%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN067-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 01:49:12 PM UTC 2026
% Result : Unsatisfiable 2.75s 1.11s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 59
% Syntax : Number of formulae : 264 ( 12 unt; 28 def)
% Number of atoms : 1048 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1380 ( 596 ~; 756 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 29 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-1 aty)
% Number of variables : 225 ( 0 sgn 225 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_p(f2(X0))
| ~ big_p(a)
| big_p(X1)
| big_p(f4(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f2,negated_conjecture,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_p(f2(X0))
| ~ big_p(a)
| big_p(X1)
| big_r(X1,f3(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f3,negated_conjecture,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_p(f2(X0))
| ~ big_p(a)
| big_p(X1)
| big_r(f3(X1),f4(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f4,negated_conjecture,
! [X2,X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_p(f2(X0))
| ~ big_p(a)
| ~ big_p(X1)
| ~ big_r(X2,X1)
| big_p(f6(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f7,negated_conjecture,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(X0,f1(X0))
| ~ big_p(a)
| big_p(X1)
| big_p(f4(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
fof(f8,negated_conjecture,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(X0,f1(X0))
| ~ big_p(a)
| big_p(X1)
| big_r(X1,f3(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
fof(f9,negated_conjecture,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(X0,f1(X0))
| ~ big_p(a)
| big_p(X1)
| big_r(f3(X1),f4(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
fof(f10,negated_conjecture,
! [X2,X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(X0,f1(X0))
| ~ big_p(a)
| ~ big_p(X1)
| ~ big_r(X2,X1)
| big_p(f6(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
fof(f13,negated_conjecture,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(f1(X0),f2(X0))
| ~ big_p(a)
| big_p(X1)
| big_p(f4(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
fof(f14,negated_conjecture,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(f1(X0),f2(X0))
| ~ big_p(a)
| big_p(X1)
| big_r(X1,f3(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
fof(f15,negated_conjecture,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(f1(X0),f2(X0))
| ~ big_p(a)
| big_p(X1)
| big_r(f3(X1),f4(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
fof(f16,negated_conjecture,
! [X2,X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(f1(X0),f2(X0))
| ~ big_p(a)
| ~ big_p(X1)
| ~ big_r(X2,X1)
| big_p(f6(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
fof(f22,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_p(f2(X1))
| ~ big_p(a)
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_p(f6(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
fof(f23,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_p(f2(X1))
| ~ big_p(a)
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(X3,f5(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
fof(f24,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_p(f2(X1))
| ~ big_p(a)
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(f5(X3),f6(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
fof(f28,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(X1,f1(X1))
| ~ big_p(a)
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_p(f6(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
fof(f29,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(X1,f1(X1))
| ~ big_p(a)
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(X3,f5(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).
fof(f30,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(X1,f1(X1))
| ~ big_p(a)
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(f5(X3),f6(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_30) ).
fof(f34,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(f1(X1),f2(X1))
| ~ big_p(a)
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_p(f6(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_34) ).
fof(f35,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(f1(X1),f2(X1))
| ~ big_p(a)
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(X3,f5(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_35) ).
fof(f36,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(f1(X1),f2(X1))
| ~ big_p(a)
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(f5(X3),f6(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_36) ).
fof(f37,negated_conjecture,
( big_p(a)
| big_p(a)
| big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_37) ).
fof(f54,negated_conjecture,
( ~ big_p(c2)
| big_p(c1)
| ~ big_p(c4)
| big_p(c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_54) ).
fof(f55,negated_conjecture,
( ~ big_p(c2)
| big_p(c1)
| ~ big_p(c4)
| big_r(c4,c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_55) ).
fof(f60,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(c2)
| big_p(c1)
| ~ big_p(X0)
| ~ big_r(c4,X1)
| ~ big_r(X1,X0)
| ~ big_p(X2)
| ~ big_r(c4,X3)
| ~ big_r(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_60) ).
fof(f66,negated_conjecture,
( ~ big_p(c2)
| big_r(c2,c1)
| ~ big_p(c4)
| big_p(c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_66) ).
fof(f67,negated_conjecture,
( ~ big_p(c2)
| big_r(c2,c1)
| ~ big_p(c4)
| big_r(c4,c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_67) ).
fof(f72,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(c2)
| big_r(c2,c1)
| ~ big_p(X0)
| ~ big_r(c4,X1)
| ~ big_r(X1,X0)
| ~ big_p(X2)
| ~ big_r(c4,X3)
| ~ big_r(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_72) ).
fof(f78,negated_conjecture,
! [X0,X1] :
( ~ big_p(X0)
| ~ big_r(c2,X1)
| ~ big_r(X1,X0)
| ~ big_p(c4)
| big_p(c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_78) ).
fof(f79,negated_conjecture,
! [X0,X1] :
( ~ big_p(X0)
| ~ big_r(c2,X1)
| ~ big_r(X1,X0)
| ~ big_p(c4)
| big_r(c4,c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_79) ).
fof(f84,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ big_p(X0)
| ~ big_r(c2,X1)
| ~ big_r(X1,X0)
| ~ big_p(X2)
| ~ big_r(c4,X3)
| ~ big_r(X3,X2)
| ~ big_p(X4)
| ~ big_r(c4,X5)
| ~ big_r(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_84) ).
fof(f93,plain,
big_p(a),
inference(duplicate_literal_removal,[],[f37]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(f1(X1),f2(X1))
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(f5(X3),f6(X3)) ),
inference(duplicate_literal_removal,[],[f36]) ).
fof(f95,plain,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(f1(X1),f2(X1))
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(X3,f5(X3)) ),
inference(duplicate_literal_removal,[],[f35]) ).
fof(f96,plain,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(f1(X1),f2(X1))
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_p(f6(X3)) ),
inference(duplicate_literal_removal,[],[f34]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(X1,f1(X1))
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(f5(X3),f6(X3)) ),
inference(duplicate_literal_removal,[],[f30]) ).
fof(f101,plain,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(X1,f1(X1))
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(X3,f5(X3)) ),
inference(duplicate_literal_removal,[],[f29]) ).
fof(f102,plain,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_r(X1,f1(X1))
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_p(f6(X3)) ),
inference(duplicate_literal_removal,[],[f28]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_p(f2(X1))
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(f5(X3),f6(X3)) ),
inference(duplicate_literal_removal,[],[f24]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_p(f2(X1))
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_r(X3,f5(X3)) ),
inference(duplicate_literal_removal,[],[f23]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( ~ big_p(a)
| ~ big_p(X0)
| ~ big_r(X1,X0)
| big_p(f2(X1))
| ~ big_p(X2)
| ~ big_r(X3,X2)
| big_p(f6(X3)) ),
inference(duplicate_literal_removal,[],[f22]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(f1(X0),f2(X0))
| ~ big_p(X1)
| ~ big_r(X2,X1)
| big_p(f6(X2)) ),
inference(duplicate_literal_removal,[],[f16]) ).
fof(f115,plain,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(f1(X0),f2(X0))
| big_p(X1)
| big_r(f3(X1),f4(X1)) ),
inference(duplicate_literal_removal,[],[f15]) ).
fof(f116,plain,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(f1(X0),f2(X0))
| big_p(X1)
| big_r(X1,f3(X1)) ),
inference(duplicate_literal_removal,[],[f14]) ).
fof(f117,plain,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(f1(X0),f2(X0))
| big_p(X1)
| big_p(f4(X1)) ),
inference(duplicate_literal_removal,[],[f13]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(X0,f1(X0))
| ~ big_p(X1)
| ~ big_r(X2,X1)
| big_p(f6(X2)) ),
inference(duplicate_literal_removal,[],[f10]) ).
fof(f121,plain,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(X0,f1(X0))
| big_p(X1)
| big_r(f3(X1),f4(X1)) ),
inference(duplicate_literal_removal,[],[f9]) ).
fof(f122,plain,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(X0,f1(X0))
| big_p(X1)
| big_r(X1,f3(X1)) ),
inference(duplicate_literal_removal,[],[f8]) ).
fof(f123,plain,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_r(X0,f1(X0))
| big_p(X1)
| big_p(f4(X1)) ),
inference(duplicate_literal_removal,[],[f7]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_p(f2(X0))
| ~ big_p(X1)
| ~ big_r(X2,X1)
| big_p(f6(X2)) ),
inference(duplicate_literal_removal,[],[f4]) ).
fof(f127,plain,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_p(f2(X0))
| big_p(X1)
| big_r(f3(X1),f4(X1)) ),
inference(duplicate_literal_removal,[],[f3]) ).
fof(f128,plain,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_p(f2(X0))
| big_p(X1)
| big_r(X1,f3(X1)) ),
inference(duplicate_literal_removal,[],[f2]) ).
fof(f129,plain,
! [X0,X1] :
( ~ big_p(a)
| big_p(X0)
| big_p(f2(X0))
| big_p(X1)
| big_p(f4(X1)) ),
inference(duplicate_literal_removal,[],[f1]) ).
fof(f131,definition,
( spl0_1
<=> ! [X4,X5] :
( ~ big_p(X4)
| ~ big_r(c4,X5)
| ~ big_r(X5,X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f132,plain,
( ! [X4,X5] :
( ~ big_r(c4,X5)
| ~ big_p(X4)
| ~ big_r(X5,X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,definition,
( spl0_2
<=> ! [X0,X1] :
( ~ big_p(X0)
| ~ big_r(c2,X1)
| ~ big_r(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f135,plain,
( ! [X0,X1] :
( ~ big_r(c2,X1)
| ~ big_p(X0)
| ~ big_r(X1,X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f136,plain,
( spl0_1
| spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f84,f134,f131,f131]) ).
fof(f138,definition,
( spl0_3
<=> big_r(c4,c3) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f140,plain,
( big_r(c4,c3)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f143,definition,
( spl0_4
<=> big_p(c3) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f148,definition,
( spl0_5
<=> big_p(a) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f153,definition,
( spl0_6
<=> big_p(c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f155,plain,
( ~ big_p(c4)
| spl0_6 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f157,plain,
( spl0_3
| ~ spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f79,f134,f153,f138]) ).
fof(f158,plain,
( spl0_4
| ~ spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f78,f134,f153,f143]) ).
fof(f165,definition,
( spl0_7
<=> big_r(c2,c1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f167,plain,
( big_r(c2,c1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f169,definition,
( spl0_8
<=> big_p(c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f171,plain,
( ~ big_p(c2)
| spl0_8 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( spl0_1
| spl0_1
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f72,f169,f165,f131,f131]) ).
fof(f177,plain,
( spl0_3
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f67,f169,f165,f153,f138]) ).
fof(f178,plain,
( spl0_4
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f66,f169,f165,f153,f143]) ).
fof(f185,definition,
( spl0_9
<=> big_p(c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f188,plain,
( spl0_1
| spl0_1
| spl0_9
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f60,f169,f185,f131,f131]) ).
fof(f193,plain,
( spl0_3
| ~ spl0_6
| spl0_9
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f55,f169,f185,f153,f138]) ).
fof(f194,plain,
( spl0_4
| ~ spl0_6
| spl0_9
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f54,f169,f185,f153,f143]) ).
fof(f211,plain,
spl0_5,
inference(avatar_split_clause,[],[f93,f148]) ).
fof(f213,definition,
( spl0_10
<=> ! [X2,X3] :
( ~ big_p(X2)
| big_r(f5(X3),f6(X3))
| ~ big_r(X3,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f214,plain,
( ! [X2,X3] :
( big_r(f5(X3),f6(X3))
| ~ big_p(X2)
| ~ big_r(X3,X2) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f216,definition,
( spl0_11
<=> ! [X0,X1] :
( ~ big_p(X0)
| big_r(f1(X1),f2(X1))
| ~ big_r(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f217,plain,
( ! [X0,X1] :
( big_r(f1(X1),f2(X1))
| ~ big_p(X0)
| ~ big_r(X1,X0) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f218,plain,
( spl0_10
| spl0_11
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f94,f148,f216,f213]) ).
fof(f220,definition,
( spl0_12
<=> ! [X2,X3] :
( ~ big_p(X2)
| big_r(X3,f5(X3))
| ~ big_r(X3,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f221,plain,
( ! [X2,X3] :
( big_r(X3,f5(X3))
| ~ big_p(X2)
| ~ big_r(X3,X2) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f222,plain,
( spl0_12
| spl0_11
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f95,f148,f216,f220]) ).
fof(f224,definition,
( spl0_13
<=> ! [X2,X3] :
( ~ big_p(X2)
| big_p(f6(X3))
| ~ big_r(X3,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f225,plain,
( ! [X2,X3] :
( big_p(f6(X3))
| ~ big_p(X2)
| ~ big_r(X3,X2) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f226,plain,
( spl0_13
| spl0_11
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f96,f148,f216,f224]) ).
fof(f228,definition,
( spl0_14
<=> ! [X2] :
( big_p(X2)
| big_r(f3(X2),f4(X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f229,plain,
( ! [X2] :
( big_r(f3(X2),f4(X2))
| big_p(X2) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,definition,
( spl0_15
<=> ! [X2] :
( big_p(X2)
| big_r(X2,f3(X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f233,plain,
( ! [X2] :
( big_r(X2,f3(X2))
| big_p(X2) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f236,definition,
( spl0_16
<=> ! [X2] :
( big_p(X2)
| big_p(f4(X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f237,plain,
( ! [X2] :
( big_p(f4(X2))
| big_p(X2) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f240,definition,
( spl0_17
<=> ! [X0,X1] :
( ~ big_p(X0)
| big_r(X1,f1(X1))
| ~ big_r(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f241,plain,
( ! [X0,X1] :
( big_r(X1,f1(X1))
| ~ big_p(X0)
| ~ big_r(X1,X0) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f242,plain,
( spl0_10
| spl0_17
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f100,f148,f240,f213]) ).
fof(f243,plain,
( spl0_12
| spl0_17
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f101,f148,f240,f220]) ).
fof(f244,plain,
( spl0_13
| spl0_17
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f102,f148,f240,f224]) ).
fof(f249,definition,
( spl0_18
<=> ! [X0,X1] :
( ~ big_p(X0)
| big_p(f2(X1))
| ~ big_r(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f250,plain,
( ! [X0,X1] :
( big_p(f2(X1))
| ~ big_p(X0)
| ~ big_r(X1,X0) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( spl0_10
| spl0_18
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f106,f148,f249,f213]) ).
fof(f252,plain,
( spl0_12
| spl0_18
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f107,f148,f249,f220]) ).
fof(f253,plain,
( spl0_13
| spl0_18
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f108,f148,f249,f224]) ).
fof(f258,definition,
( spl0_19
<=> ! [X0] :
( big_p(X0)
| big_r(f1(X0),f2(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f259,plain,
( ! [X0] :
( big_r(f1(X0),f2(X0))
| big_p(X0) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f262,plain,
( spl0_13
| spl0_19
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f114,f148,f258,f224]) ).
fof(f263,plain,
( spl0_14
| spl0_19
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f115,f148,f258,f228]) ).
fof(f264,plain,
( spl0_15
| spl0_19
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f116,f148,f258,f232]) ).
fof(f265,plain,
( spl0_16
| spl0_19
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f117,f148,f258,f236]) ).
fof(f267,definition,
( spl0_20
<=> ! [X0] :
( big_p(X0)
| big_r(X0,f1(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f268,plain,
( ! [X0] :
( big_r(X0,f1(X0))
| big_p(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f271,plain,
( spl0_13
| spl0_20
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f120,f148,f267,f224]) ).
fof(f272,plain,
( spl0_14
| spl0_20
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f121,f148,f267,f228]) ).
fof(f273,plain,
( spl0_15
| spl0_20
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f122,f148,f267,f232]) ).
fof(f274,plain,
( spl0_16
| spl0_20
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f123,f148,f267,f236]) ).
fof(f276,definition,
( spl0_21
<=> ! [X0] :
( big_p(X0)
| big_p(f2(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f277,plain,
( ! [X0] :
( big_p(f2(X0))
| big_p(X0) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f280,plain,
( spl0_13
| spl0_21
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f126,f148,f276,f224]) ).
fof(f281,plain,
( spl0_14
| spl0_21
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f127,f148,f276,f228]) ).
fof(f282,plain,
( spl0_15
| spl0_21
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f128,f148,f276,f232]) ).
fof(f283,plain,
( spl0_16
| spl0_21
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f129,f148,f276,f236]) ).
fof(f284,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(f3(c2),X0)
| big_p(c2) )
| ~ spl0_2
| ~ spl0_15 ),
inference(resolution,[],[f135,f233]) ).
fof(f286,plain,
( ! [X0] :
( ~ big_r(f3(c2),X0)
| ~ big_p(X0) )
| ~ spl0_2
| spl0_8
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f284,f171]) ).
fof(f287,plain,
( ~ big_p(f4(c2))
| big_p(c2)
| ~ spl0_2
| spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(resolution,[],[f286,f229]) ).
fof(f298,plain,
( big_p(c2)
| ~ spl0_2
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f287,f237]) ).
fof(f299,plain,
( $false
| ~ spl0_2
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f298,f171]) ).
fof(f300,plain,
( ~ spl0_2
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f299]) ).
fof(f313,definition,
( spl0_26
<=> ! [X1] :
( ~ big_p(X1)
| ~ big_r(f5(c2),X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f314,plain,
( ! [X1] :
( ~ big_r(f5(c2),X1)
| ~ big_p(X1) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f316,definition,
( spl0_27
<=> ! [X0] :
( ~ big_p(X0)
| ~ big_r(c2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f317,plain,
( ! [X0] :
( ~ big_r(c2,X0)
| ~ big_p(X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f325,definition,
( spl0_28
<=> ! [X1] :
( ~ big_p(X1)
| ~ big_r(f1(c2),X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f326,plain,
( ! [X1] :
( ~ big_r(f1(c2),X1)
| ~ big_p(X1) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f328,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(f3(c4),X0)
| big_p(c4) )
| ~ spl0_1
| ~ spl0_15 ),
inference(resolution,[],[f132,f233]) ).
fof(f329,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(f1(c4),X0)
| big_p(c4) )
| ~ spl0_1
| ~ spl0_20 ),
inference(resolution,[],[f132,f268]) ).
fof(f331,plain,
( ! [X0] :
( ~ big_r(f1(c4),X0)
| ~ big_p(X0) )
| ~ spl0_1
| spl0_6
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f329,f155]) ).
fof(f332,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(f3(c4),X0) )
| ~ spl0_1
| spl0_6
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f328,f155]) ).
fof(f333,plain,
( ! [X0,X1] :
( ~ big_p(X0)
| ~ big_r(c4,X0)
| ~ big_p(X1)
| ~ big_r(f5(c4),X1) )
| ~ spl0_1
| ~ spl0_12 ),
inference(resolution,[],[f221,f132]) ).
fof(f335,definition,
( spl0_29
<=> ! [X1] :
( ~ big_p(X1)
| ~ big_r(f5(c4),X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f336,plain,
( ! [X1] :
( ~ big_r(f5(c4),X1)
| ~ big_p(X1) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f338,definition,
( spl0_30
<=> ! [X0] :
( ~ big_p(X0)
| ~ big_r(c4,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f339,plain,
( ! [X0] :
( ~ big_r(c4,X0)
| ~ big_p(X0) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f340,plain,
( spl0_29
| spl0_30
| ~ spl0_1
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f333,f220,f131,f338,f335]) ).
fof(f341,plain,
( ~ big_p(f2(c4))
| big_p(c4)
| ~ spl0_1
| spl0_6
| ~ spl0_19
| ~ spl0_20 ),
inference(resolution,[],[f331,f259]) ).
fof(f359,plain,
( big_p(c4)
| ~ spl0_1
| spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f341,f277]) ).
fof(f360,plain,
( $false
| ~ spl0_1
| spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f359,f155]) ).
fof(f361,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f360]) ).
fof(f368,definition,
( spl0_35
<=> ! [X0] :
( ~ big_p(X0)
| ~ big_r(f1(c4),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f369,plain,
( ! [X0] :
( ~ big_r(f1(c4),X0)
| ~ big_p(X0) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f372,definition,
( spl0_36
<=> ! [X0] :
( ~ big_p(X0)
| ~ big_r(f3(c4),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f373,plain,
( ! [X0] :
( ~ big_r(f3(c4),X0)
| ~ big_p(X0) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f379,plain,
( ! [X0] :
( ~ big_p(f6(c4))
| ~ big_p(X0)
| ~ big_r(c4,X0) )
| ~ spl0_10
| ~ spl0_29 ),
inference(resolution,[],[f336,f214]) ).
fof(f397,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(c4,X0) )
| ~ spl0_10
| ~ spl0_13
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f379,f225]) ).
fof(f398,plain,
( spl0_30
| ~ spl0_10
| ~ spl0_13
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f397,f335,f224,f213,f338]) ).
fof(f399,plain,
( ~ big_p(c3)
| ~ spl0_3
| ~ spl0_30 ),
inference(resolution,[],[f339,f140]) ).
fof(f406,plain,
( spl0_36
| ~ spl0_1
| spl0_6
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f332,f232,f153,f131,f372]) ).
fof(f425,plain,
( ~ spl0_4
| ~ spl0_3
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f399,f338,f138,f143]) ).
fof(f426,plain,
( ! [X0] :
( ~ big_p(f2(c4))
| ~ big_p(X0)
| ~ big_r(c4,X0) )
| ~ spl0_11
| ~ spl0_35 ),
inference(resolution,[],[f369,f217]) ).
fof(f432,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(c4,X0) )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f426,f250]) ).
fof(f435,plain,
( ~ big_p(f4(c4))
| big_p(c4)
| ~ spl0_14
| ~ spl0_36 ),
inference(resolution,[],[f373,f229]) ).
fof(f441,plain,
( big_p(c4)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f435,f237]) ).
fof(f442,plain,
( $false
| spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f441,f155]) ).
fof(f443,plain,
( spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f447,plain,
( ! [X0,X1] :
( ~ big_p(X0)
| ~ big_r(f5(c2),X0)
| ~ big_p(X1)
| ~ big_r(c2,X1) )
| ~ spl0_2
| ~ spl0_12 ),
inference(resolution,[],[f135,f221]) ).
fof(f448,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(f1(c2),X0)
| big_p(c2) )
| ~ spl0_2
| ~ spl0_20 ),
inference(resolution,[],[f135,f268]) ).
fof(f450,plain,
( spl0_27
| spl0_26
| ~ spl0_2
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f447,f220,f134,f313,f316]) ).
fof(f454,plain,
( ! [X0,X1] :
( ~ big_p(X0)
| ~ big_r(c4,X0)
| ~ big_p(X1)
| ~ big_r(f1(c4),X1) )
| ~ spl0_1
| ~ spl0_17 ),
inference(resolution,[],[f241,f132]) ).
fof(f455,plain,
( ! [X0,X1] :
( ~ big_p(X0)
| ~ big_r(c2,X0)
| ~ big_p(X1)
| ~ big_r(f1(c2),X1) )
| ~ spl0_2
| ~ spl0_17 ),
inference(resolution,[],[f241,f135]) ).
fof(f456,plain,
( spl0_28
| spl0_27
| ~ spl0_2
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f455,f240,f134,f316,f325]) ).
fof(f460,plain,
( ~ big_p(c1)
| ~ spl0_7
| ~ spl0_27 ),
inference(resolution,[],[f317,f167]) ).
fof(f467,plain,
( spl0_8
| spl0_28
| ~ spl0_2
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f448,f267,f134,f325,f169]) ).
fof(f473,plain,
( ~ big_p(f2(c2))
| big_p(c2)
| ~ spl0_19
| ~ spl0_28 ),
inference(resolution,[],[f326,f259]) ).
fof(f474,plain,
( ! [X0] :
( ~ big_p(f2(c2))
| ~ big_p(X0)
| ~ big_r(c2,X0) )
| ~ spl0_11
| ~ spl0_28 ),
inference(resolution,[],[f326,f217]) ).
fof(f479,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(c2,X0) )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f474,f250]) ).
fof(f480,plain,
( big_p(c2)
| ~ spl0_19
| ~ spl0_21
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f473,f277]) ).
fof(f489,plain,
( spl0_27
| ~ spl0_11
| ~ spl0_18
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f479,f325,f249,f216,f316]) ).
fof(f490,plain,
( spl0_8
| ~ spl0_19
| ~ spl0_21
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f480,f325,f276,f258,f169]) ).
fof(f491,plain,
( ~ spl0_9
| ~ spl0_7
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f460,f316,f165,f185]) ).
fof(f492,plain,
( spl0_30
| ~ spl0_11
| ~ spl0_18
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f432,f368,f249,f216,f338]) ).
fof(f493,plain,
( spl0_35
| spl0_30
| ~ spl0_1
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f454,f240,f131,f338,f368]) ).
fof(f514,plain,
( ! [X0] :
( ~ big_p(f6(c2))
| ~ big_p(X0)
| ~ big_r(c2,X0) )
| ~ spl0_10
| ~ spl0_26 ),
inference(resolution,[],[f314,f214]) ).
fof(f532,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(c2,X0) )
| ~ spl0_10
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f514,f225]) ).
fof(f533,plain,
( spl0_27
| ~ spl0_10
| ~ spl0_13
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f532,f313,f224,f213,f316]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f136]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl0_2
| spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f157]) ).
cnf(s8,plain,
( spl0_2
| spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f158]) ).
cnf(s14,plain,
( spl0_1
| spl0_1
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f172]) ).
cnf(s15,plain,
( spl0_1
| spl0_7
| ~ spl0_8 ),
inference(rat,[],[s14]) ).
cnf(s20,plain,
( spl0_3
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f177]) ).
cnf(s21,plain,
( spl0_4
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f178]) ).
cnf(s27,plain,
( spl0_1
| spl0_1
| ~ spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f188]) ).
cnf(s28,plain,
( spl0_1
| ~ spl0_8
| spl0_9 ),
inference(rat,[],[s27]) ).
cnf(s33,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f193]) ).
cnf(s34,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f194]) ).
cnf(s52,plain,
spl0_5,
inference(sat_conversion,[],[f211]) ).
cnf(s53,plain,
( ~ spl0_5
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f218]) ).
cnf(s54,plain,
( ~ spl0_5
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f222]) ).
cnf(s55,plain,
( ~ spl0_5
| spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f226]) ).
cnf(s59,plain,
( ~ spl0_5
| spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f242]) ).
cnf(s60,plain,
( ~ spl0_5
| spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f243]) ).
cnf(s61,plain,
( ~ spl0_5
| spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f244]) ).
cnf(s65,plain,
( ~ spl0_5
| spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f251]) ).
cnf(s66,plain,
( ~ spl0_5
| spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f252]) ).
cnf(s67,plain,
( ~ spl0_5
| spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f253]) ).
cnf(s73,plain,
( ~ spl0_5
| spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f262]) ).
cnf(s74,plain,
( ~ spl0_5
| spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f263]) ).
cnf(s75,plain,
( ~ spl0_5
| spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f264]) ).
cnf(s76,plain,
( ~ spl0_5
| spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f265]) ).
cnf(s79,plain,
( ~ spl0_5
| spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f271]) ).
cnf(s80,plain,
( ~ spl0_5
| spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f272]) ).
cnf(s81,plain,
( ~ spl0_5
| spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f273]) ).
cnf(s82,plain,
( ~ spl0_5
| spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f274]) ).
cnf(s85,plain,
( ~ spl0_5
| spl0_13
| spl0_21 ),
inference(sat_conversion,[],[f280]) ).
cnf(s86,plain,
( ~ spl0_5
| spl0_14
| spl0_21 ),
inference(sat_conversion,[],[f281]) ).
cnf(s87,plain,
( ~ spl0_5
| spl0_15
| spl0_21 ),
inference(sat_conversion,[],[f282]) ).
cnf(s88,plain,
( ~ spl0_5
| spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f283]) ).
cnf(s90,plain,
( ~ spl0_2
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f300]) ).
cnf(s95,plain,
( ~ spl0_1
| ~ spl0_12
| spl0_29
| spl0_30 ),
inference(sat_conversion,[],[f340]) ).
cnf(s98,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f361]) ).
cnf(s104,plain,
( ~ spl0_10
| ~ spl0_13
| ~ spl0_29
| spl0_30 ),
inference(sat_conversion,[],[f398]) ).
cnf(s107,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_15
| spl0_36 ),
inference(sat_conversion,[],[f406]) ).
cnf(s114,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_30 ),
inference(sat_conversion,[],[f425]) ).
cnf(s117,plain,
( spl0_6
| ~ spl0_14
| ~ spl0_16
| ~ spl0_36 ),
inference(sat_conversion,[],[f443]) ).
cnf(s118,plain,
( ~ spl0_2
| ~ spl0_12
| spl0_26
| spl0_27 ),
inference(sat_conversion,[],[f450]) ).
cnf(s119,plain,
( ~ spl0_2
| ~ spl0_17
| spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f456]) ).
cnf(s122,plain,
( ~ spl0_2
| spl0_8
| ~ spl0_20
| spl0_28 ),
inference(sat_conversion,[],[f467]) ).
cnf(s127,plain,
( ~ spl0_11
| ~ spl0_18
| spl0_27
| ~ spl0_28 ),
inference(sat_conversion,[],[f489]) ).
cnf(s128,plain,
( spl0_8
| ~ spl0_19
| ~ spl0_21
| ~ spl0_28 ),
inference(sat_conversion,[],[f490]) ).
cnf(s129,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_27 ),
inference(sat_conversion,[],[f491]) ).
cnf(s130,plain,
( ~ spl0_11
| ~ spl0_18
| spl0_30
| ~ spl0_35 ),
inference(sat_conversion,[],[f492]) ).
cnf(s131,plain,
( ~ spl0_1
| ~ spl0_17
| spl0_30
| spl0_35 ),
inference(sat_conversion,[],[f493]) ).
cnf(s140,plain,
( ~ spl0_10
| ~ spl0_13
| ~ spl0_26
| spl0_27 ),
inference(sat_conversion,[],[f533]) ).
cnf(s142,plain,
( spl0_21
| spl0_8
| ~ spl0_2 ),
inference(rat,[],[s90,s86,s87,s88,s52]) ).
cnf(s143,plain,
( spl0_20
| spl0_8
| ~ spl0_2 ),
inference(rat,[],[s90,s80,s81,s82,s52]) ).
cnf(s144,plain,
( spl0_8
| ~ spl0_2 ),
inference(rat,[],[s90,s74,s75,s76,s128,s122,s143,s142,s52]) ).
cnf(s146,plain,
( spl0_13
| ~ spl0_28
| spl0_27 ),
inference(rat,[],[s127,s55,s67,s52]) ).
cnf(s147,plain,
( spl0_12
| ~ spl0_28
| spl0_27 ),
inference(rat,[],[s127,s54,s66,s52]) ).
cnf(s148,plain,
( ~ spl0_28
| spl0_1 ),
inference(rat,[],[s127,s53,s65,s140,s118,s147,s146,s129,s28,s15,s144,s2,s52]) ).
cnf(s149,plain,
( spl0_28
| spl0_27
| ~ spl0_2 ),
inference(rat,[],[s140,s118,s59,s60,s61,s119,s52]) ).
cnf(s150,plain,
spl0_1,
inference(rat,[],[s149,s148,s129,s28,s15,s144,s2]) ).
cnf(s151,plain,
( spl0_30
| spl0_13 ),
inference(rat,[],[s130,s131,s67,s61,s55,s150,s52]) ).
cnf(s152,plain,
( spl0_9
| spl0_13
| ~ spl0_8 ),
inference(rat,[],[s114,s33,s34,s98,s73,s79,s85,s151,s52,s150]) ).
cnf(s154,plain,
( spl0_27
| ~ spl0_12
| ~ spl0_10
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s140,s118]) ).
cnf(s155,plain,
( spl0_30
| ~ spl0_12
| ~ spl0_10
| ~ spl0_13 ),
inference(rat,[],[s95,s104,s150]) ).
cnf(s156,plain,
( spl0_20
| spl0_6 ),
inference(rat,[],[s107,s117,s80,s81,s82,s150,s52]) ).
cnf(s157,plain,
( ~ spl0_20
| spl0_6
| ~ spl0_21 ),
inference(rat,[],[s107,s117,s74,s75,s76,s98,s52,s150]) ).
cnf(s158,plain,
( spl0_6
| ~ spl0_21 ),
inference(rat,[],[s157,s156]) ).
cnf(s159,plain,
( ~ spl0_6
| spl0_9
| ~ spl0_30
| ~ spl0_8 ),
inference(rat,[],[s114,s33,s34]) ).
cnf(s160,plain,
spl0_6,
inference(rat,[],[s107,s117,s86,s87,s88,s158,s150,s52]) ).
cnf(s162,plain,
( spl0_27
| ~ spl0_2 ),
inference(rat,[],[s127,s53,s65,s154,s147,s146,s149,s52]) ).
cnf(s163,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s114,s21,s20,s129,s152,s151,s144,s162,s160]) ).
cnf(s164,plain,
( spl0_12
| spl0_30 ),
inference(rat,[],[s130,s131,s54,s60,s66,s150,s52]) ).
cnf(s165,plain,
( ~ spl0_12
| spl0_30
| ~ spl0_13 ),
inference(rat,[],[s130,s131,s53,s59,s65,s155,s52,s150]) ).
cnf(s166,plain,
( spl0_30
| ~ spl0_13 ),
inference(rat,[],[s165,s164]) ).
cnf(s167,plain,
~ spl0_2,
inference(rat,[],[s114,s21,s20,s129,s159,s166,s163,s162,s144,s160]) ).
cnf(s168,plain,
spl0_4,
inference(rat,[],[s8,s167,s160]) ).
cnf(s169,plain,
spl0_3,
inference(rat,[],[s7,s167,s160]) ).
cnf(s170,plain,
~ spl0_30,
inference(rat,[],[s114,s168,s169]) ).
cnf(s171,plain,
spl0_13,
inference(rat,[],[s151,s170]) ).
cnf(s173,plain,
$false,
inference(rat,[],[s166,s171,s170]) ).
fof(f534,plain,
$false,
inference(avatar_sat_refutation,[],[s173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN067-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n008.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Mon Sep 28 15:28:40 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running first-order theorem proving
% 0.09/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.75/1.11 % (2340168)Input is clausal, will run a generic CNF schedule.
% 2.75/1.11 % (2340242)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=903925498:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.75/1.11 % (2340241)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=2314784573:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.75/1.11 % (2340249)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2626025608:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.75/1.11 % (2340251)dis-21_1_sil=8000:lcm=predicate:random_seed=110437303: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)
% 2.75/1.11 % (2340243)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3184112858:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.75/1.11 % (2340247)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1974050610:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.75/1.11 % (2340245)lrs+10_1_sil=8000:sp=occurrence:random_seed=1434815415:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.75/1.11 % (2340249)First to succeed.
% 2.75/1.11 % (2340251)Also succeeded, but the first one will report.
% 2.75/1.11 % (2340249)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2340168"
% 2.75/1.11 % (2340247)Also succeeded, but the first one will report.
% 2.75/1.11 % (2340245)Also succeeded, but the first one will report.
% 2.75/1.11 % (2340249)Refutation found. Thanks to Tanya!
% 2.75/1.11 % SZS status Unsatisfiable for theBenchmark
% 2.75/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.20 % (2340249)------------------------------
% 3.45/1.20 % (2340249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.20 % (2340249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.20 % (2340249)CaDiCaL version: 2.1.3
% 3.45/1.20 % (2340249)Termination reason: Refutation
% 3.45/1.20 % (2340249)Time elapsed: 0.010 s
% 3.45/1.20 % (2340249)Peak memory usage: 89 MB
% 3.45/1.20 % (2340249)Instructions burned: 14 (million)
% 3.45/1.20 % (2340249)------------------------------
% 3.45/1.20 % (2340249)------------------------------
% 3.45/1.20 % (2340168)Success in time 0.395 s
% 3.45/1.20 % Vampire exiting
%------------------------------------------------------------------------------