%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN036-1 : 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 : n002.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 02:06:28 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 42
% Syntax : Number of formulae : 198 ( 12 unt; 26 def)
% Number of atoms : 750 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 839 ( 287 ~; 526 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 27 prp; 0-1 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-1 aty)
% Number of variables : 112 ( 0 sgn 112 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,negated_conjecture,
! [X2,X3,X0,X1] :
( big_p(X0)
| big_p(f1(X0))
| ~ big_q(X1)
| big_p(X2)
| ~ big_q(f2(X3))
| ~ big_q(X3)
| big_p(c6)
| ~ big_q(c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f5,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( big_p(X0)
| big_p(f1(X0))
| ~ big_q(X1)
| big_p(X2)
| ~ big_q(X3)
| big_q(c8)
| big_p(c9)
| big_q(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f7,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( big_p(X0)
| big_p(f1(X0))
| ~ big_q(X1)
| big_p(X2)
| big_q(X3)
| ~ big_q(c8)
| big_p(c9)
| big_q(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
fof(f25,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(X0)
| ~ big_p(f1(X0))
| big_q(c1)
| ~ big_p(c2)
| big_q(f2(X1))
| big_q(X1)
| ~ big_p(X2)
| big_q(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_25) ).
fof(f33,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( ~ big_p(c3)
| big_p(X0)
| big_q(c4)
| big_p(X1)
| big_q(f2(X2))
| big_q(X2)
| ~ big_p(X3)
| big_q(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_33) ).
fof(f49,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( big_p(c3)
| ~ big_p(X0)
| big_q(c4)
| big_p(X1)
| big_q(f2(X2))
| big_q(X2)
| ~ big_p(X3)
| big_q(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_49) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ big_p(c11)
| big_p(X0)
| ~ big_q(X1)
| big_p(X2)
| ~ big_q(X3)
| big_q(c16)
| ~ big_p(X4)
| big_q(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_65) ).
fof(f67,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ big_p(c11)
| big_p(X0)
| ~ big_q(X1)
| big_p(X2)
| big_q(X3)
| ~ big_q(c16)
| ~ big_p(X4)
| big_q(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_67) ).
fof(f72,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( ~ big_p(c11)
| big_p(X0)
| ~ big_q(X1)
| big_p(X2)
| ~ big_q(f4(X3))
| ~ big_q(X3)
| ~ big_p(X4)
| ~ big_q(c20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_72) ).
fof(f81,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( big_p(c11)
| ~ big_p(X0)
| ~ big_q(X1)
| big_p(X2)
| ~ big_q(X3)
| big_q(c16)
| ~ big_p(X4)
| big_q(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_81) ).
fof(f83,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( big_p(c11)
| ~ big_p(X0)
| ~ big_q(X1)
| big_p(X2)
| big_q(X3)
| ~ big_q(c16)
| ~ big_p(X4)
| big_q(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_83) ).
fof(f88,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( big_p(c11)
| ~ big_p(X0)
| ~ big_q(X1)
| big_p(X2)
| ~ big_q(f4(X3))
| ~ big_q(X3)
| ~ big_p(X4)
| ~ big_q(c20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_88) ).
fof(f101,negated_conjecture,
! [X2,X3,X0,X1] :
( big_p(X0)
| big_p(f3(X0))
| big_q(c14)
| big_p(X1)
| big_q(f4(X2))
| big_q(X2)
| big_p(c19)
| big_q(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_101) ).
fof(f121,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( ~ big_p(X0)
| ~ big_p(f3(X0))
| ~ big_q(X1)
| ~ big_p(c15)
| ~ big_q(X2)
| big_q(c16)
| ~ big_p(X3)
| big_q(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_121) ).
fof(f123,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( ~ big_p(X0)
| ~ big_p(f3(X0))
| ~ big_q(X1)
| ~ big_p(c15)
| big_q(X2)
| ~ big_q(c16)
| ~ big_p(X3)
| big_q(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_123) ).
fof(f128,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ big_p(X0)
| ~ big_p(f3(X0))
| ~ big_q(X1)
| ~ big_p(c15)
| ~ big_q(f4(X2))
| ~ big_q(X2)
| ~ big_p(X3)
| ~ big_q(c20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_128) ).
fof(f130,definition,
( spl0_1
<=> big_q(c20) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f132,plain,
( ~ big_q(c20)
| spl0_1 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f134,definition,
( spl0_2
<=> ! [X3] : ~ big_p(X3) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f135,plain,
( ! [X3] : ~ big_p(X3)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl0_3
<=> ! [X2] :
( ~ big_q(f4(X2))
| ~ big_q(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f138,plain,
( ! [X2] :
( ~ big_q(f4(X2))
| ~ big_q(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,definition,
( spl0_4
<=> big_p(c15) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f142,plain,
( ~ big_p(c15)
| spl0_4 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f144,definition,
( spl0_5
<=> ! [X1] : ~ big_q(X1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f145,plain,
( ! [X1] : ~ big_q(X1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,definition,
( spl0_6
<=> ! [X0] :
( ~ big_p(X0)
| ~ big_p(f3(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f148,plain,
( ! [X0] :
( ~ big_p(f3(X0))
| ~ big_p(X0) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f149,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f128,f147,f144,f140,f137,f134,f130]) ).
fof(f151,definition,
( spl0_7
<=> ! [X3] : big_q(X3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f152,plain,
( ! [X3] : big_q(X3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,definition,
( spl0_8
<=> big_p(c19) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f156,plain,
( big_p(c19)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f159,definition,
( spl0_9
<=> ! [X2] :
( big_q(f4(X2))
| big_q(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f160,plain,
( ! [X2] :
( big_q(f4(X2))
| big_q(X2) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f172,definition,
( spl0_12
<=> big_q(c16) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f176,plain,
( spl0_7
| spl0_2
| ~ spl0_12
| spl0_7
| ~ spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f123,f147,f144,f140,f151,f172,f134,f151]) ).
fof(f178,plain,
( spl0_7
| spl0_2
| spl0_12
| spl0_5
| ~ spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f121,f147,f144,f140,f144,f172,f134,f151]) ).
fof(f180,definition,
( spl0_13
<=> ! [X1] : big_p(X1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f181,plain,
( ! [X1] : big_p(X1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f183,definition,
( spl0_14
<=> big_q(c14) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f185,plain,
( big_q(c14)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f195,definition,
( spl0_15
<=> ! [X0] :
( big_p(X0)
| big_p(f3(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f196,plain,
( ! [X0] :
( big_p(f3(X0))
| big_p(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f208,plain,
( spl0_7
| spl0_8
| spl0_9
| spl0_13
| spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f101,f195,f183,f180,f159,f154,f151]) ).
fof(f222,definition,
( spl0_18
<=> big_p(c11) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f233,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_13
| spl0_5
| spl0_2
| spl0_18 ),
inference(avatar_split_clause,[],[f88,f222,f134,f144,f180,f137,f134,f130]) ).
fof(f238,plain,
( spl0_7
| spl0_2
| ~ spl0_12
| spl0_7
| spl0_13
| spl0_5
| spl0_2
| spl0_18 ),
inference(avatar_split_clause,[],[f83,f222,f134,f144,f180,f151,f172,f134,f151]) ).
fof(f240,plain,
( spl0_7
| spl0_2
| spl0_12
| spl0_5
| spl0_13
| spl0_5
| spl0_2
| spl0_18 ),
inference(avatar_split_clause,[],[f81,f222,f134,f144,f180,f144,f172,f134,f151]) ).
fof(f249,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_13
| spl0_5
| spl0_13
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f72,f222,f180,f144,f180,f137,f134,f130]) ).
fof(f254,plain,
( spl0_7
| spl0_2
| ~ spl0_12
| spl0_7
| spl0_13
| spl0_5
| spl0_13
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f67,f222,f180,f144,f180,f151,f172,f134,f151]) ).
fof(f256,plain,
( spl0_7
| spl0_2
| spl0_12
| spl0_5
| spl0_13
| spl0_5
| spl0_13
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f65,f222,f180,f144,f180,f144,f172,f134,f151]) ).
fof(f262,definition,
( spl0_20
<=> big_q(c8) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f270,definition,
( spl0_22
<=> big_p(c3) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f275,definition,
( spl0_23
<=> big_p(c9) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f277,plain,
( big_p(c9)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f282,definition,
( spl0_24
<=> big_q(c7) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f284,plain,
( ~ big_q(c7)
| spl0_24 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f286,definition,
( spl0_25
<=> big_p(c6) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f288,plain,
( big_p(c6)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f290,definition,
( spl0_26
<=> ! [X2] :
( ~ big_q(f2(X2))
| ~ big_q(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f291,plain,
( ! [X2] :
( ~ big_q(f2(X2))
| ~ big_q(X2) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f295,definition,
( spl0_27
<=> ! [X2] :
( big_q(f2(X2))
| big_q(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f296,plain,
( ! [X2] :
( big_q(f2(X2))
| big_q(X2) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f300,definition,
( spl0_28
<=> big_q(c4) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f302,plain,
( big_q(c4)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f310,plain,
( spl0_7
| spl0_2
| spl0_27
| spl0_13
| spl0_28
| spl0_2
| spl0_22 ),
inference(avatar_split_clause,[],[f49,f270,f134,f300,f180,f295,f134,f151]) ).
fof(f326,plain,
( spl0_7
| spl0_2
| spl0_27
| spl0_13
| spl0_28
| spl0_13
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f33,f270,f180,f300,f180,f295,f134,f151]) ).
fof(f328,definition,
( spl0_29
<=> big_p(c2) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f330,plain,
( ~ big_p(c2)
| spl0_29 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f332,definition,
( spl0_30
<=> big_q(c1) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f334,plain,
( big_q(c1)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f336,definition,
( spl0_31
<=> ! [X0] :
( ~ big_p(X0)
| ~ big_p(f1(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f337,plain,
( ! [X0] :
( ~ big_p(f1(X0))
| ~ big_p(X0) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f345,plain,
( spl0_7
| spl0_2
| spl0_27
| ~ spl0_29
| spl0_30
| spl0_31 ),
inference(avatar_split_clause,[],[f25,f336,f332,f328,f295,f134,f151]) ).
fof(f355,definition,
( spl0_32
<=> ! [X0] :
( big_p(X0)
| big_p(f1(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f356,plain,
( ! [X0] :
( big_p(X0)
| big_p(f1(X0)) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f366,plain,
( spl0_7
| spl0_23
| ~ spl0_20
| spl0_7
| spl0_13
| spl0_5
| spl0_32 ),
inference(avatar_split_clause,[],[f7,f355,f144,f180,f151,f262,f275,f151]) ).
fof(f368,plain,
( spl0_7
| spl0_23
| spl0_20
| spl0_5
| spl0_13
| spl0_5
| spl0_32 ),
inference(avatar_split_clause,[],[f5,f355,f144,f180,f144,f262,f275,f151]) ).
fof(f369,plain,
( ~ spl0_24
| spl0_25
| spl0_26
| spl0_13
| spl0_5
| spl0_32 ),
inference(avatar_split_clause,[],[f4,f355,f144,f180,f290,f286,f282]) ).
fof(f377,plain,
( $false
| ~ spl0_7
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f284,f152]) ).
fof(f378,plain,
( ~ spl0_7
| spl0_24 ),
inference(avatar_contradiction_clause,[],[f377]) ).
fof(f383,plain,
( $false
| ~ spl0_13
| spl0_29 ),
inference(forward_subsumption_resolution,[],[f330,f181]) ).
fof(f384,plain,
( ~ spl0_13
| spl0_29 ),
inference(avatar_contradiction_clause,[],[f383]) ).
fof(f385,plain,
( $false
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f152,f145]) ).
fof(f386,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f385]) ).
fof(f393,plain,
( $false
| spl0_1
| ~ spl0_7 ),
inference(resolution,[],[f152,f132]) ).
fof(f394,plain,
( spl0_1
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f393]) ).
fof(f395,plain,
( ! [X2] : ~ big_q(X2)
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f138,f152]) ).
fof(f396,plain,
( $false
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f395,f152]) ).
fof(f397,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f396]) ).
fof(f398,plain,
( $false
| ~ spl0_5
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f185,f145]) ).
fof(f399,plain,
( ~ spl0_5
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f398]) ).
fof(f400,plain,
( ! [X2] : big_q(X2)
| ~ spl0_5
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f296,f145]) ).
fof(f403,plain,
( ! [X2] : big_q(X2)
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f160,f145]) ).
fof(f404,plain,
( $false
| ~ spl0_5
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f400,f145]) ).
fof(f405,plain,
( ~ spl0_5
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f404]) ).
fof(f406,plain,
( $false
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f403,f145]) ).
fof(f407,plain,
( ~ spl0_5
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f406]) ).
fof(f408,plain,
( $false
| ~ spl0_5
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f302,f145]) ).
fof(f409,plain,
( ~ spl0_5
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f408]) ).
fof(f410,plain,
( ! [X2] : ~ big_q(X2)
| ~ spl0_7
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f291,f152]) ).
fof(f413,plain,
( $false
| ~ spl0_7
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f410,f152]) ).
fof(f414,plain,
( ~ spl0_7
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f413]) ).
fof(f419,plain,
( $false
| ~ spl0_2
| ~ spl0_23 ),
inference(resolution,[],[f277,f135]) ).
fof(f420,plain,
( ~ spl0_2
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f419]) ).
fof(f421,plain,
( $false
| ~ spl0_2
| ~ spl0_25 ),
inference(resolution,[],[f288,f135]) ).
fof(f422,plain,
( ~ spl0_2
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f421]) ).
fof(f423,plain,
( ! [X0] : big_p(f1(X0))
| ~ spl0_2
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f356,f135]) ).
fof(f424,plain,
( $false
| ~ spl0_2
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f423,f135]) ).
fof(f425,plain,
( ~ spl0_2
| ~ spl0_32 ),
inference(avatar_contradiction_clause,[],[f424]) ).
fof(f429,plain,
( ! [X0] : big_p(X0)
| ~ spl0_2
| ~ spl0_15 ),
inference(resolution,[],[f196,f135]) ).
fof(f430,plain,
( $false
| ~ spl0_2
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f429,f135]) ).
fof(f431,plain,
( ~ spl0_2
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f430]) ).
fof(f432,plain,
( $false
| ~ spl0_2
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f156,f135]) ).
fof(f433,plain,
( ~ spl0_2
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f432]) ).
fof(f434,plain,
( $false
| ~ spl0_2
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f181,f135]) ).
fof(f435,plain,
( ~ spl0_2
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f442,plain,
( $false
| ~ spl0_5
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f334,f145]) ).
fof(f443,plain,
( ~ spl0_5
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f446,plain,
( ! [X0] : ~ big_p(X0)
| ~ spl0_6
| ~ spl0_13 ),
inference(resolution,[],[f181,f148]) ).
fof(f447,plain,
( $false
| spl0_4
| ~ spl0_13 ),
inference(resolution,[],[f181,f142]) ).
fof(f448,plain,
( spl0_4
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f447]) ).
fof(f451,plain,
( $false
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f446,f181]) ).
fof(f452,plain,
( ~ spl0_6
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f451]) ).
fof(f459,plain,
( ! [X0] : ~ big_p(X0)
| ~ spl0_13
| ~ spl0_31 ),
inference(resolution,[],[f337,f181]) ).
fof(f460,plain,
( $false
| ~ spl0_13
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f459,f181]) ).
fof(f461,plain,
( ~ spl0_13
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f460]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f149]) ).
cnf(s6,plain,
( spl0_7
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_2
| spl0_7
| ~ spl0_12 ),
inference(sat_conversion,[],[f176]) ).
cnf(s7,plain,
( spl0_2
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7
| ~ spl0_12 ),
inference(rat,[],[s6]) ).
cnf(s10,plain,
( spl0_5
| ~ spl0_4
| spl0_2
| spl0_5
| spl0_6
| spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f178]) ).
cnf(s11,plain,
( spl0_2
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7
| spl0_12 ),
inference(rat,[],[s10]) ).
cnf(s35,plain,
( spl0_7
| spl0_8
| spl0_9
| spl0_13
| spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f208]) ).
cnf(s53,plain,
( spl0_2
| ~ spl0_1
| spl0_2
| spl0_3
| spl0_5
| spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f233]) ).
cnf(s54,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_5
| spl0_13
| spl0_18 ),
inference(rat,[],[s53]) ).
cnf(s60,plain,
( spl0_2
| spl0_7
| spl0_5
| spl0_2
| spl0_7
| ~ spl0_12
| spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f238]) ).
cnf(s61,plain,
( spl0_2
| spl0_5
| spl0_7
| ~ spl0_12
| spl0_13
| spl0_18 ),
inference(rat,[],[s60]) ).
cnf(s64,plain,
( spl0_2
| spl0_5
| spl0_2
| spl0_5
| spl0_7
| spl0_12
| spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f240]) ).
cnf(s65,plain,
( spl0_2
| spl0_5
| spl0_7
| spl0_12
| spl0_13
| spl0_18 ),
inference(rat,[],[s64]) ).
cnf(s75,plain,
( spl0_13
| spl0_2
| spl0_3
| spl0_5
| ~ spl0_1
| spl0_13
| ~ spl0_18 ),
inference(sat_conversion,[],[f249]) ).
cnf(s76,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_5
| spl0_13
| ~ spl0_18 ),
inference(rat,[],[s75]) ).
cnf(s85,plain,
( spl0_7
| spl0_13
| spl0_2
| spl0_7
| ~ spl0_12
| spl0_5
| spl0_13
| ~ spl0_18 ),
inference(sat_conversion,[],[f254]) ).
cnf(s86,plain,
( spl0_2
| spl0_5
| spl0_7
| ~ spl0_12
| spl0_13
| ~ spl0_18 ),
inference(rat,[],[s85]) ).
cnf(s89,plain,
( spl0_5
| spl0_13
| spl0_5
| spl0_7
| spl0_12
| spl0_2
| spl0_13
| ~ spl0_18 ),
inference(sat_conversion,[],[f256]) ).
cnf(s90,plain,
( spl0_2
| spl0_5
| spl0_7
| spl0_12
| spl0_13
| ~ spl0_18 ),
inference(rat,[],[s89]) ).
cnf(s116,plain,
( spl0_2
| spl0_2
| spl0_7
| spl0_13
| spl0_22
| spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f310]) ).
cnf(s117,plain,
( spl0_2
| spl0_7
| spl0_13
| spl0_22
| spl0_27
| spl0_28 ),
inference(rat,[],[s116]) ).
cnf(s143,plain,
( spl0_13
| spl0_7
| spl0_2
| spl0_13
| ~ spl0_22
| spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f326]) ).
cnf(s144,plain,
( spl0_2
| spl0_7
| spl0_13
| ~ spl0_22
| spl0_27
| spl0_28 ),
inference(rat,[],[s143]) ).
cnf(s153,plain,
( spl0_2
| spl0_7
| spl0_27
| ~ spl0_29
| spl0_30
| spl0_31 ),
inference(sat_conversion,[],[f345]) ).
cnf(s175,plain,
( spl0_7
| spl0_5
| spl0_7
| spl0_13
| ~ spl0_20
| spl0_23
| spl0_32 ),
inference(sat_conversion,[],[f366]) ).
cnf(s176,plain,
( spl0_5
| spl0_7
| spl0_13
| ~ spl0_20
| spl0_23
| spl0_32 ),
inference(rat,[],[s175]) ).
cnf(s179,plain,
( spl0_5
| spl0_5
| spl0_7
| spl0_13
| spl0_20
| spl0_23
| spl0_32 ),
inference(sat_conversion,[],[f368]) ).
cnf(s180,plain,
( spl0_5
| spl0_7
| spl0_13
| spl0_20
| spl0_23
| spl0_32 ),
inference(rat,[],[s179]) ).
cnf(s181,plain,
( spl0_5
| spl0_13
| ~ spl0_24
| spl0_25
| spl0_26
| spl0_32 ),
inference(sat_conversion,[],[f369]) ).
cnf(s187,plain,
( ~ spl0_7
| spl0_24 ),
inference(sat_conversion,[],[f378]) ).
cnf(s190,plain,
( ~ spl0_13
| spl0_29 ),
inference(sat_conversion,[],[f384]) ).
cnf(s191,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f386]) ).
cnf(s195,plain,
( spl0_1
| ~ spl0_7 ),
inference(sat_conversion,[],[f394]) ).
cnf(s196,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(sat_conversion,[],[f397]) ).
cnf(s197,plain,
( ~ spl0_5
| ~ spl0_14 ),
inference(sat_conversion,[],[f399]) ).
cnf(s199,plain,
( ~ spl0_5
| ~ spl0_27 ),
inference(sat_conversion,[],[f405]) ).
cnf(s200,plain,
( ~ spl0_5
| ~ spl0_9 ),
inference(sat_conversion,[],[f407]) ).
cnf(s201,plain,
( ~ spl0_5
| ~ spl0_28 ),
inference(sat_conversion,[],[f409]) ).
cnf(s203,plain,
( ~ spl0_7
| ~ spl0_26 ),
inference(sat_conversion,[],[f414]) ).
cnf(s206,plain,
( ~ spl0_2
| ~ spl0_23 ),
inference(sat_conversion,[],[f420]) ).
cnf(s207,plain,
( ~ spl0_2
| ~ spl0_25 ),
inference(sat_conversion,[],[f422]) ).
cnf(s208,plain,
( ~ spl0_2
| ~ spl0_32 ),
inference(sat_conversion,[],[f425]) ).
cnf(s210,plain,
( ~ spl0_2
| ~ spl0_15 ),
inference(sat_conversion,[],[f431]) ).
cnf(s211,plain,
( ~ spl0_2
| ~ spl0_8 ),
inference(sat_conversion,[],[f433]) ).
cnf(s212,plain,
( ~ spl0_2
| ~ spl0_13 ),
inference(sat_conversion,[],[f435]) ).
cnf(s216,plain,
( ~ spl0_5
| ~ spl0_30 ),
inference(sat_conversion,[],[f443]) ).
cnf(s217,plain,
( spl0_4
| ~ spl0_13 ),
inference(sat_conversion,[],[f448]) ).
cnf(s220,plain,
( ~ spl0_6
| ~ spl0_13 ),
inference(sat_conversion,[],[f452]) ).
cnf(s224,plain,
( ~ spl0_13
| ~ spl0_31 ),
inference(sat_conversion,[],[f461]) ).
cnf(s226,plain,
( spl0_18
| spl0_5
| spl0_7
| spl0_2
| spl0_13 ),
inference(rat,[],[s61,s65]) ).
cnf(s227,plain,
( ~ spl0_18
| spl0_5
| spl0_7
| spl0_2
| spl0_13 ),
inference(rat,[],[s86,s90]) ).
cnf(s228,plain,
( spl0_5
| spl0_13
| spl0_7
| spl0_2 ),
inference(rat,[],[s227,s226]) ).
cnf(s229,plain,
( spl0_28
| spl0_27
| spl0_7
| spl0_2
| spl0_13 ),
inference(rat,[],[s117,s144]) ).
cnf(s230,plain,
( spl0_13
| spl0_2
| spl0_7 ),
inference(rat,[],[s229,s199,s201,s228]) ).
cnf(s231,plain,
( spl0_5
| spl0_2
| spl0_7
| spl0_6
| ~ spl0_4 ),
inference(rat,[],[s7,s11]) ).
cnf(s232,plain,
( spl0_2
| spl0_7 ),
inference(rat,[],[s153,s199,s216,s231,s190,s217,s220,s224,s230]) ).
cnf(s233,plain,
( spl0_5
| spl0_32
| spl0_23
| spl0_7
| spl0_13 ),
inference(rat,[],[s176,s180]) ).
cnf(s234,plain,
spl0_7,
inference(rat,[],[s35,s197,s200,s233,s206,s208,s210,s211,s212,s232]) ).
cnf(s235,plain,
~ spl0_26,
inference(rat,[],[s203,s234]) ).
cnf(s237,plain,
~ spl0_3,
inference(rat,[],[s196,s234]) ).
cnf(s238,plain,
spl0_1,
inference(rat,[],[s195,s234]) ).
cnf(s239,plain,
~ spl0_5,
inference(rat,[],[s191,s234]) ).
cnf(s240,plain,
spl0_24,
inference(rat,[],[s187,s234]) ).
cnf(s243,plain,
( ~ spl0_13
| spl0_2 ),
inference(rat,[],[s1,s217,s220,s237,s238,s239]) ).
cnf(s244,plain,
( spl0_13
| spl0_2 ),
inference(rat,[],[s54,s76,s238,s239,s237]) ).
cnf(s245,plain,
spl0_2,
inference(rat,[],[s244,s243]) ).
cnf(s249,plain,
~ spl0_13,
inference(rat,[],[s212,s245]) ).
cnf(s252,plain,
~ spl0_32,
inference(rat,[],[s208,s245]) ).
cnf(s253,plain,
~ spl0_25,
inference(rat,[],[s207,s245]) ).
cnf(s257,plain,
$false,
inference(rat,[],[s181,s252,s240,s235,s239,s249,s253]) ).
fof(f462,plain,
$false,
inference(avatar_sat_refutation,[],[s257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN036-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:24:22 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.29 % (444404)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (444413)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3297227233:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (444410)% WARNING: option uhcvi not known.
% 0.20/0.29 % (444413) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-444404-444413"...
% 0.20/0.29 % (444409)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1077451840_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (444410)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3640576776:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (444411)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2146273532:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (444412)dis+10_1_sil=32000:sp=arity:random_seed=1503204291:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (444414)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3118149600:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (444415)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3743734987:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (444413)...printing done.
% 0.20/0.29 % (444413)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (444413)------------------------------
% 0.20/0.29 % (444413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (444413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (444413)CaDiCaL version: 2.1.3
% 0.20/0.29 % (444413)Termination reason: Refutation
% 0.20/0.29 % (444413)Time elapsed: 0.008 s
% 0.20/0.29 % (444413)Peak memory usage: 12 MB
% 0.20/0.29 % (444413)Instructions burned: 27 (million)
% 0.20/0.29 % (444404)Success in time 0.048 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------