%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN067-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 02:06:39 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 54
% Syntax : Number of formulae : 250 ( 13 unt; 23 def)
% Number of atoms : 1050 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 1417 ( 617 ~; 777 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 26 ( 25 usr; 24 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-1 aty)
% Number of variables : 223 ( 0 sgn 223 !; 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_36) ).
fof(f37,negated_conjecture,
( big_p(a)
| big_p(a)
| big_p(a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_37) ).
fof(f54,negated_conjecture,
( ~ big_p(c2)
| big_p(c1)
| ~ big_p(c4)
| big_p(c3) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_84) ).
fof(f90,plain,
big_p(a),
inference(duplicate_literal_removal,[],[f37]) ).
fof(f91,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(f92,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(f93,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(f97,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(f98,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(f99,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(f103,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(f104,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(f105,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(f111,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(f112,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(f113,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(f114,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(f117,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(f118,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(f119,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(f120,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(f123,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(f124,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(f125,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(f126,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(f128,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(f129,plain,
( ! [X4,X5] :
( ~ big_r(c4,X5)
| ~ big_r(X5,X4)
| ~ big_p(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,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(f132,plain,
( ! [X0,X1] :
( ~ big_r(c2,X1)
| ~ big_r(X1,X0)
| ~ big_p(X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f133,plain,
( spl0_1
| spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f84,f131,f128,f128]) ).
fof(f135,definition,
( spl0_3
<=> big_r(c4,c3) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f137,plain,
( big_r(c4,c3)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f140,definition,
( spl0_4
<=> big_p(c3) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f142,plain,
( big_p(c3)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f145,definition,
( spl0_5
<=> big_p(a) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f150,definition,
( spl0_6
<=> big_p(c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f152,plain,
( ~ big_p(c4)
| spl0_6 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f154,plain,
( spl0_3
| ~ spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f79,f131,f150,f135]) ).
fof(f155,plain,
( spl0_4
| ~ spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f78,f131,f150,f140]) ).
fof(f161,definition,
( spl0_7
<=> big_r(c2,c1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f163,plain,
( big_r(c2,c1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl0_8
<=> big_p(c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f167,plain,
( ~ big_p(c2)
| spl0_8 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl0_1
| spl0_1
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f72,f165,f161,f128,f128]) ).
fof(f172,plain,
( spl0_3
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f67,f165,f161,f150,f135]) ).
fof(f173,plain,
( spl0_4
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f66,f165,f161,f150,f140]) ).
fof(f175,definition,
( spl0_9
<=> big_p(c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f177,plain,
( big_p(c1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( spl0_1
| spl0_1
| spl0_9
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f60,f165,f175,f128,f128]) ).
fof(f182,plain,
( spl0_3
| ~ spl0_6
| spl0_9
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f55,f165,f175,f150,f135]) ).
fof(f183,plain,
( spl0_4
| ~ spl0_6
| spl0_9
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f54,f165,f175,f150,f140]) ).
fof(f190,plain,
spl0_5,
inference(avatar_split_clause,[],[f90,f145]) ).
fof(f192,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(f193,plain,
( ! [X2,X3] :
( big_r(f5(X3),f6(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f195,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(f196,plain,
( ! [X0,X1] :
( big_r(f1(X1),f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f197,plain,
( spl0_10
| spl0_11
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f91,f145,f195,f192]) ).
fof(f199,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(f200,plain,
( ! [X2,X3] :
( big_r(X3,f5(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f201,plain,
( spl0_12
| spl0_11
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f92,f145,f195,f199]) ).
fof(f203,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(f204,plain,
( ! [X2,X3] :
( ~ big_r(X3,X2)
| big_p(f6(X3))
| ~ big_p(X2) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f205,plain,
( spl0_13
| spl0_11
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f93,f145,f195,f203]) ).
fof(f207,definition,
( spl0_14
<=> ! [X2] :
( big_p(X2)
| big_r(f3(X2),f4(X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f208,plain,
( ! [X2] :
( big_r(f3(X2),f4(X2))
| big_p(X2) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f211,definition,
( spl0_15
<=> ! [X2] :
( big_p(X2)
| big_r(X2,f3(X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f212,plain,
( ! [X2] :
( big_r(X2,f3(X2))
| big_p(X2) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f215,definition,
( spl0_16
<=> ! [X2] :
( big_p(X2)
| big_p(f4(X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f216,plain,
( ! [X2] :
( big_p(f4(X2))
| big_p(X2) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f219,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(f220,plain,
( ! [X0,X1] :
( big_r(X1,f1(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f221,plain,
( spl0_10
| spl0_17
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f97,f145,f219,f192]) ).
fof(f222,plain,
( spl0_12
| spl0_17
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f98,f145,f219,f199]) ).
fof(f223,plain,
( spl0_13
| spl0_17
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f99,f145,f219,f203]) ).
fof(f228,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(f229,plain,
( ! [X0,X1] :
( ~ big_r(X1,X0)
| big_p(f2(X1))
| ~ big_p(X0) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f230,plain,
( spl0_10
| spl0_18
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f103,f145,f228,f192]) ).
fof(f231,plain,
( spl0_12
| spl0_18
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f104,f145,f228,f199]) ).
fof(f232,plain,
( spl0_13
| spl0_18
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f105,f145,f228,f203]) ).
fof(f237,definition,
( spl0_19
<=> ! [X0] :
( big_p(X0)
| big_r(f1(X0),f2(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f238,plain,
( ! [X0] :
( big_r(f1(X0),f2(X0))
| big_p(X0) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f241,plain,
( spl0_13
| spl0_19
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f111,f145,f237,f203]) ).
fof(f242,plain,
( spl0_14
| spl0_19
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f112,f145,f237,f207]) ).
fof(f243,plain,
( spl0_15
| spl0_19
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f113,f145,f237,f211]) ).
fof(f244,plain,
( spl0_16
| spl0_19
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f114,f145,f237,f215]) ).
fof(f246,definition,
( spl0_20
<=> ! [X0] :
( big_p(X0)
| big_r(X0,f1(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f247,plain,
( ! [X0] :
( big_r(X0,f1(X0))
| big_p(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,plain,
( spl0_13
| spl0_20
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f117,f145,f246,f203]) ).
fof(f251,plain,
( spl0_14
| spl0_20
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f118,f145,f246,f207]) ).
fof(f252,plain,
( spl0_15
| spl0_20
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f119,f145,f246,f211]) ).
fof(f253,plain,
( spl0_16
| spl0_20
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f120,f145,f246,f215]) ).
fof(f255,definition,
( spl0_21
<=> ! [X0] :
( big_p(X0)
| big_p(f2(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f256,plain,
( ! [X0] :
( big_p(f2(X0))
| big_p(X0) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f259,plain,
( spl0_13
| spl0_21
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f123,f145,f255,f203]) ).
fof(f260,plain,
( spl0_14
| spl0_21
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f124,f145,f255,f207]) ).
fof(f261,plain,
( spl0_15
| spl0_21
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f125,f145,f255,f211]) ).
fof(f262,plain,
( spl0_16
| spl0_21
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f126,f145,f255,f215]) ).
fof(f264,plain,
( ! [X0] :
( ~ big_r(c2,f3(X0))
| ~ big_p(f4(X0))
| big_p(X0) )
| ~ spl0_2
| ~ spl0_14 ),
inference(resolution,[],[f132,f208]) ).
fof(f265,plain,
( ! [X0] :
( ~ big_r(c2,f3(X0))
| big_p(X0) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f264,f216]) ).
fof(f266,plain,
( big_p(c2)
| big_p(c2)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(resolution,[],[f265,f212]) ).
fof(f267,plain,
( big_p(c2)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(duplicate_literal_removal,[],[f266]) ).
fof(f268,plain,
( $false
| ~ spl0_2
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f267,f167]) ).
fof(f269,plain,
( ~ spl0_2
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f268]) ).
fof(f280,plain,
( ! [X0,X1] :
( ~ big_r(X0,X1)
| ~ big_r(c2,f5(X0))
| ~ big_p(X1)
| ~ big_p(f6(X0)) )
| ~ spl0_2
| ~ spl0_10 ),
inference(resolution,[],[f193,f132]) ).
fof(f281,plain,
( ! [X0,X1] :
( ~ big_r(X0,X1)
| ~ big_r(c2,f5(X0))
| ~ big_p(X1) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f280,f204]) ).
fof(f287,definition,
( spl0_22
<=> ! [X0] :
( ~ big_r(c2,X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f288,plain,
( ! [X0] :
( ~ big_r(c2,X0)
| ~ big_p(X0) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f302,plain,
( ! [X0,X1] :
( ~ big_r(c2,X0)
| ~ big_p(X0)
| ~ big_r(c2,X1)
| ~ big_p(X1) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(resolution,[],[f281,f200]) ).
fof(f303,plain,
( spl0_22
| spl0_22
| ~ spl0_2
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f302,f203,f199,f192,f131,f287,f287]) ).
fof(f308,plain,
( ! [X0] :
( big_p(X0)
| ~ big_r(c2,f1(X0))
| ~ big_p(f2(X0)) )
| ~ spl0_2
| ~ spl0_19 ),
inference(resolution,[],[f238,f132]) ).
fof(f309,plain,
( ! [X0] :
( ~ big_r(c2,f1(X0))
| big_p(X0) )
| ~ spl0_2
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f308,f256]) ).
fof(f310,plain,
( big_p(c2)
| big_p(c2)
| ~ spl0_2
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(resolution,[],[f309,f247]) ).
fof(f311,plain,
( big_p(c2)
| ~ spl0_2
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f310]) ).
fof(f338,plain,
( ! [X0,X1] :
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ big_r(c2,f1(X0))
| ~ big_p(f2(X0)) )
| ~ spl0_2
| ~ spl0_11 ),
inference(resolution,[],[f196,f132]) ).
fof(f339,plain,
( ! [X0,X1] :
( ~ big_r(X0,X1)
| ~ big_r(c2,f1(X0))
| ~ big_p(X1) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f338,f229]) ).
fof(f364,plain,
( ! [X0,X1] :
( ~ big_r(c2,X0)
| ~ big_p(X0)
| ~ big_r(c2,X1)
| ~ big_p(X1) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(resolution,[],[f339,f220]) ).
fof(f366,plain,
( spl0_22
| spl0_22
| ~ spl0_2
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f364,f228,f219,f195,f131,f287,f287]) ).
fof(f418,plain,
( ~ big_p(c1)
| ~ spl0_7
| ~ spl0_22 ),
inference(resolution,[],[f288,f163]) ).
fof(f423,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f418,f177]) ).
fof(f424,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f423]) ).
fof(f429,plain,
( ! [X0] :
( ~ big_r(c4,f3(X0))
| ~ big_p(f4(X0))
| big_p(X0) )
| ~ spl0_1
| ~ spl0_14 ),
inference(resolution,[],[f129,f208]) ).
fof(f430,plain,
( ! [X0,X1] :
( ~ big_r(c4,f5(X0))
| ~ big_r(X0,X1)
| ~ big_p(f6(X0))
| ~ big_p(X1) )
| ~ spl0_1
| ~ spl0_10 ),
inference(resolution,[],[f129,f193]) ).
fof(f431,plain,
( ! [X0,X1] :
( ~ big_r(c4,f1(X0))
| ~ big_p(f2(X0))
| ~ big_r(X0,X1)
| ~ big_p(X1) )
| ~ spl0_1
| ~ spl0_11 ),
inference(resolution,[],[f129,f196]) ).
fof(f432,plain,
( ! [X0] :
( ~ big_r(c4,f1(X0))
| ~ big_p(f2(X0))
| big_p(X0) )
| ~ spl0_1
| ~ spl0_19 ),
inference(resolution,[],[f129,f238]) ).
fof(f433,plain,
( ! [X0] :
( ~ big_r(c4,f1(X0))
| big_p(X0) )
| ~ spl0_1
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f432,f256]) ).
fof(f434,plain,
( ! [X0,X1] :
( ~ big_r(c4,f1(X0))
| ~ big_r(X0,X1)
| ~ big_p(X1) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f431,f229]) ).
fof(f437,plain,
( big_p(c4)
| big_p(c4)
| ~ spl0_1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(resolution,[],[f433,f247]) ).
fof(f438,plain,
( big_p(c4)
| ~ spl0_1
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f437]) ).
fof(f439,plain,
( $false
| ~ spl0_1
| spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f438,f152]) ).
fof(f440,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f443,plain,
( $false
| ~ spl0_2
| spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f311,f167]) ).
fof(f444,plain,
( ~ spl0_2
| spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f443]) ).
fof(f487,definition,
( spl0_36
<=> ! [X0] :
( ~ big_r(c4,X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f488,plain,
( ! [X0] :
( ~ big_r(c4,X0)
| ~ big_p(X0) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f524,plain,
( ~ big_p(f4(c4))
| big_p(c4)
| big_p(c4)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(resolution,[],[f429,f212]) ).
fof(f525,plain,
( ~ big_p(f4(c4))
| big_p(c4)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(duplicate_literal_removal,[],[f524]) ).
fof(f526,plain,
( ! [X0,X1] :
( ~ big_r(c4,X0)
| ~ big_p(X0)
| ~ big_r(c4,X1)
| ~ big_p(X1) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(resolution,[],[f434,f220]) ).
fof(f538,plain,
( spl0_36
| spl0_36
| ~ spl0_1
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f526,f228,f219,f195,f128,f487,f487]) ).
fof(f539,plain,
( ! [X0,X1] :
( ~ big_r(c4,X0)
| ~ big_p(f6(c4))
| ~ big_p(X0)
| ~ big_r(c4,X1)
| ~ big_p(X1) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_12 ),
inference(resolution,[],[f430,f200]) ).
fof(f550,plain,
( ~ big_p(c3)
| ~ spl0_3
| ~ spl0_36 ),
inference(resolution,[],[f488,f137]) ).
fof(f555,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f550,f142]) ).
fof(f556,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f555]) ).
fof(f558,plain,
( ! [X0,X1] :
( ~ big_r(c4,X0)
| ~ big_p(X0)
| ~ big_r(c4,X1)
| ~ big_p(X1) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f539,f204]) ).
fof(f559,plain,
( spl0_36
| spl0_36
| ~ spl0_1
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f558,f203,f199,f192,f128,f487,f487]) ).
fof(f564,plain,
( big_p(c4)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f525,f216]) ).
fof(f568,plain,
( $false
| ~ spl0_1
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f564,f152]) ).
fof(f569,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f568]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f133]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl0_2
| spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s8,plain,
( spl0_2
| spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f155]) ).
cnf(s13,plain,
( spl0_1
| spl0_1
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f168]) ).
cnf(s14,plain,
( spl0_1
| spl0_7
| ~ spl0_8 ),
inference(rat,[],[s13]) ).
cnf(s18,plain,
( spl0_3
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f172]) ).
cnf(s19,plain,
( spl0_4
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f173]) ).
cnf(s20,plain,
( spl0_1
| spl0_1
| ~ spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f178]) ).
cnf(s21,plain,
( spl0_1
| ~ spl0_8
| spl0_9 ),
inference(rat,[],[s20]) ).
cnf(s25,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f182]) ).
cnf(s26,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f183]) ).
cnf(s34,plain,
spl0_5,
inference(sat_conversion,[],[f190]) ).
cnf(s35,plain,
( ~ spl0_5
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f197]) ).
cnf(s36,plain,
( ~ spl0_5
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f201]) ).
cnf(s37,plain,
( ~ spl0_5
| spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f205]) ).
cnf(s41,plain,
( ~ spl0_5
| spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f221]) ).
cnf(s42,plain,
( ~ spl0_5
| spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f222]) ).
cnf(s43,plain,
( ~ spl0_5
| spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f223]) ).
cnf(s47,plain,
( ~ spl0_5
| spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f230]) ).
cnf(s48,plain,
( ~ spl0_5
| spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f231]) ).
cnf(s49,plain,
( ~ spl0_5
| spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f232]) ).
cnf(s55,plain,
( ~ spl0_5
| spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f241]) ).
cnf(s56,plain,
( ~ spl0_5
| spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f242]) ).
cnf(s57,plain,
( ~ spl0_5
| spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f243]) ).
cnf(s58,plain,
( ~ spl0_5
| spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f244]) ).
cnf(s61,plain,
( ~ spl0_5
| spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f250]) ).
cnf(s62,plain,
( ~ spl0_5
| spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f251]) ).
cnf(s63,plain,
( ~ spl0_5
| spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f252]) ).
cnf(s64,plain,
( ~ spl0_5
| spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f253]) ).
cnf(s67,plain,
( ~ spl0_5
| spl0_13
| spl0_21 ),
inference(sat_conversion,[],[f259]) ).
cnf(s68,plain,
( ~ spl0_5
| spl0_14
| spl0_21 ),
inference(sat_conversion,[],[f260]) ).
cnf(s69,plain,
( ~ spl0_5
| spl0_15
| spl0_21 ),
inference(sat_conversion,[],[f261]) ).
cnf(s70,plain,
( ~ spl0_5
| spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f262]) ).
cnf(s71,plain,
( ~ spl0_2
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f269]) ).
cnf(s73,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_2
| spl0_22 ),
inference(sat_conversion,[],[f303]) ).
cnf(s74,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| spl0_22 ),
inference(rat,[],[s73]) ).
cnf(s78,plain,
( spl0_22
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18
| ~ spl0_2
| spl0_22 ),
inference(sat_conversion,[],[f366]) ).
cnf(s79,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18
| spl0_22 ),
inference(rat,[],[s78]) ).
cnf(s81,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_22 ),
inference(sat_conversion,[],[f424]) ).
cnf(s82,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f440]) ).
cnf(s83,plain,
( ~ spl0_2
| spl0_8
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f444]) ).
cnf(s93,plain,
( spl0_36
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18
| ~ spl0_1
| spl0_36 ),
inference(sat_conversion,[],[f538]) ).
cnf(s94,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18
| spl0_36 ),
inference(rat,[],[s93]) ).
cnf(s95,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_36 ),
inference(sat_conversion,[],[f556]) ).
cnf(s96,plain,
( spl0_36
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_1
| spl0_36 ),
inference(sat_conversion,[],[f559]) ).
cnf(s97,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| spl0_36 ),
inference(rat,[],[s96]) ).
cnf(s99,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f569]) ).
cnf(s101,plain,
( spl0_21
| spl0_8
| ~ spl0_2 ),
inference(rat,[],[s71,s68,s69,s70,s34]) ).
cnf(s102,plain,
( spl0_20
| spl0_8
| ~ spl0_2 ),
inference(rat,[],[s71,s62,s63,s64,s34]) ).
cnf(s103,plain,
( ~ spl0_20
| ~ spl0_21
| ~ spl0_2
| spl0_8 ),
inference(rat,[],[s71,s56,s57,s58,s83,s34]) ).
cnf(s104,plain,
( spl0_8
| ~ spl0_2 ),
inference(rat,[],[s103,s102,s101]) ).
cnf(s106,plain,
( spl0_13
| spl0_1 ),
inference(rat,[],[s79,s37,s43,s49,s81,s14,s21,s104,s2,s34]) ).
cnf(s107,plain,
( spl0_12
| spl0_1 ),
inference(rat,[],[s79,s36,s42,s48,s81,s14,s21,s104,s2,s34]) ).
cnf(s108,plain,
( ~ spl0_12
| ~ spl0_2
| spl0_22
| ~ spl0_13 ),
inference(rat,[],[s79,s35,s41,s47,s74,s34]) ).
cnf(s109,plain,
spl0_1,
inference(rat,[],[s108,s107,s106,s81,s14,s21,s104,s2]) ).
cnf(s110,plain,
( spl0_9
| ~ spl0_36
| ~ spl0_6
| ~ spl0_8 ),
inference(rat,[],[s95,s26,s25]) ).
cnf(s111,plain,
( spl0_13
| ~ spl0_21
| ~ spl0_2 ),
inference(rat,[],[s95,s19,s18,s81,s110,s79,s94,s82,s37,s43,s49,s55,s61,s104,s109,s34]) ).
cnf(s112,plain,
( ~ spl0_6
| ~ spl0_36
| ~ spl0_22
| ~ spl0_8 ),
inference(rat,[],[s95,s19,s18,s81,s110]) ).
cnf(s113,plain,
( spl0_19
| spl0_6 ),
inference(rat,[],[s99,s56,s57,s58,s109,s34]) ).
cnf(s114,plain,
( ~ spl0_19
| spl0_6
| ~ spl0_21 ),
inference(rat,[],[s99,s62,s63,s64,s82,s34,s109]) ).
cnf(s115,plain,
( spl0_6
| ~ spl0_21 ),
inference(rat,[],[s114,s113]) ).
cnf(s116,plain,
( spl0_36
| ~ spl0_10
| ~ spl0_13 ),
inference(rat,[],[s94,s36,s42,s48,s97,s34,s109]) ).
cnf(s117,plain,
( spl0_22
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s79,s36,s42,s48,s108,s34]) ).
cnf(s118,plain,
( spl0_36
| ~ spl0_13 ),
inference(rat,[],[s94,s35,s41,s47,s116,s34,s109]) ).
cnf(s119,plain,
( ~ spl0_21
| ~ spl0_2 ),
inference(rat,[],[s118,s112,s117,s115,s111,s104]) ).
cnf(s120,plain,
~ spl0_2,
inference(rat,[],[s112,s118,s117,s99,s67,s68,s69,s70,s119,s104,s109,s34]) ).
cnf(s121,plain,
spl0_36,
inference(rat,[],[s94,s37,s43,s49,s118,s109,s34]) ).
cnf(s122,plain,
~ spl0_6,
inference(rat,[],[s95,s7,s8,s121,s120]) ).
cnf(s124,plain,
~ spl0_21,
inference(rat,[],[s115,s122]) ).
cnf(s125,plain,
spl0_16,
inference(rat,[],[s70,s34,s124]) ).
cnf(s126,plain,
spl0_15,
inference(rat,[],[s69,s34,s124]) ).
cnf(s127,plain,
spl0_14,
inference(rat,[],[s68,s34,s124]) ).
cnf(s131,plain,
$false,
inference(rat,[],[s99,s125,s122,s109,s126,s127]) ).
fof(f570,plain,
$false,
inference(avatar_sat_refutation,[],[s131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN067-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 15:28:00 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28 % (3150876)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (3150885)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=651925791:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (3150882)% WARNING: option uhcvi not known.
% 0.20/0.28 % (3150881)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1501922947_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (3150882)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4178026389:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (3150883)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4293715819:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (3150884)dis+10_1_sil=32000:sp=arity:random_seed=3542675551:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (3150886)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3469672743:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (3150887)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3649212039:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (3150885) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3150876-3150885"...
% 0.20/0.28 % (3150884) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3150876-3150884"...
% 0.20/0.28 % (3150885)...printing done.
% 0.20/0.28 % (3150882) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3150876-3150882"...
% 0.20/0.28 % (3150885)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3150885)------------------------------
% 0.20/0.28 % (3150885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3150885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3150885)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3150885)Termination reason: Refutation
% 0.20/0.28 % (3150885)Time elapsed: 0.019 s
% 0.20/0.28 % (3150885)Peak memory usage: 12 MB
% 0.20/0.28 % (3150885)Instructions burned: 74 (million)
% 0.20/0.28 % (3150876)Success in time 0.056 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------