%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN056^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Wed Sep 30 08:41:39 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 109 ( 11 unt; 0 typ; 14 def)
% Number of atoms : 798 ( 188 equ; 0 cnn)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 691 ( 182 ~; 162 |; 62 &; 224 @)
% ( 13 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 20 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 77 !; 33 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cR: $i > $o ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_2,type,
cS: $i > $o ).
thf(func_def_3,type,
cQ: $i > $o ).
thf(func_def_7,type,
sP0: $o ).
thf(f1,conjecture,
( ( ( ? [X0: $i] : ( cQ @ X0 )
=> ? [X0: $i] : ( cP @ X0 ) )
& ! [X0: $i,X1: $i] :
( ( ( cP @ X0 )
& ( cQ @ X1 ) )
=> ( ( ( cR @ X0 )
=> ( cS @ X1 ) )
& ( ( cS @ X1 )
=> ( cR @ X0 ) ) ) )
& ( ? [X0: $i] : ( cP @ X0 )
=> ? [X0: $i] : ( cQ @ X0 ) ) )
=> ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
=> ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) ) )
& ( ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) )
=> ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPELL26) ).
thf(f2,negated_conjecture,
~ ( ( ( ? [X0: $i] : ( cQ @ X0 )
=> ? [X0: $i] : ( cP @ X0 ) )
& ! [X0: $i,X1: $i] :
( ( ( cP @ X0 )
& ( cQ @ X1 ) )
=> ( ( ( cR @ X0 )
=> ( cS @ X1 ) )
& ( ( cS @ X1 )
=> ( cR @ X0 ) ) ) )
& ( ? [X0: $i] : ( cP @ X0 )
=> ? [X0: $i] : ( cQ @ X0 ) ) )
=> ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
=> ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) ) )
& ( ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) )
=> ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ? [X0: $i] : ( cQ @ X0 )
=> ? [X1: $i] : ( cP @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( ( cP @ X2 )
& ( cQ @ X3 ) )
=> ( ( ( cR @ X2 )
=> ( cS @ X3 ) )
& ( ( cS @ X3 )
=> ( cR @ X2 ) ) ) )
& ( ? [X4: $i] : ( cP @ X4 )
=> ? [X5: $i] : ( cQ @ X5 ) ) )
=> ( ( ! [X6: $i] :
( ( cP @ X6 )
=> ( cR @ X6 ) )
=> ! [X7: $i] :
( ( cQ @ X7 )
=> ( cS @ X7 ) ) )
& ( ! [X8: $i] :
( ( cQ @ X8 )
=> ( cS @ X8 ) )
=> ! [X9: $i] :
( ( cP @ X9 )
=> ( cR @ X9 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
=> ? [X5: $i] :
( $true
= ( cQ @ X5 ) ) )
& ( ? [X0: $i] :
( ( cQ @ X0 )
= $true )
=> ? [X1: $i] :
( ( cP @ X1 )
= $true ) )
& ! [X2: $i,X3: $i] :
( ( ( ( cQ @ X3 )
= $true )
& ( $true
= ( cP @ X2 ) ) )
=> ( ( ( $true
= ( cS @ X3 ) )
=> ( $true
= ( cR @ X2 ) ) )
& ( ( $true
= ( cR @ X2 ) )
=> ( $true
= ( cS @ X3 ) ) ) ) ) )
=> ( ( ! [X8: $i] :
( ( $true
= ( cQ @ X8 ) )
=> ( ( cS @ X8 )
= $true ) )
=> ! [X9: $i] :
( ( $true
= ( cP @ X9 ) )
=> ( $true
= ( cR @ X9 ) ) ) )
& ( ! [X6: $i] :
( ( $true
= ( cP @ X6 ) )
=> ( $true
= ( cR @ X6 ) ) )
=> ! [X7: $i] :
( ( $true
= ( cQ @ X7 ) )
=> ( $true
= ( cS @ X7 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( ! [X8: $i] :
( ( ( cS @ X8 )
= $true )
| ( $true
!= ( cQ @ X8 ) ) )
& ? [X9: $i] :
( ( $true
= ( cP @ X9 ) )
& ( $true
!= ( cR @ X9 ) ) ) )
| ( ! [X6: $i] :
( ( $true
!= ( cP @ X6 ) )
| ( $true
= ( cR @ X6 ) ) )
& ? [X7: $i] :
( ( $true
= ( cQ @ X7 ) )
& ( $true
!= ( cS @ X7 ) ) ) ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
!= $true )
| ? [X5: $i] :
( $true
= ( cQ @ X5 ) ) )
& ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cQ @ X0 )
!= $true ) )
& ! [X2: $i,X3: $i] :
( ( ( ( $true
= ( cS @ X3 ) )
| ( $true
!= ( cR @ X2 ) ) )
& ( ( $true
!= ( cS @ X3 ) )
| ( $true
= ( cR @ X2 ) ) ) )
| ( ( cQ @ X3 )
!= $true )
| ( $true
!= ( cP @ X2 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X3: $i,X2: $i] :
( ( ( cQ @ X3 )
!= $true )
| ( $true
!= ( cP @ X2 ) )
| ( ( ( $true
= ( cS @ X3 ) )
| ( $true
!= ( cR @ X2 ) ) )
& ( ( $true
!= ( cS @ X3 ) )
| ( $true
= ( cR @ X2 ) ) ) ) )
& ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cQ @ X0 )
!= $true ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
!= $true )
| ? [X5: $i] :
( $true
= ( cQ @ X5 ) ) )
& ( ( ! [X8: $i] :
( ( ( cS @ X8 )
= $true )
| ( $true
!= ( cQ @ X8 ) ) )
& ? [X9: $i] :
( ( $true
= ( cP @ X9 ) )
& ( $true
!= ( cR @ X9 ) ) ) )
| ( ! [X6: $i] :
( ( $true
!= ( cP @ X6 ) )
| ( $true
= ( cR @ X6 ) ) )
& ? [X7: $i] :
( ( $true
= ( cQ @ X7 ) )
& ( $true
!= ( cS @ X7 ) ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,definition,
( ( ! [X6: $i] :
( ( $true
!= ( cP @ X6 ) )
| ( $true
= ( cR @ X6 ) ) )
& ? [X7: $i] :
( ( $true
= ( cQ @ X7 ) )
& ( $true
!= ( cS @ X7 ) ) ) )
| ( sP0 != $true ) ),
introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction]) ).
thf(f8,plain,
( ! [X3: $i,X2: $i] :
( ( ( cQ @ X3 )
!= $true )
| ( $true
!= ( cP @ X2 ) )
| ( ( ( $true
= ( cS @ X3 ) )
| ( $true
!= ( cR @ X2 ) ) )
& ( ( $true
!= ( cS @ X3 ) )
| ( $true
= ( cR @ X2 ) ) ) ) )
& ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cQ @ X0 )
!= $true ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
!= $true )
| ? [X5: $i] :
( $true
= ( cQ @ X5 ) ) )
& ( ( ! [X8: $i] :
( ( ( cS @ X8 )
= $true )
| ( $true
!= ( cQ @ X8 ) ) )
& ? [X9: $i] :
( ( $true
= ( cP @ X9 ) )
& ( $true
!= ( cR @ X9 ) ) ) )
| ( sP0 = $true ) ) ),
inference(definition_folding,[],[f6,f7]) ).
thf(f9,plain,
( ( ! [X6: $i] :
( ( $true
!= ( cP @ X6 ) )
| ( $true
= ( cR @ X6 ) ) )
& ? [X7: $i] :
( ( $true
= ( cQ @ X7 ) )
& ( $true
!= ( cS @ X7 ) ) ) )
| ( sP0 != $true ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cR @ X0 )
= $true ) )
& ? [X1: $i] :
( ( ( cQ @ X1 )
= $true )
& ( ( cS @ X1 )
!= $true ) ) )
| ( sP0 != $true ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cR @ X0 )
= $true ) )
& ( $true
= ( cQ @ sK1 ) )
& ( $true
!= ( cS @ sK1 ) ) )
| ( sP0 != $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1)],[f10]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cP @ X1 )
!= $true )
| ( ( ( ( cS @ X0 )
= $true )
| ( $true
!= ( cR @ X1 ) ) )
& ( ( ( cS @ X0 )
!= $true )
| ( $true
= ( cR @ X1 ) ) ) ) )
& ( ? [X2: $i] :
( $true
= ( cP @ X2 ) )
| ! [X3: $i] :
( ( cQ @ X3 )
!= $true ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
!= $true )
| ? [X5: $i] :
( $true
= ( cQ @ X5 ) ) )
& ( ( ! [X6: $i] :
( ( $true
= ( cS @ X6 ) )
| ( $true
!= ( cQ @ X6 ) ) )
& ? [X7: $i] :
( ( $true
= ( cP @ X7 ) )
& ( $true
!= ( cR @ X7 ) ) ) )
| ( sP0 = $true ) ) ),
inference(rectify,[],[f8]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cP @ X1 )
!= $true )
| ( ( ( ( cS @ X0 )
= $true )
| ( $true
!= ( cR @ X1 ) ) )
& ( ( ( cS @ X0 )
!= $true )
| ( $true
= ( cR @ X1 ) ) ) ) )
& ( ( $true
= ( cP @ sK2 ) )
| ! [X3: $i] :
( ( cQ @ X3 )
!= $true ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
!= $true )
| ( $true
= ( cQ @ sK3 ) ) )
& ( ( ! [X6: $i] :
( ( $true
= ( cS @ X6 ) )
| ( $true
!= ( cQ @ X6 ) ) )
& ( $true
= ( cP @ sK4 ) )
& ( ( cR @ sK4 )
!= $true ) )
| ( sP0 = $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2),skolemize(X5,sK3),skolemize(X7,sK4)],[f12]) ).
thf(f14,plain,
( ( $true
!= ( cS @ sK1 ) )
| ( sP0 != $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( ( $true
= ( cQ @ sK1 ) )
| ( sP0 != $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( sP0 != $true )
| ( ( cR @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f17,plain,
( ( ( cR @ sK4 )
!= $true )
| ( sP0 = $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( ( $true
= ( cP @ sK4 ) )
| ( sP0 = $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
! [X6: $i] :
( ( $true
= ( cS @ X6 ) )
| ( $true
!= ( cQ @ X6 ) )
| ( sP0 = $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
! [X4: $i] :
( ( $true
= ( cQ @ sK3 ) )
| ( ( cP @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
! [X3: $i] :
( ( $true
= ( cP @ sK2 ) )
| ( ( cQ @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f22,plain,
! [X0: $i,X1: $i] :
( ( ( cP @ X1 )
!= $true )
| ( $true
= ( cR @ X1 ) )
| ( ( cS @ X0 )
!= $true )
| ( ( cQ @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f23,plain,
! [X0: $i,X1: $i] :
( ( ( cS @ X0 )
= $true )
| ( ( cQ @ X0 )
!= $true )
| ( $true
!= ( cR @ X1 ) )
| ( ( cP @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f27,definition,
( spl5_1
<=> ( sP0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f31,definition,
( spl5_2
<=> ! [X6: $i] :
( ( $true
= ( cS @ X6 ) )
| ( $true
!= ( cQ @ X6 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f32,plain,
( ! [X6: $i] :
( ( $true
!= ( cQ @ X6 ) )
| ( $true
= ( cS @ X6 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f33,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f19,f31,f27]) ).
thf(f35,definition,
( spl5_3
<=> ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cR @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f36,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cR @ X0 )
= $true ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f37,plain,
( ~ spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f16,f35,f27]) ).
thf(f39,definition,
( spl5_4
<=> ! [X0: $i] :
( ( ( cS @ X0 )
!= $true )
| ( ( cQ @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f40,plain,
( ! [X0: $i] :
( ( ( cS @ X0 )
!= $true )
| ( ( cQ @ X0 )
!= $true ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f41,plain,
( spl5_4
| spl5_3 ),
inference(avatar_split_clause,[],[f22,f35,f39]) ).
thf(f43,definition,
( spl5_5
<=> ( ( cR @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f45,plain,
( ( ( cR @ sK4 )
!= $true )
| spl5_5 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f46,plain,
( spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f17,f43,f27]) ).
thf(f48,definition,
( spl5_6
<=> ( $true
= ( cP @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
= ( cP @ sK4 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f51,plain,
( spl5_1
| spl5_6 ),
inference(avatar_split_clause,[],[f18,f48,f27]) ).
thf(f53,definition,
( spl5_7
<=> ( $true
= ( cS @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f55,plain,
( ( $true
!= ( cS @ sK1 ) )
| spl5_7 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f56,plain,
( ~ spl5_7
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f14,f27,f53]) ).
thf(f58,definition,
( spl5_8
<=> ! [X1: $i] :
( ( $true
!= ( cR @ X1 ) )
| ( ( cP @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f59,plain,
( ! [X1: $i] :
( ( ( cP @ X1 )
!= $true )
| ( $true
!= ( cR @ X1 ) ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f60,plain,
( spl5_2
| spl5_8 ),
inference(avatar_split_clause,[],[f23,f58,f31]) ).
thf(f62,definition,
( spl5_9
<=> ! [X4: $i] :
( ( cP @ X4 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f63,plain,
( ! [X4: $i] :
( ( cP @ X4 )
!= $true )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f65,definition,
( spl5_10
<=> ( $true
= ( cQ @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
thf(f67,plain,
( ( $true
= ( cQ @ sK3 ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f68,plain,
( spl5_9
| spl5_10 ),
inference(avatar_split_clause,[],[f20,f65,f62]) ).
thf(f70,definition,
( spl5_11
<=> ( $true
= ( cQ @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
thf(f72,plain,
( ( $true
= ( cQ @ sK1 ) )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f73,plain,
( ~ spl5_1
| spl5_11 ),
inference(avatar_split_clause,[],[f15,f70,f27]) ).
thf(f75,definition,
( spl5_12
<=> ! [X3: $i] :
( ( cQ @ X3 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
thf(f76,plain,
( ! [X3: $i] :
( ( cQ @ X3 )
!= $true )
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f75]) ).
thf(f78,definition,
( spl5_13
<=> ( $true
= ( cP @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_13])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
= ( cP @ sK2 ) )
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f81,plain,
( spl5_12
| spl5_13 ),
inference(avatar_split_clause,[],[f21,f78,f75]) ).
thf(f82,plain,
( $false
| ~ spl5_6
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f50,f63]) ).
thf(f83,plain,
( ~ spl5_6
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[],[f82]) ).
thf(f84,plain,
( $false
| ~ spl5_10
| ~ spl5_12 ),
inference(forward_subsumption_resolution,[],[f67,f76]) ).
thf(f85,plain,
( ~ spl5_10
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f84]) ).
thf(f88,plain,
( ( ( cR @ sK4 )
= $true )
| ( $true != $true )
| ~ spl5_3
| ~ spl5_6 ),
inference(constrained_superposition,[],[f36,f50]) ).
thf(f90,plain,
( ( ( cR @ sK4 )
= $true )
| ~ spl5_3
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f88]) ).
thf(f92,plain,
( $false
| ~ spl5_3
| spl5_5
| ~ spl5_6 ),
inference(forward_subsumption_resolution,[],[f90,f45]) ).
thf(f93,plain,
( ~ spl5_3
| spl5_5
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f92]) ).
thf(f94,plain,
( ( $true != $true )
| ( $true
= ( cS @ sK1 ) )
| ~ spl5_2
| ~ spl5_11 ),
inference(constrained_superposition,[],[f32,f72]) ).
thf(f95,plain,
( ( $true
= ( cS @ sK1 ) )
| ~ spl5_2
| ~ spl5_11 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f96,plain,
( $false
| ~ spl5_2
| spl5_7
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f95,f55]) ).
thf(f97,plain,
( ~ spl5_2
| spl5_7
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f96]) ).
thf(f98,plain,
( ! [X1: $i] :
( ( cP @ X1 )
!= $true )
| ~ spl5_3
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f59,f36]) ).
thf(f99,plain,
( spl5_9
| ~ spl5_3
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f98,f58,f35,f62]) ).
thf(f100,plain,
( ( $true != $true )
| ~ spl5_9
| ~ spl5_13 ),
inference(constrained_superposition,[],[f63,f80]) ).
thf(f101,plain,
( $false
| ~ spl5_9
| ~ spl5_13 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f102,plain,
( ~ spl5_9
| ~ spl5_13 ),
inference(avatar_contradiction_clause,[],[f101]) ).
thf(f103,plain,
( ( $true != $true )
| ~ spl5_11
| ~ spl5_12 ),
inference(constrained_superposition,[],[f76,f72]) ).
thf(f104,plain,
( $false
| ~ spl5_11
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f105,plain,
( ~ spl5_11
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f104]) ).
thf(f107,plain,
( ! [X6: $i] :
( $true
!= ( cQ @ X6 ) )
| ~ spl5_2
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f32,f40]) ).
thf(f108,plain,
( spl5_12
| ~ spl5_2
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f107,f39,f31,f75]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( ~ spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
( spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f41]) ).
cnf(s4,plain,
( spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f46]) ).
cnf(s5,plain,
( spl5_1
| spl5_6 ),
inference(sat_conversion,[],[f51]) ).
cnf(s6,plain,
( ~ spl5_1
| ~ spl5_7 ),
inference(sat_conversion,[],[f56]) ).
cnf(s7,plain,
( spl5_2
| spl5_8 ),
inference(sat_conversion,[],[f60]) ).
cnf(s8,plain,
( spl5_9
| spl5_10 ),
inference(sat_conversion,[],[f68]) ).
cnf(s9,plain,
( ~ spl5_1
| spl5_11 ),
inference(sat_conversion,[],[f73]) ).
cnf(s10,plain,
( spl5_12
| spl5_13 ),
inference(sat_conversion,[],[f81]) ).
cnf(s11,plain,
( ~ spl5_6
| ~ spl5_9 ),
inference(sat_conversion,[],[f83]) ).
cnf(s12,plain,
( ~ spl5_10
| ~ spl5_12 ),
inference(sat_conversion,[],[f85]) ).
cnf(s13,plain,
( ~ spl5_3
| spl5_5
| ~ spl5_6 ),
inference(sat_conversion,[],[f93]) ).
cnf(s14,plain,
( ~ spl5_2
| spl5_7
| ~ spl5_11 ),
inference(sat_conversion,[],[f97]) ).
cnf(s15,plain,
( ~ spl5_3
| ~ spl5_8
| spl5_9 ),
inference(sat_conversion,[],[f99]) ).
cnf(s16,plain,
( ~ spl5_9
| ~ spl5_13 ),
inference(sat_conversion,[],[f102]) ).
cnf(s17,plain,
( ~ spl5_11
| ~ spl5_12 ),
inference(sat_conversion,[],[f105]) ).
cnf(s18,plain,
( ~ spl5_2
| ~ spl5_4
| spl5_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s19,plain,
spl5_1,
inference(rat,[],[s18,s12,s3,s8,s13,s11,s1,s4,s5]) ).
cnf(s20,plain,
spl5_11,
inference(rat,[],[s9,s19]) ).
cnf(s21,plain,
~ spl5_7,
inference(rat,[],[s6,s19]) ).
cnf(s22,plain,
spl5_3,
inference(rat,[],[s2,s19]) ).
cnf(s23,plain,
~ spl5_12,
inference(rat,[],[s17,s20]) ).
cnf(s24,plain,
~ spl5_2,
inference(rat,[],[s14,s20,s21]) ).
cnf(s25,plain,
spl5_13,
inference(rat,[],[s10,s23]) ).
cnf(s26,plain,
spl5_8,
inference(rat,[],[s7,s24]) ).
cnf(s27,plain,
~ spl5_9,
inference(rat,[],[s16,s25]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s15,s22,s27,s26]) ).
thf(f109,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN056^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n010.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 16:14:33 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.26 % (3061446)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.26 % (3061453)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=757202319:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.07/0.26 % (3061453)Instruction limit reached!
% 0.07/0.26 % (3061453)------------------------------
% 0.07/0.26 % (3061453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (3061453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (3061453)CaDiCaL version: 2.1.3
% 0.07/0.26 % (3061453)Termination reason: Instruction limit
% 0.07/0.26 % (3061453)Time elapsed: 0.002 s
% 0.07/0.26 % (3061453)Peak memory usage: 12 MB
% 0.07/0.26 % (3061453)Instructions burned: 3 (million)
% 0.07/0.26 % (3061452)lrs+10_16_si=on:nwc=1.5:random_seed=3178134323:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.07/0.26 % (3061452) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3061446-3061452"...
% 0.07/0.26 % (3061456)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3663528179:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.07/0.26 % (3061459)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1304122096:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.07/0.26 % (3061452)...printing done.
% 0.07/0.26 % (3061459)Instruction limit reached!
% 0.07/0.26 % (3061459)------------------------------
% 0.07/0.26 % (3061459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (3061459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (3061459)CaDiCaL version: 2.1.3
% 0.07/0.26 % (3061459)Termination reason: Instruction limit
% 0.07/0.26 % (3061459)Termination phase: Saturation
% 0.07/0.26 % (3061459)Time elapsed: 0.002 s
% 0.07/0.26 % (3061459)Peak memory usage: 12 MB
% 0.07/0.26 % (3061459)Instructions burned: 4 (million)
% 0.07/0.26 % (3061457)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.07/0.26 % (3061457)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.07/0.26 % (3061452)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (3061452)------------------------------
% 0.07/0.26 % (3061452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (3061452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (3061452)CaDiCaL version: 2.1.3
% 0.07/0.26 % (3061452)Termination reason: Refutation
% 0.07/0.26 % (3061452)Time elapsed: 0.005 s
% 0.07/0.26 % (3061452)Peak memory usage: 13 MB
% 0.07/0.26 % (3061452)Instructions burned: 7 (million)
% 0.07/0.26 % (3061446)Success in time 0.039 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------