%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO634-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 02:28:29 PM UTC 2026
% Result : Unsatisfiable 3.48s 1.13s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 32
% Syntax : Number of formulae : 135 ( 26 unt; 20 def)
% Number of atoms : 429 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 482 ( 188 ~; 274 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 14 ( 5 avg)
% Number of predicates : 22 ( 21 usr; 21 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 116 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ 'E'(f(X0),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(f(X1),s(s(s(s(s(s(s(s('0'))))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21_01) ).
fof(f3,axiom,
! [X0] : 'E'(f(X0),s(s(s(s(s(s(s(s(s(s('0'))))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11_03) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ 'E'(f(X0),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s('0'))))))))
| 'E'(f(X1),s(s(s(s(s(s('0'))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_06) ).
fof(f9,axiom,
! [X0] : 'E'(f(X0),s(s(s(s(s(s(s(s(s('0')))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17_09) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ 'E'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X3),s(s(s(s('0')))))
| ~ 'E'(f(X4),s(s('0')))
| ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X6),s(s(s('0'))))
| ~ 'E'(f(X7),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X8),s(s(s(s(s(s('0')))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X9)),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_11) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ 'E'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X5),s(s(s(s(s(s('0')))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X6)),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9_12) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ 'E'(f(X0),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f(X1),s(s(s(s(s(s(s('0')))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_14) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ 'E'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X3),s(s(s(s('0')))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X5),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X6),s(s(s(s(s(s('0')))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X7)),s(s(s('0')))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18_15) ).
fof(f17,axiom,
! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ 'E'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),s('0'))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X5),s(s('0')))
| ~ 'E'(f(X6),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X7),s(s(s('0'))))
| ~ 'E'(f(X8),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X9),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X10),'0') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_17) ).
fof(f19,axiom,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ 'E'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X3),s(s(s(s('0')))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X5),s(s(s('0'))))
| ~ 'E'(f(X6),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X7),s(s(s(s(s(s('0')))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X8)),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0_19) ).
fof(f20,axiom,
! [X2,X3,X0,X1,X4] :
( ~ 'E'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X4),s(s(s(s(s(s('0')))))))
| 'E'(f(X1),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15_20) ).
fof(f22,axiom,
! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ 'E'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),s('0'))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X5),s(s('0')))
| ~ 'E'(f(X6),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X7),s(s(s('0'))))
| ~ 'E'(f(X8),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X9),s(s(s(s(s(s('0')))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X10)),'0') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10_22) ).
fof(f25,definition,
( spl0_1
<=> ! [X10] : 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X10)),'0') ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f26,plain,
( ! [X10] : 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X10)),'0')
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,definition,
( spl0_2
<=> ! [X9] : ~ 'E'(f(X9),s(s(s(s(s(s('0'))))))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f29,plain,
( ! [X9] : ~ 'E'(f(X9),s(s(s(s(s(s('0')))))))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,definition,
( spl0_3
<=> ! [X8] : ~ 'E'(f(X8),s(s(s(s(s(s(s(s(s('0')))))))))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f32,plain,
( ! [X8] : ~ 'E'(f(X8),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,definition,
( spl0_4
<=> ! [X7] : ~ 'E'(f(X7),s(s(s('0')))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f35,plain,
( ! [X7] : ~ 'E'(f(X7),s(s(s('0'))))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,definition,
( spl0_5
<=> ! [X6] : ~ 'E'(f(X6),s(s(s(s(s(s(s('0')))))))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f38,plain,
( ! [X6] : ~ 'E'(f(X6),s(s(s(s(s(s(s('0'))))))))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,definition,
( spl0_6
<=> ! [X5] : ~ 'E'(f(X5),s(s('0'))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f41,plain,
( ! [X5] : ~ 'E'(f(X5),s(s('0')))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,definition,
( spl0_7
<=> ! [X4] : ~ 'E'(f(X4),s(s(s(s('0'))))) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f44,plain,
( ! [X4] : ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,definition,
( spl0_8
<=> ! [X3] : ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f47,plain,
( ! [X3] : ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f49,definition,
( spl0_9
<=> ! [X2] : ~ 'E'(f(X2),s('0')) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f50,plain,
( ! [X2] : ~ 'E'(f(X2),s('0'))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl0_10
<=> ! [X1] : ~ 'E'(f(X1),s(s(s(s(s('0')))))) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f53,plain,
( ! [X1] : ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,definition,
( spl0_11
<=> ! [X0] : ~ 'E'(f(X0),s(s(s(s(s(s(s(s('0'))))))))) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f56,plain,
( ! [X0] : ~ 'E'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f57,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_6
| spl0_7
| spl0_8
| spl0_9
| spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f22,f55,f52,f49,f46,f43,f40,f37,f34,f31,f28,f25]) ).
fof(f59,definition,
( spl0_12
<=> ! [X1] :
( ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(f(X1),s(s(s(s(s('0')))))) ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f60,plain,
( ! [X1] :
( ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(f(X1),s(s(s(s(s('0')))))) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( spl0_2
| spl0_3
| spl0_5
| spl0_12
| spl0_11 ),
inference(avatar_split_clause,[],[f20,f55,f59,f37,f31,f28]) ).
fof(f63,definition,
( spl0_13
<=> ! [X8] : 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X8)),s(s('0'))) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f64,plain,
( ! [X8] : 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X8)),s(s('0')))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( spl0_13
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_7
| spl0_8
| spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f19,f55,f52,f46,f43,f37,f34,f31,f28,f63]) ).
fof(f67,definition,
( spl0_14
<=> ! [X10] : ~ 'E'(f(X10),'0') ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f68,plain,
( ! [X10] : ~ 'E'(f(X10),'0')
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
( spl0_14
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_6
| spl0_7
| spl0_8
| spl0_9
| spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f17,f55,f52,f49,f46,f43,f40,f37,f34,f31,f28,f67]) ).
fof(f71,definition,
( spl0_15
<=> ! [X7] : 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X7)),s(s(s('0')))) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f72,plain,
( ! [X7] : 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X7)),s(s(s('0'))))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( spl0_15
| spl0_2
| spl0_3
| spl0_5
| spl0_7
| spl0_8
| spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f15,f55,f52,f46,f43,f37,f31,f28,f71]) ).
fof(f75,definition,
( spl0_16
<=> ! [X1] :
( ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(f(X1),s(s(s(s(s(s(s('0')))))))) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f76,plain,
( ! [X1] :
( ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(f(X1),s(s(s(s(s(s(s('0')))))))) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( spl0_11
| spl0_16
| spl0_3 ),
inference(avatar_split_clause,[],[f14,f31,f75,f55]) ).
fof(f79,definition,
( spl0_17
<=> ! [X6] : 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X6)),s(s(s(s('0'))))) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f80,plain,
( ! [X6] : 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X6)),s(s(s(s('0')))))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( spl0_17
| spl0_2
| spl0_3
| spl0_5
| spl0_8
| spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f12,f55,f52,f46,f37,f31,f28,f79]) ).
fof(f83,definition,
( spl0_18
<=> ! [X9] : 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X9)),s('0')) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f84,plain,
( ! [X9] : 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X9)),s('0'))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( spl0_18
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_6
| spl0_7
| spl0_8
| spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f11,f55,f52,f46,f43,f40,f37,f34,f31,f28,f83]) ).
fof(f87,definition,
( spl0_19
<=> ! [X1] :
( ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(f(X1),s(s(s(s(s(s('0'))))))) ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f88,plain,
( ! [X1] :
( ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(f(X1),s(s(s(s(s(s('0'))))))) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f89,plain,
( spl0_5
| spl0_11
| spl0_19
| spl0_3 ),
inference(avatar_split_clause,[],[f6,f31,f87,f55,f37]) ).
fof(f91,definition,
( spl0_20
<=> ! [X1] :
( ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(f(X1),s(s(s(s(s(s(s(s('0'))))))))) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f92,plain,
( ! [X1] :
( ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(f(X1),s(s(s(s(s(s(s(s('0'))))))))) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f93,plain,
( spl0_20
| spl0_3 ),
inference(avatar_split_clause,[],[f1,f31,f91]) ).
fof(f94,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f32,f9]) ).
fof(f95,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f94]) ).
fof(f96,plain,
( ! [X0] : 'E'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| ~ spl0_20 ),
inference(resolution,[],[f3,f92]) ).
fof(f97,plain,
( $false
| ~ spl0_11
| ~ spl0_20 ),
inference(resolution,[],[f96,f56]) ).
fof(f98,plain,
( ~ spl0_11
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f97]) ).
fof(f99,plain,
( ! [X0] : 'E'(f(X0),s(s(s(s(s(s(s('0'))))))))
| ~ spl0_16 ),
inference(resolution,[],[f76,f3]) ).
fof(f100,plain,
( $false
| ~ spl0_5
| ~ spl0_16 ),
inference(resolution,[],[f99,f38]) ).
fof(f101,plain,
( ~ spl0_5
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f102,plain,
( $false
| ~ spl0_8 ),
inference(resolution,[],[f47,f3]) ).
fof(f103,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f102]) ).
fof(f104,plain,
( ! [X0] : 'E'(f(X0),s(s(s(s(s('0'))))))
| ~ spl0_12 ),
inference(resolution,[],[f60,f3]) ).
fof(f105,plain,
( ! [X0] : 'E'(f(X0),s(s(s(s(s(s('0')))))))
| ~ spl0_19 ),
inference(resolution,[],[f88,f3]) ).
fof(f106,plain,
( $false
| ~ spl0_2
| ~ spl0_19 ),
inference(resolution,[],[f105,f29]) ).
fof(f107,plain,
( ~ spl0_2
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f106]) ).
fof(f108,plain,
( $false
| ~ spl0_10
| ~ spl0_12 ),
inference(resolution,[],[f53,f104]) ).
fof(f109,plain,
( ~ spl0_10
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f108]) ).
fof(f110,plain,
( $false
| ~ spl0_7
| ~ spl0_17 ),
inference(resolution,[],[f80,f44]) ).
fof(f111,plain,
( ~ spl0_7
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f110]) ).
fof(f112,plain,
( $false
| ~ spl0_1
| ~ spl0_14 ),
inference(resolution,[],[f26,f68]) ).
fof(f113,plain,
( ~ spl0_1
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f112]) ).
fof(f114,plain,
( $false
| ~ spl0_4
| ~ spl0_15 ),
inference(resolution,[],[f72,f35]) ).
fof(f115,plain,
( ~ spl0_4
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f114]) ).
fof(f116,plain,
( $false
| ~ spl0_6
| ~ spl0_13 ),
inference(resolution,[],[f41,f64]) ).
fof(f117,plain,
( ~ spl0_6
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f116]) ).
fof(f118,plain,
( $false
| ~ spl0_9
| ~ spl0_18 ),
inference(resolution,[],[f50,f84]) ).
fof(f119,plain,
( ~ spl0_9
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f118]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_6
| spl0_7
| spl0_8
| spl0_9
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f57]) ).
cnf(s2,plain,
( spl0_2
| spl0_3
| spl0_5
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
( spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_7
| spl0_8
| spl0_10
| spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f65]) ).
cnf(s4,plain,
( spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_6
| spl0_7
| spl0_8
| spl0_9
| spl0_10
| spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
( spl0_2
| spl0_3
| spl0_5
| spl0_7
| spl0_8
| spl0_10
| spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
( spl0_3
| spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f77]) ).
cnf(s7,plain,
( spl0_2
| spl0_3
| spl0_5
| spl0_8
| spl0_10
| spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f81]) ).
cnf(s8,plain,
( spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_6
| spl0_7
| spl0_8
| spl0_10
| spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f85]) ).
cnf(s9,plain,
( spl0_3
| spl0_5
| spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f89]) ).
cnf(s10,plain,
( spl0_3
| spl0_20 ),
inference(sat_conversion,[],[f93]) ).
cnf(s11,plain,
~ spl0_3,
inference(sat_conversion,[],[f95]) ).
cnf(s12,plain,
( ~ spl0_11
| ~ spl0_20 ),
inference(sat_conversion,[],[f98]) ).
cnf(s13,plain,
( ~ spl0_5
| ~ spl0_16 ),
inference(sat_conversion,[],[f101]) ).
cnf(s14,plain,
~ spl0_8,
inference(sat_conversion,[],[f103]) ).
cnf(s15,plain,
( ~ spl0_2
| ~ spl0_19 ),
inference(sat_conversion,[],[f107]) ).
cnf(s16,plain,
( ~ spl0_10
| ~ spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s17,plain,
( ~ spl0_7
| ~ spl0_17 ),
inference(sat_conversion,[],[f111]) ).
cnf(s18,plain,
( ~ spl0_1
| ~ spl0_14 ),
inference(sat_conversion,[],[f113]) ).
cnf(s19,plain,
( ~ spl0_4
| ~ spl0_15 ),
inference(sat_conversion,[],[f115]) ).
cnf(s20,plain,
( ~ spl0_6
| ~ spl0_13 ),
inference(sat_conversion,[],[f117]) ).
cnf(s21,plain,
( ~ spl0_9
| ~ spl0_18 ),
inference(sat_conversion,[],[f119]) ).
cnf(s22,plain,
spl0_20,
inference(rat,[],[s10,s11]) ).
cnf(s23,plain,
~ spl0_11,
inference(rat,[],[s12,s22]) ).
cnf(s24,plain,
( spl0_5
| spl0_19 ),
inference(rat,[],[s9,s23,s11]) ).
cnf(s25,plain,
( spl0_2
| spl0_4
| spl0_5
| spl0_6
| spl0_7
| spl0_10
| spl0_18 ),
inference(rat,[],[s8,s23,s14,s11]) ).
cnf(s26,plain,
( spl0_2
| spl0_5
| spl0_10
| spl0_17 ),
inference(rat,[],[s7,s23,s14,s11]) ).
cnf(s27,plain,
spl0_16,
inference(rat,[],[s6,s23,s11]) ).
cnf(s28,plain,
~ spl0_5,
inference(rat,[],[s13,s27]) ).
cnf(s29,plain,
spl0_19,
inference(rat,[],[s24,s28]) ).
cnf(s30,plain,
~ spl0_2,
inference(rat,[],[s15,s29]) ).
cnf(s31,plain,
( spl0_7
| spl0_10
| spl0_15 ),
inference(rat,[],[s5,s23,s14,s28,s11,s30]) ).
cnf(s32,plain,
( spl0_4
| spl0_6
| spl0_7
| spl0_9
| spl0_10
| spl0_14 ),
inference(rat,[],[s4,s23,s14,s28,s11,s30]) ).
cnf(s33,plain,
( spl0_4
| spl0_7
| spl0_10
| spl0_13 ),
inference(rat,[],[s3,s23,s14,s28,s11,s30]) ).
cnf(s34,plain,
spl0_12,
inference(rat,[],[s2,s23,s28,s11,s30]) ).
cnf(s35,plain,
~ spl0_10,
inference(rat,[],[s16,s34]) ).
cnf(s36,plain,
spl0_17,
inference(rat,[],[s26,s30,s28,s35]) ).
cnf(s37,plain,
~ spl0_7,
inference(rat,[],[s17,s36]) ).
cnf(s38,plain,
spl0_15,
inference(rat,[],[s31,s35,s37]) ).
cnf(s39,plain,
~ spl0_4,
inference(rat,[],[s19,s38]) ).
cnf(s40,plain,
spl0_13,
inference(rat,[],[s33,s37,s35,s39]) ).
cnf(s41,plain,
~ spl0_6,
inference(rat,[],[s20,s40]) ).
cnf(s42,plain,
spl0_18,
inference(rat,[],[s25,s39,s35,s37,s30,s28,s41]) ).
cnf(s43,plain,
~ spl0_9,
inference(rat,[],[s21,s42]) ).
cnf(s44,plain,
spl0_14,
inference(rat,[],[s32,s41,s35,s39,s37,s43]) ).
cnf(s45,plain,
~ spl0_1,
inference(rat,[],[s18,s44]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s1,s23,s35,s43,s14,s37,s41,s28,s39,s11,s30,s45]) ).
fof(f120,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO634-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 17:59:25 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.48/1.13 % (8880)Input is clausal, will run a generic CNF schedule.
% 3.48/1.13 % (8889)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1984796815:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.48/1.13 % (8889)Refutation not found, incomplete strategy
% 3.48/1.13 % (8889)------------------------------
% 3.48/1.13 % (8889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.13 % (8889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.13 % (8889)CaDiCaL version: 2.1.3
% 3.48/1.13 % (8889)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.13 % (8889)Time elapsed: 0.0000 s
% 3.48/1.13 % (8889)Peak memory usage: 86 MB
% 3.48/1.13 % (8885)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=426997060:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.48/1.13 % (8888)lrs+10_1_sil=8000:sp=occurrence:random_seed=3932941557:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.48/1.13 % (8887)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=244420204:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.48/1.13 % (8886)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=559330155:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.48/1.13 % (8888)Refutation not found, incomplete strategy
% 3.48/1.13 % (8888)------------------------------
% 3.48/1.13 % (8888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.13 % (8888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.13 % (8888)CaDiCaL version: 2.1.3
% 3.48/1.13 % (8888)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.13 % (8888)Time elapsed: 0.001 s
% 3.48/1.13 % (8888)Peak memory usage: 86 MB
% 3.48/1.13 % (8891)dis-21_1_sil=8000:lcm=predicate:random_seed=2646381319: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)
% 3.48/1.13 % (8891)First to succeed.
% 3.48/1.13 % (8891)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8880"
% 3.48/1.13 % (8890)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3432720778:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.48/1.13 % (8890)Also succeeded, but the first one will report.
% 3.48/1.13 % (8889)------------------------------
% 3.48/1.13 % (8889)------------------------------
% 3.48/1.13 % (8899)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2295912258:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.48/1.13 % (8899)Refutation not found, incomplete strategy
% 3.48/1.13 % (8899)------------------------------
% 3.48/1.13 % (8899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.13 % (8899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.13 % (8899)CaDiCaL version: 2.1.3
% 3.48/1.13 % (8899)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.13 % (8899)Time elapsed: 0.0000 s
% 3.48/1.13 % (8899)Peak memory usage: 86 MB
% 3.48/1.13 % (8888)------------------------------
% 3.48/1.13 % (8888)------------------------------
% 3.48/1.13 % (8891)Refutation found. Thanks to Tanya!
% 3.48/1.13 % SZS status Unsatisfiable for theBenchmark
% 3.48/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.33 % (8891)------------------------------
% 3.80/1.33 % (8891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.33 % (8891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.33 % (8891)CaDiCaL version: 2.1.3
% 3.80/1.33 % (8891)Termination reason: Refutation
% 3.80/1.33 % (8891)Time elapsed: 0.005 s
% 3.80/1.33 % (8891)Peak memory usage: 89 MB
% 3.80/1.33 % (8891)Instructions burned: 6 (million)
% 3.80/1.33 % (8891)------------------------------
% 3.80/1.33 % (8891)------------------------------
% 3.80/1.33 % (8880)Success in time 0.471 s
% 3.80/1.33 % Vampire exiting
%------------------------------------------------------------------------------