != X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f36,plain,
( v_y = v_x(v_y)
| ~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[],[f34,f1]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| X0 = X1
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f34,plain,
c_lessequals(v_y,v_x(v_y),tc_set(t_a)),
inference(duplicate_literal_removal,[],[f33]) ).
fof(f33,plain,
( c_lessequals(v_y,v_x(v_y),tc_set(t_a))
| c_lessequals(v_y,v_x(v_y),tc_set(t_a)) ),
inference(resolution,[],[f32,f3]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X1,X0,X2),X1,X2)
| c_lessequals(X1,X0,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f32,plain,
! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_y),t_a),v_y,t_a)
| c_lessequals(X0,v_x(v_y),tc_set(t_a)) ),
inference(resolution,[],[f29,f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X1,X0,X2),X0,X2)
| c_lessequals(X1,X0,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f29,plain,
! [X0] :
( c_in(X0,v_x(v_y),t_a)
| ~ c_in(X0,v_y,t_a) ),
inference(resolution,[],[f26,f11]) ).
fof(f26,plain,
! [X0,X1] :
( ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X0,X1,t_a)
| c_in(X0,v_x(X1),t_a) ),
inference(resolution,[],[f2,f14]) ).
fof(f14,axiom,
! [X8] :
( c_lessequals(X8,v_x(X8),tc_set(t_a))
| ~ c_in(X8,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| c_in(X3,X0,X2)
| ~ c_in(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f1172,plain,
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| ~ spl0_9
| spl0_37
| ~ spl0_38 ),
inference(duplicate_literal_removal,[],[f1170]) ).
fof(f1170,plain,
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| ~ spl0_9
| spl0_37
| ~ spl0_38 ),
inference(resolution,[],[f1163,f4]) ).
fof(f1163,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(v_x(v_y),X0,t_a),v_y,t_a)
| c_lessequals(v_x(v_y),X0,tc_set(t_a)) )
| ~ spl0_9
| spl0_37
| ~ spl0_38 ),
inference(resolution,[],[f1154,f3]) ).
fof(f1154,plain,
( ! [X0] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a) )
| ~ spl0_9
| spl0_37
| ~ spl0_38 ),
inference(subsumption_resolution,[],[f1152,f868]) ).
fof(f868,plain,
( ~ c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| spl0_37 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f867,plain,
( spl0_37
<=> c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1152,plain,
( ! [X0] :
( ~ c_in(X0,v_x(v_y),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(X0,v_y,t_a) )
| ~ spl0_9
| ~ spl0_38 ),
inference(resolution,[],[f1107,f234]) ).
fof(f234,plain,
( c_in(v_x(v_y),v_S,tc_set(t_a))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f233,plain,
( spl0_9
<=> c_in(v_x(v_y),v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1107,plain,
( ! [X0,X1] :
( ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X0,X1,t_a)
| 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) )
| ~ spl0_38 ),
inference(subsumption_resolution,[],[f1102,f37]) ).
fof(f1102,plain,
( ! [X0,X1] :
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,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_38 ),
inference(resolution,[],[f1096,f343]) ).
fof(f343,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| c_in(X0,X1,t_a)
| ~ c_in(X0,X2,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(subsumption_resolution,[],[f341,f10]) ).
fof(f10,axiom,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f341,plain,
! [X2,X0,X1] :
( c_in(X0,X1,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X0,X2,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,X2,t_a),v_c,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,v_S,tc_set(t_a)) ),
inference(resolution,[],[f145,f9]) ).
fof(f9,axiom,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f145,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| c_in(X0,X1,X2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X3,X1,X2),X1,tc_set(X2))
| ~ c_in(X0,X5,X2)
| c_in(c_Zorn_Ochain__extend__1(X3,X5,X2),X3,tc_set(X2))
| ~ c_in(X3,c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X5,X4,tc_set(X2)) ),
inference(resolution,[],[f8,f5]) ).
fof(f5,axiom,
! [X2,X3,X4,X5] :
( c_in(c_union(c_insert(X4,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X5,X2),tc_set(tc_set(X2)))
| c_in(c_Zorn_Ochain__extend__1(X3,X4,X2),X3,tc_set(X2))
| ~ c_in(X3,c_Zorn_Ochain(X5,X2),tc_set(tc_set(X2)))
| ~ c_in(X4,X5,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
fof(f8,axiom,
! [X2,X3,X6,X7,X4,X5] :
( ~ c_in(c_union(c_insert(X6,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X5,X2),tc_set(tc_set(X2)))
| c_in(X4,X7,X2)
| ~ c_in(X3,c_Zorn_Omaxchain(X5,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X3,X7,X2),X7,tc_set(X2))
| ~ c_in(X4,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
fof(f1096,plain,
( ! [X0] :
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_y,tc_set(t_a))
| c_lessequals(v_x(v_y),X0,tc_set(t_a)) )
| ~ spl0_38 ),
inference(resolution,[],[f1070,f12]) ).
fof(f12,axiom,
! [X8] :
( ~ c_in(X8,v_c,tc_set(t_a))
| c_lessequals(X8,v_y,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1070,plain,
( ! [X0] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_lessequals(v_x(v_y),X0,tc_set(t_a)) )
| ~ spl0_38 ),
inference(duplicate_literal_removal,[],[f1008]) ).
fof(f1008,plain,
( ! [X0] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_lessequals(v_x(v_y),X0,tc_set(t_a))
| c_lessequals(v_x(v_y),X0,tc_set(t_a)) )
| ~ spl0_38 ),
inference(resolution,[],[f958,f4]) ).
fof(f958,plain,
( ! [X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),X1,t_a),X0,t_a)
| c_lessequals(v_x(v_y),X1,tc_set(t_a)) )
| ~ spl0_38 ),
inference(resolution,[],[f872,f3]) ).
fof(f872,plain,
( ! [X0,X1] :
( ~ c_in(X1,v_x(v_y),t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(X1,X0,t_a) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f871]) ).
fof(f871,plain,
( spl0_38
<=> ! [X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,v_x(v_y),t_a)
| c_in(X1,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1148,plain,
( ~ spl0_45
| spl0_46
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f1095,f753,f1145,f1141]) ).
fof(f1141,plain,
( spl0_45
<=> c_lessequals(v_y,c_Zorn_Omaxchain__super__lemma__1(v_c,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1145,plain,
( spl0_46
<=> v_y = c_Zorn_Omaxchain__super__lemma__1(v_c,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f753,plain,
( spl0_36
<=> c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a),v_c,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1095,plain,
( v_y = c_Zorn_Omaxchain__super__lemma__1(v_c,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a)
| ~ c_lessequals(v_y,c_Zorn_Omaxchain__super__lemma__1(v_c,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a),tc_set(t_a))
| ~ spl0_36 ),
inference(resolution,[],[f1093,f1]) ).
fof(f1093,plain,
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a),v_y,tc_set(t_a))
| ~ spl0_36 ),
inference(resolution,[],[f755,f12]) ).
fof(f755,plain,
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a),v_c,tc_set(t_a))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f1134,plain,
( ~ spl0_9
| ~ spl0_37
| ~ spl0_38 ),
inference(avatar_contradiction_clause,[],[f1133]) ).
fof(f1133,plain,
( $false
| ~ spl0_9
| ~ spl0_37
| ~ spl0_38 ),
inference(subsumption_resolution,[],[f1126,f37]) ).
fof(f1126,plain,
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| ~ spl0_9
| ~ spl0_37
| ~ spl0_38 ),
inference(duplicate_literal_removal,[],[f1124]) ).
fof(f1124,plain,
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| ~ spl0_9
| ~ spl0_37
| ~ spl0_38 ),
inference(resolution,[],[f1117,f4]) ).
fof(f1117,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(v_x(v_y),X0,t_a),v_y,t_a)
| c_lessequals(v_x(v_y),X0,tc_set(t_a)) )
| ~ spl0_9
| ~ spl0_37
| ~ spl0_38 ),
inference(resolution,[],[f1106,f3]) ).
fof(f1106,plain,
( ! [X0] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a) )
| ~ spl0_9
| ~ spl0_37
| ~ spl0_38 ),
inference(subsumption_resolution,[],[f1101,f37]) ).
fof(f1101,plain,
( ! [X0] :
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_y),t_a) )
| ~ spl0_9
| ~ spl0_37
| ~ spl0_38 ),
inference(resolution,[],[f1096,f935]) ).
fof(f935,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| c_in(X0,X1,t_a)
| ~ c_in(X0,v_x(v_y),t_a) )
| ~ spl0_9
| ~ spl0_37 ),
inference(subsumption_resolution,[],[f932,f9]) ).
fof(f932,plain,
( ! [X0,X1] :
( c_in(X0,X1,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_x(v_y),t_a) )
| ~ spl0_9
| ~ spl0_37 ),
inference(resolution,[],[f907,f8]) ).
fof(f907,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)))
| ~ spl0_9
| ~ spl0_37 ),
inference(subsumption_resolution,[],[f904,f234]) ).
fof(f904,plain,
( ~ c_in(v_x(v_y),v_S,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)))
| ~ spl0_37 ),
inference(resolution,[],[f903,f81]) ).
fof(f81,plain,
! [X0] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X0,t_a),X0,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a))
| 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))) ),
inference(resolution,[],[f6,f10]) ).
fof(f6,axiom,
! [X2,X3,X4,X5] :
( ~ c_in(X3,c_Zorn_Ochain(X5,X2),tc_set(tc_set(X2)))
| ~ c_in(X4,X5,tc_set(X2))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X3,X4,X2),X4,tc_set(X2))
| c_in(c_union(c_insert(X4,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X5,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
fof(f903,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))
| ~ spl0_37 ),
inference(duplicate_literal_removal,[],[f889]) ).
fof(f889,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))
| ~ spl0_37 ),
inference(resolution,[],[f879,f32]) ).
fof(f879,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),X0,t_a),v_y,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),X0,tc_set(t_a)) )
| ~ spl0_37 ),
inference(resolution,[],[f875,f3]) ).
fof(f875,plain,
( ! [X0] :
( ~ c_in(X0,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a)
| c_in(X0,v_y,t_a) )
| ~ spl0_37 ),
inference(resolution,[],[f874,f2]) ).
fof(f874,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_y,tc_set(t_a))
| ~ spl0_37 ),
inference(resolution,[],[f869,f12]) ).
fof(f869,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f1092,plain,
( ~ spl0_24
| spl0_36
| ~ spl0_38 ),
inference(avatar_contradiction_clause,[],[f1091]) ).
fof(f1091,plain,
( $false
| ~ spl0_24
| spl0_36
| ~ spl0_38 ),
inference(subsumption_resolution,[],[f1084,f37]) ).
fof(f1084,plain,
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| ~ spl0_24
| spl0_36
| ~ spl0_38 ),
inference(duplicate_literal_removal,[],[f1082]) ).
fof(f1082,plain,
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| ~ spl0_24
| spl0_36
| ~ spl0_38 ),
inference(resolution,[],[f1006,f4]) ).
fof(f1006,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(v_x(v_y),X0,t_a),v_y,t_a)
| c_lessequals(v_x(v_y),X0,tc_set(t_a)) )
| ~ spl0_24
| spl0_36
| ~ spl0_38 ),
inference(resolution,[],[f958,f784]) ).
fof(f784,plain,
( ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| ~ spl0_24
| spl0_36 ),
inference(superposition,[],[f754,f412]) ).
fof(f412,plain,
( v_y = c_Zorn_Ochain__extend__1(v_c,v_y,t_a)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f410,plain,
( spl0_24
<=> v_y = c_Zorn_Ochain__extend__1(v_c,v_y,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f754,plain,
( ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a),v_c,tc_set(t_a))
| spl0_36 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f983,plain,
( ~ spl0_43
| spl0_44
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f909,f867,f980,f976]) ).
fof(f976,plain,
( spl0_43
<=> c_lessequals(v_x(v_x(v_y)),c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f980,plain,
( spl0_44
<=> v_x(v_x(v_y)) = c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f909,plain,
( v_x(v_x(v_y)) = c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a)
| ~ c_lessequals(v_x(v_x(v_y)),c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),tc_set(t_a))
| ~ spl0_37 ),
inference(resolution,[],[f902,f1]) ).
fof(f902,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_x(v_y)),tc_set(t_a))
| ~ spl0_37 ),
inference(duplicate_literal_removal,[],[f890]) ).
fof(f890,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(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_x(v_y)),tc_set(t_a))
| ~ spl0_37 ),
inference(resolution,[],[f879,f47]) ).
fof(f47,plain,
! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_y)),t_a),v_y,t_a)
| c_lessequals(X0,v_x(v_x(v_y)),tc_set(t_a)) ),
inference(subsumption_resolution,[],[f43,f11]) ).
fof(f43,plain,
! [X0] :
( ~ c_in(v_y,v_S,tc_set(t_a))
| c_lessequals(X0,v_x(v_x(v_y)),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_y)),t_a),v_y,t_a) ),
inference(resolution,[],[f38,f29]) ).
fof(f38,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(X1)),t_a),v_x(X1),t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(X0,v_x(v_x(X1)),tc_set(t_a)) ),
inference(resolution,[],[f30,f4]) ).
fof(f30,plain,
! [X0,X1] :
( c_in(X0,v_x(v_x(X1)),t_a)
| ~ c_in(X0,v_x(X1),t_a)
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(resolution,[],[f26,f13]) ).
fof(f13,axiom,
! [X8] :
( c_in(v_x(X8),v_S,tc_set(t_a))
| ~ c_in(X8,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f969,plain,
( ~ spl0_41
| spl0_42
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f906,f867,f966,f962]) ).
fof(f962,plain,
( spl0_41
<=> c_lessequals(v_x(v_y),c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f966,plain,
( spl0_42
<=> v_x(v_y) = c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f906,plain,
( v_x(v_y) = c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a)
| ~ c_lessequals(v_x(v_y),c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),tc_set(t_a))
| ~ spl0_37 ),
inference(resolution,[],[f903,f1]) ).
fof(f950,plain,
( spl0_38
| ~ spl0_9
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f936,f867,f233,f871]) ).
fof(f936,plain,
( ! [X0,X1] :
( c_in(X0,X1,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X0,v_x(v_y),t_a) )
| ~ spl0_9
| ~ spl0_37 ),
inference(subsumption_resolution,[],[f933,f9]) ).
fof(f933,plain,
( ! [X0,X1] :
( c_in(X0,X1,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X0,v_x(v_y),t_a) )
| ~ spl0_9
| ~ spl0_37 ),
inference(resolution,[],[f907,f7]) ).
fof(f7,axiom,
! [X2,X3,X6,X7,X4,X5] :
( ~ c_in(c_union(c_insert(X6,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X5,X2),tc_set(tc_set(X2)))
| c_in(X4,X7,X2)
| ~ c_in(X3,c_Zorn_Omaxchain(X5,X2),tc_set(tc_set(X2)))
| c_in(c_Zorn_Omaxchain__super__lemma__1(X3,X7,X2),X3,tc_set(X2))
| ~ c_in(X4,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
fof(f888,plain,
( ~ spl0_39
| spl0_40
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f876,f867,f885,f881]) ).
fof(f881,plain,
( spl0_39
<=> c_lessequals(v_y,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f885,plain,
( spl0_40
<=> v_y = c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f876,plain,
( v_y = c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a)
| ~ c_lessequals(v_y,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),tc_set(t_a))
| ~ spl0_37 ),
inference(resolution,[],[f874,f1]) ).
fof(f873,plain,
( spl0_37
| spl0_38
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f389,f233,f871,f867]) ).
fof(f389,plain,
( ! [X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,v_x(v_y),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(X1,X0,t_a) )
| ~ spl0_9 ),
inference(resolution,[],[f301,f234]) ).
fof(f301,plain,
! [X2,X0,X1] :
( ~ c_in(X2,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X0,X2,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(X0,X1,t_a) ),
inference(subsumption_resolution,[],[f299,f10]) ).
fof(f299,plain,
! [X2,X0,X1] :
( c_in(X0,X1,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X0,X2,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,X2,t_a),v_c,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,v_S,tc_set(t_a)) ),
inference(resolution,[],[f113,f9]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| c_in(X0,X1,X2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X3,X1,X2),X3,tc_set(X2))
| ~ c_in(X0,X5,X2)
| c_in(c_Zorn_Ochain__extend__1(X3,X5,X2),X3,tc_set(X2))
| ~ c_in(X3,c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X5,X4,tc_set(X2)) ),
inference(resolution,[],[f7,f5]) ).
fof(f760,plain,
( ~ spl0_22
| spl0_23
| spl0_36 ),
inference(avatar_contradiction_clause,[],[f759]) ).
fof(f759,plain,
( $false
| ~ spl0_22
| spl0_23
| spl0_36 ),
inference(subsumption_resolution,[],[f757,f408]) ).
fof(f408,plain,
( ~ c_lessequals(v_y,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a))
| spl0_23 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f406,plain,
( spl0_23
<=> c_lessequals(v_y,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f757,plain,
( c_lessequals(v_y,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a))
| ~ spl0_22
| spl0_36 ),
inference(resolution,[],[f754,f552]) ).
fof(f552,plain,
( ! [X0] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_lessequals(v_y,X0,tc_set(t_a)) )
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f510]) ).
fof(f510,plain,
( ! [X0] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_lessequals(v_y,X0,tc_set(t_a))
| c_lessequals(v_y,X0,tc_set(t_a)) )
| ~ spl0_22 ),
inference(resolution,[],[f421,f4]) ).
fof(f421,plain,
( ! [X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,X1,t_a),X0,t_a)
| c_lessequals(v_y,X1,tc_set(t_a)) )
| ~ spl0_22 ),
inference(resolution,[],[f397,f3]) ).
fof(f397,plain,
( ! [X0,X1] :
( ~ c_in(X1,v_y,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(X1,X0,t_a) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f396,plain,
( spl0_22
<=> ! [X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,v_y,t_a)
| c_in(X1,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f756,plain,
( spl0_35
| spl0_36
| ~ spl0_21
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f534,f396,f392,f753,f750]) ).
fof(f750,plain,
( spl0_35
<=> ! [X0] :
( c_lessequals(v_y,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,X0,t_a),v_x(v_y),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f392,plain,
( spl0_21
<=> c_in(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_c,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f534,plain,
( ! [X0] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a),v_c,tc_set(t_a))
| c_lessequals(v_y,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,X0,t_a),v_x(v_y),t_a) )
| ~ spl0_21
| ~ spl0_22 ),
inference(resolution,[],[f421,f437]) ).
fof(f437,plain,
( ! [X0] :
( ~ c_in(X0,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a)
| c_in(X0,v_x(v_y),t_a) )
| ~ spl0_21 ),
inference(resolution,[],[f436,f2]) ).
fof(f436,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_y),tc_set(t_a))
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f422]) ).
fof(f422,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_y),tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_y),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f404,f32]) ).
fof(f404,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),X0,t_a),v_y,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),X0,tc_set(t_a)) )
| ~ spl0_21 ),
inference(resolution,[],[f401,f3]) ).
fof(f401,plain,
( ! [X0] :
( ~ c_in(X0,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),t_a)
| c_in(X0,v_y,t_a) )
| ~ spl0_21 ),
inference(resolution,[],[f399,f2]) ).
fof(f399,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_y,tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f394,f12]) ).
fof(f394,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f748,plain,
( ~ spl0_33
| spl0_34
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f447,f392,f745,f741]) ).
fof(f741,plain,
( spl0_33
<=> c_lessequals(v_x(v_x(v_x(v_x(v_x(v_y))))),c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f745,plain,
( spl0_34
<=> v_x(v_x(v_x(v_x(v_x(v_y))))) = c_Zorn_Ochain__extend__1(v_c,v_y,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f447,plain,
( v_x(v_x(v_x(v_x(v_x(v_y))))) = c_Zorn_Ochain__extend__1(v_c,v_y,t_a)
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_x(v_y))))),c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f432,f1]) ).
fof(f432,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a))
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f426]) ).
fof(f426,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f404,f185]) ).
fof(f185,plain,
! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_x(v_y))))),t_a),v_y,t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a)) ),
inference(subsumption_resolution,[],[f173,f11]) ).
fof(f173,plain,
! [X0] :
( c_lessequals(X0,v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a))
| ~ c_in(v_y,v_S,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_x(v_y))))),t_a),v_y,t_a) ),
inference(resolution,[],[f132,f29]) ).
fof(f132,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_x(X1))))),t_a),v_x(X1),t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(v_x(X1))))),tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(subsumption_resolution,[],[f124,f13]) ).
fof(f124,plain,
! [X0,X1] :
( c_lessequals(X0,v_x(v_x(v_x(v_x(v_x(X1))))),tc_set(t_a))
| ~ c_in(v_x(X1),v_S,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_x(X1))))),t_a),v_x(X1),t_a)
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(resolution,[],[f77,f30]) ).
fof(f77,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(X1)))),t_a),v_x(X1),t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(X1)))),tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(subsumption_resolution,[],[f71,f13]) ).
fof(f71,plain,
! [X0,X1] :
( c_lessequals(X0,v_x(v_x(v_x(v_x(X1)))),tc_set(t_a))
| ~ c_in(v_x(X1),v_S,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(X1)))),t_a),v_x(X1),t_a)
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(resolution,[],[f48,f30]) ).
fof(f48,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X1,v_x(v_x(v_x(X0))),t_a),v_x(X0),t_a)
| c_lessequals(X1,v_x(v_x(v_x(X0))),tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(subsumption_resolution,[],[f44,f13]) ).
fof(f44,plain,
! [X0,X1] :
( ~ c_in(v_x(X0),v_S,tc_set(t_a))
| c_lessequals(X1,v_x(v_x(v_x(X0))),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,v_x(v_x(v_x(X0))),t_a),v_x(X0),t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(resolution,[],[f38,f30]) ).
fof(f661,plain,
( ~ spl0_31
| spl0_32
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f444,f392,f658,f654]) ).
fof(f654,plain,
( spl0_31
<=> c_lessequals(v_x(v_x(v_x(v_x(v_y)))),c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f658,plain,
( spl0_32
<=> v_x(v_x(v_x(v_x(v_y)))) = c_Zorn_Ochain__extend__1(v_c,v_y,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f444,plain,
( v_x(v_x(v_x(v_x(v_y)))) = c_Zorn_Ochain__extend__1(v_c,v_y,t_a)
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_y)))),c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f433,f1]) ).
fof(f433,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a))
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f425]) ).
fof(f425,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f404,f131]) ).
fof(f131,plain,
! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_y)))),t_a),v_y,t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)) ),
inference(subsumption_resolution,[],[f123,f11]) ).
fof(f123,plain,
! [X0] :
( c_lessequals(X0,v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a))
| ~ c_in(v_y,v_S,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) ),
inference(resolution,[],[f77,f29]) ).
fof(f628,plain,
( ~ spl0_29
| spl0_30
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f442,f392,f625,f621]) ).
fof(f621,plain,
( spl0_29
<=> c_lessequals(v_x(v_x(v_x(v_y))),c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f625,plain,
( spl0_30
<=> v_x(v_x(v_x(v_y))) = c_Zorn_Ochain__extend__1(v_c,v_y,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f442,plain,
( v_x(v_x(v_x(v_y))) = c_Zorn_Ochain__extend__1(v_c,v_y,t_a)
| ~ c_lessequals(v_x(v_x(v_x(v_y))),c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f434,f1]) ).
fof(f434,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_x(v_y))),tc_set(t_a))
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f424]) ).
fof(f424,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_x(v_y))),tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_x(v_y))),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f404,f76]) ).
fof(f76,plain,
! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_y))),t_a),v_y,t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_y))),tc_set(t_a)) ),
inference(subsumption_resolution,[],[f70,f11]) ).
fof(f70,plain,
! [X0] :
( c_lessequals(X0,v_x(v_x(v_x(v_y))),tc_set(t_a))
| ~ c_in(v_y,v_S,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_y))),t_a),v_y,t_a) ),
inference(resolution,[],[f48,f29]) ).
fof(f488,plain,
( ~ spl0_27
| spl0_28
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f440,f392,f485,f481]) ).
fof(f481,plain,
( spl0_27
<=> c_lessequals(v_x(v_x(v_y)),c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f485,plain,
( spl0_28
<=> v_x(v_x(v_y)) = c_Zorn_Ochain__extend__1(v_c,v_y,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f440,plain,
( v_x(v_x(v_y)) = c_Zorn_Ochain__extend__1(v_c,v_y,t_a)
| ~ c_lessequals(v_x(v_x(v_y)),c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f435,f1]) ).
fof(f435,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_y)),tc_set(t_a))
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f423]) ).
fof(f423,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_y)),tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_x(v_x(v_y)),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f404,f47]) ).
fof(f469,plain,
( ~ spl0_25
| spl0_26
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f438,f392,f466,f462]) ).
fof(f462,plain,
( spl0_25
<=> c_lessequals(v_x(v_y),c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f466,plain,
( spl0_26
<=> v_x(v_y) = c_Zorn_Ochain__extend__1(v_c,v_y,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f438,plain,
( v_x(v_y) = c_Zorn_Ochain__extend__1(v_c,v_y,t_a)
| ~ c_lessequals(v_x(v_y),c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f436,f1]) ).
fof(f419,plain,
( spl0_22
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f418,f392,f396]) ).
fof(f418,plain,
( ! [X0,X1] :
( c_in(X0,X1,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X0,v_y,t_a) )
| ~ spl0_21 ),
inference(subsumption_resolution,[],[f415,f9]) ).
fof(f415,plain,
( ! [X0,X1] :
( c_in(X0,X1,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X0,v_y,t_a) )
| ~ spl0_21 ),
inference(resolution,[],[f403,f7]) ).
fof(f403,plain,
( c_in(c_union(c_insert(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)))
| ~ spl0_21 ),
inference(subsumption_resolution,[],[f400,f11]) ).
fof(f400,plain,
( ~ c_in(v_y,v_S,tc_set(t_a))
| c_in(c_union(c_insert(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)))
| ~ spl0_21 ),
inference(resolution,[],[f399,f81]) ).
fof(f413,plain,
( ~ spl0_23
| spl0_24
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f402,f392,f410,f406]) ).
fof(f402,plain,
( v_y = c_Zorn_Ochain__extend__1(v_c,v_y,t_a)
| ~ c_lessequals(v_y,c_Zorn_Ochain__extend__1(v_c,v_y,t_a),tc_set(t_a))
| ~ spl0_21 ),
inference(resolution,[],[f399,f1]) ).
fof(f398,plain,
( spl0_21
| spl0_22 ),
inference(avatar_split_clause,[],[f387,f396,f392]) ).
fof(f387,plain,
! [X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,v_y,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| c_in(X1,X0,t_a) ),
inference(resolution,[],[f301,f11]) ).
fof(f385,plain,
( ~ spl0_19
| spl0_20
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f371,f233,f382,f378]) ).
fof(f378,plain,
( spl0_19
<=> c_lessequals(v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),v_y,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f382,plain,
( spl0_20
<=> v_y = v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f371,plain,
( v_y = v_x(v_x(v_x(v_x(v_x(v_x(v_y))))))
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),v_y,tc_set(t_a))
| ~ spl0_9 ),
inference(resolution,[],[f368,f1]) ).
fof(f368,plain,
( c_lessequals(v_y,v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a))
| ~ spl0_9 ),
inference(duplicate_literal_removal,[],[f367]) ).
fof(f367,plain,
( c_lessequals(v_y,v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a))
| c_lessequals(v_y,v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a))
| ~ spl0_9 ),
inference(resolution,[],[f346,f3]) ).
fof(f346,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),t_a),v_y,t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a)) )
| ~ spl0_9 ),
inference(resolution,[],[f253,f29]) ).
fof(f253,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),t_a),v_x(v_y),t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a)) )
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f248,f234]) ).
fof(f248,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),t_a),v_x(v_y),t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a))
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) )
| ~ spl0_9 ),
inference(resolution,[],[f243,f132]) ).
fof(f243,plain,
( ! [X0] :
( c_in(X0,v_x(v_x(v_y)),t_a)
| ~ c_in(X0,v_x(v_y),t_a) )
| ~ spl0_9 ),
inference(resolution,[],[f234,f26]) ).
fof(f365,plain,
( ~ spl0_17
| spl0_18
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f351,f233,f362,f358]) ).
fof(f358,plain,
( spl0_17
<=> c_lessequals(v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),v_x(v_y),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f362,plain,
( spl0_18
<=> v_x(v_y) = v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f351,plain,
( v_x(v_y) = v_x(v_x(v_x(v_x(v_x(v_x(v_y))))))
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),v_x(v_y),tc_set(t_a))
| ~ spl0_9 ),
inference(resolution,[],[f348,f1]) ).
fof(f348,plain,
( c_lessequals(v_x(v_y),v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a))
| ~ spl0_9 ),
inference(duplicate_literal_removal,[],[f347]) ).
fof(f347,plain,
( c_lessequals(v_x(v_y),v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a))
| c_lessequals(v_x(v_y),v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a))
| ~ spl0_9 ),
inference(resolution,[],[f253,f3]) ).
fof(f339,plain,
( ~ spl0_15
| spl0_16
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f324,f233,f336,f332]) ).
fof(f332,plain,
( spl0_15
<=> c_lessequals(v_x(v_x(v_x(v_x(v_x(v_y))))),v_x(v_y),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f336,plain,
( spl0_16
<=> v_x(v_y) = v_x(v_x(v_x(v_x(v_x(v_y))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f324,plain,
( v_x(v_y) = v_x(v_x(v_x(v_x(v_x(v_y)))))
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_x(v_y))))),v_x(v_y),tc_set(t_a))
| ~ spl0_9 ),
inference(resolution,[],[f321,f1]) ).
fof(f321,plain,
( c_lessequals(v_x(v_y),v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a))
| ~ spl0_9 ),
inference(duplicate_literal_removal,[],[f320]) ).
fof(f320,plain,
( c_lessequals(v_x(v_y),v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a))
| c_lessequals(v_x(v_y),v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a))
| ~ spl0_9 ),
inference(resolution,[],[f252,f3]) ).
fof(f252,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_x(v_y))))),t_a),v_x(v_y),t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a)) )
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f247,f234]) ).
fof(f247,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_x(v_y))))),t_a),v_x(v_y),t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a))
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) )
| ~ spl0_9 ),
inference(resolution,[],[f243,f77]) ).
fof(f317,plain,
( ~ spl0_13
| spl0_14
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f297,f233,f314,f310]) ).
fof(f310,plain,
( spl0_13
<=> c_lessequals(v_x(v_x(v_x(v_x(v_y)))),v_x(v_y),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f314,plain,
( spl0_14
<=> v_x(v_y) = v_x(v_x(v_x(v_x(v_y)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f297,plain,
( v_x(v_y) = v_x(v_x(v_x(v_x(v_y))))
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_y)))),v_x(v_y),tc_set(t_a))
| ~ spl0_9 ),
inference(resolution,[],[f294,f1]) ).
fof(f294,plain,
( c_lessequals(v_x(v_y),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a))
| ~ spl0_9 ),
inference(duplicate_literal_removal,[],[f293]) ).
fof(f293,plain,
( c_lessequals(v_x(v_y),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a))
| c_lessequals(v_x(v_y),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a))
| ~ spl0_9 ),
inference(resolution,[],[f251,f3]) ).
fof(f251,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_y)))),t_a),v_x(v_y),t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)) )
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f246,f234]) ).
fof(f246,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_x(v_y)))),t_a),v_x(v_y),t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a))
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) )
| ~ spl0_9 ),
inference(resolution,[],[f243,f48]) ).
fof(f288,plain,
( ~ spl0_11
| spl0_12
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f271,f233,f285,f281]) ).
fof(f281,plain,
( spl0_11
<=> c_lessequals(v_x(v_x(v_x(v_y))),v_x(v_y),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f285,plain,
( spl0_12
<=> v_x(v_y) = v_x(v_x(v_x(v_y))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f271,plain,
( v_x(v_y) = v_x(v_x(v_x(v_y)))
| ~ c_lessequals(v_x(v_x(v_x(v_y))),v_x(v_y),tc_set(t_a))
| ~ spl0_9 ),
inference(resolution,[],[f268,f1]) ).
fof(f268,plain,
( c_lessequals(v_x(v_y),v_x(v_x(v_x(v_y))),tc_set(t_a))
| ~ spl0_9 ),
inference(duplicate_literal_removal,[],[f267]) ).
fof(f267,plain,
( c_lessequals(v_x(v_y),v_x(v_x(v_x(v_y))),tc_set(t_a))
| c_lessequals(v_x(v_y),v_x(v_x(v_x(v_y))),tc_set(t_a))
| ~ spl0_9 ),
inference(resolution,[],[f250,f3]) ).
fof(f250,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_y))),t_a),v_x(v_y),t_a)
| c_lessequals(X0,v_x(v_x(v_x(v_y))),tc_set(t_a)) )
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f245,f234]) ).
fof(f245,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_x(v_y))),t_a),v_x(v_y),t_a)
| ~ c_in(v_x(v_y),v_S,tc_set(t_a))
| c_lessequals(X0,v_x(v_x(v_x(v_y))),tc_set(t_a)) )
| ~ spl0_9 ),
inference(resolution,[],[f243,f38]) ).
fof(f242,plain,
spl0_9,
inference(avatar_contradiction_clause,[],[f241]) ).
fof(f241,plain,
( $false
| spl0_9 ),
inference(subsumption_resolution,[],[f240,f11]) ).
fof(f240,plain,
( ~ c_in(v_y,v_S,tc_set(t_a))
| spl0_9 ),
inference(resolution,[],[f235,f13]) ).
fof(f235,plain,
( ~ c_in(v_x(v_y),v_S,tc_set(t_a))
| spl0_9 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f239,plain,
( ~ spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f228,f237,f233]) ).
fof(f237,plain,
( spl0_10
<=> ! [X0] :
( c_lessequals(v_c,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f228,plain,
! [X0] :
( c_lessequals(v_c,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a))
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f225,plain,
! [X0] :
( c_lessequals(v_c,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a))
| c_lessequals(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a))
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) ),
inference(resolution,[],[f121,f132]) ).
fof(f121,plain,
! [X0,X1] :
( c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),X1,t_a),v_x(v_x(v_y)),t_a)
| c_lessequals(v_c,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),X1,tc_set(t_a)) ),
inference(resolution,[],[f116,f3]) ).
fof(f116,plain,
! [X0,X1] :
( ~ c_in(X1,c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),t_a)
| c_in(X1,v_x(v_x(v_y)),t_a)
| c_lessequals(v_c,X0,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f111,f2]) ).
fof(f111,plain,
! [X0] :
( c_lessequals(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),v_x(v_x(v_y)),tc_set(t_a))
| c_lessequals(v_c,X0,tc_set(tc_set(t_a))) ),
inference(duplicate_literal_removal,[],[f106]) ).
fof(f106,plain,
! [X0] :
( c_lessequals(v_c,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),v_x(v_x(v_y)),tc_set(t_a))
| c_lessequals(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),v_x(v_x(v_y)),tc_set(t_a)) ),
inference(resolution,[],[f39,f47]) ).
fof(f39,plain,
! [X0,X1] :
( c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),X1,t_a),v_y,t_a)
| c_lessequals(v_c,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),X1,tc_set(t_a)) ),
inference(resolution,[],[f27,f3]) ).
fof(f27,plain,
! [X0,X1] :
( ~ c_in(X0,c_Main_OsubsetI__1(v_c,X1,tc_set(t_a)),t_a)
| c_in(X0,v_y,t_a)
| c_lessequals(v_c,X1,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f2,f19]) ).
fof(f19,plain,
! [X0] :
( c_lessequals(c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),v_y,tc_set(t_a))
| c_lessequals(v_c,X0,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f3,f12]) ).
fof(f217,plain,
( ~ spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f203,f214,f210]) ).
fof(f210,plain,
( spl0_7
<=> c_lessequals(v_x(v_x(v_x(v_x(v_x(v_y))))),v_y,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f214,plain,
( spl0_8
<=> v_y = v_x(v_x(v_x(v_x(v_x(v_y))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f203,plain,
( v_y = v_x(v_x(v_x(v_x(v_x(v_y)))))
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_x(v_y))))),v_y,tc_set(t_a)) ),
inference(resolution,[],[f200,f1]) ).
fof(f200,plain,
c_lessequals(v_y,v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a)),
inference(duplicate_literal_removal,[],[f199]) ).
fof(f199,plain,
( c_lessequals(v_y,v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a))
| c_lessequals(v_y,v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a)) ),
inference(resolution,[],[f185,f3]) ).
fof(f160,plain,
( ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f147,f157,f153]) ).
fof(f153,plain,
( spl0_5
<=> c_lessequals(v_x(v_x(v_x(v_x(v_y)))),v_y,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f157,plain,
( spl0_6
<=> v_y = v_x(v_x(v_x(v_x(v_y)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f147,plain,
( v_y = v_x(v_x(v_x(v_x(v_y))))
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_y)))),v_y,tc_set(t_a)) ),
inference(resolution,[],[f143,f1]) ).
fof(f143,plain,
c_lessequals(v_y,v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)),
inference(duplicate_literal_removal,[],[f142]) ).
fof(f142,plain,
( c_lessequals(v_y,v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a))
| c_lessequals(v_y,v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)) ),
inference(resolution,[],[f131,f3]) ).
fof(f104,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f92,f101,f97]) ).
fof(f97,plain,
( spl0_3
<=> c_lessequals(v_x(v_x(v_x(v_y))),v_y,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f101,plain,
( spl0_4
<=> v_y = v_x(v_x(v_x(v_y))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f92,plain,
( v_y = v_x(v_x(v_x(v_y)))
| ~ c_lessequals(v_x(v_x(v_x(v_y))),v_y,tc_set(t_a)) ),
inference(resolution,[],[f90,f1]) ).
fof(f90,plain,
c_lessequals(v_y,v_x(v_x(v_x(v_y))),tc_set(t_a)),
inference(duplicate_literal_removal,[],[f89]) ).
fof(f89,plain,
( c_lessequals(v_y,v_x(v_x(v_x(v_y))),tc_set(t_a))
| c_lessequals(v_y,v_x(v_x(v_x(v_y))),tc_set(t_a)) ),
inference(resolution,[],[f76,f3]) ).
fof(f66,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f55,f63,f59]) ).
fof(f59,plain,
( spl0_1
<=> c_lessequals(v_x(v_x(v_y)),v_y,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f63,plain,
( spl0_2
<=> v_y = v_x(v_x(v_y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f55,plain,
( v_y = v_x(v_x(v_y))
| ~ c_lessequals(v_x(v_x(v_y)),v_y,tc_set(t_a)) ),
inference(resolution,[],[f53,f1]) ).
fof(f53,plain,
c_lessequals(v_y,v_x(v_x(v_y)),tc_set(t_a)),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f52,plain,
( c_lessequals(v_y,v_x(v_x(v_y)),tc_set(t_a))
| c_lessequals(v_y,v_x(v_x(v_y)),tc_set(t_a)) ),
inference(resolution,[],[f47,f3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SET862-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n019.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Tue Apr 30 01:09:00 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (24268)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (24271)WARNING: value z3 for option sas not known
% 0.15/0.39 % (24269)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (24272)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (24270)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (24274)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39 % (24273)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39 % (24271)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.39 % (24275)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.41 TRYING [1]
% 0.15/0.41 TRYING [3]
% 0.15/0.41 TRYING [2]
% 0.22/0.44 TRYING [3]
% 0.22/0.44 % (24271)First to succeed.
% 0.22/0.45 TRYING [4]
% 0.22/0.45 % (24271)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45 % (24271)------------------------------
% 0.22/0.45 % (24271)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.45 % (24271)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (24271)Memory used [KB]: 1368
% 0.22/0.45 % (24271)Time elapsed: 0.058 s
% 0.22/0.45 % (24271)Instructions burned: 89 (million)
% 0.22/0.45 % (24271)------------------------------
% 0.22/0.45 % (24271)------------------------------
% 0.22/0.45 % (24268)Success in time 0.075 s
%------------------------------------------------------------------------------