%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n005.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 08:41:50 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 105 ( 8 unt; 0 typ; 14 def)
% Number of atoms : 785 ( 186 equ; 0 cnn)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 681 ( 177 ~; 158 |; 62 &; 223 @)
% ( 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,X1: $i] :
( ( ( cQ @ X1 )
& ( cP @ X0 ) )
=> ( ( ( cS @ X1 )
=> ( cR @ X0 ) )
& ( ( cR @ X0 )
=> ( cS @ X1 ) ) ) )
& ( ? [X0: $i] : ( cQ @ X0 )
=> ? [X0: $i] : ( cP @ X0 ) )
& ( ? [X0: $i] : ( cP @ X0 )
=> ? [X0: $i] : ( cQ @ X0 ) ) )
=> ( ( ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) )
=> ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
=> ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPELL26) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i,X1: $i] :
( ( ( cQ @ X1 )
& ( cP @ X0 ) )
=> ( ( ( cS @ X1 )
=> ( cR @ X0 ) )
& ( ( cR @ X0 )
=> ( cS @ X1 ) ) ) )
& ( ? [X0: $i] : ( cQ @ X0 )
=> ? [X0: $i] : ( cP @ X0 ) )
& ( ? [X0: $i] : ( cP @ X0 )
=> ? [X0: $i] : ( cQ @ X0 ) ) )
=> ( ( ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) )
=> ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
=> ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( ( cQ @ X1 )
& ( cP @ X0 ) )
=> ( ( ( cS @ X1 )
=> ( cR @ X0 ) )
& ( ( cR @ X0 )
=> ( cS @ X1 ) ) ) )
& ( ? [X2: $i] : ( cQ @ X2 )
=> ? [X3: $i] : ( cP @ X3 ) )
& ( ? [X4: $i] : ( cP @ X4 )
=> ? [X5: $i] : ( cQ @ X5 ) ) )
=> ( ( ! [X6: $i] :
( ( cQ @ X6 )
=> ( cS @ X6 ) )
=> ! [X7: $i] :
( ( cP @ X7 )
=> ( cR @ X7 ) ) )
& ( ! [X8: $i] :
( ( cP @ X8 )
=> ( cR @ X8 ) )
=> ! [X9: $i] :
( ( cQ @ X9 )
=> ( cS @ X9 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( ( ( cQ @ X1 )
= $true )
& ( ( cP @ X0 )
= $true ) )
=> ( ( ( ( cS @ X1 )
= $true )
=> ( ( cR @ X0 )
= $true ) )
& ( ( ( cR @ X0 )
= $true )
=> ( ( cS @ X1 )
= $true ) ) ) )
& ( ? [X2: $i] :
( ( cQ @ X2 )
= $true )
=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) )
& ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
=> ? [X5: $i] :
( ( cQ @ X5 )
= $true ) ) )
=> ( ( ! [X6: $i] :
( ( ( cQ @ X6 )
= $true )
=> ( ( cS @ X6 )
= $true ) )
=> ! [X7: $i] :
( ( ( cP @ X7 )
= $true )
=> ( ( cR @ X7 )
= $true ) ) )
& ( ! [X8: $i] :
( ( ( cP @ X8 )
= $true )
=> ( ( cR @ X8 )
= $true ) )
=> ! [X9: $i] :
( ( ( cQ @ X9 )
= $true )
=> ( ( cS @ X9 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( ? [X7: $i] :
( ( ( cR @ X7 )
!= $true )
& ( ( cP @ X7 )
= $true ) )
& ! [X6: $i] :
( ( ( cS @ X6 )
= $true )
| ( ( cQ @ X6 )
!= $true ) ) )
| ( ? [X9: $i] :
( ( ( cS @ X9 )
!= $true )
& ( ( cQ @ X9 )
= $true ) )
& ! [X8: $i] :
( ( ( cR @ X8 )
= $true )
| ( ( cP @ X8 )
!= $true ) ) ) )
& ! [X0: $i,X1: $i] :
( ( ( ( ( cR @ X0 )
= $true )
| ( ( cS @ X1 )
!= $true ) )
& ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X0 )
!= $true ) ) )
| ( ( cQ @ X1 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ! [X2: $i] :
( ( cQ @ X2 )
!= $true ) )
& ( ? [X5: $i] :
( ( cQ @ X5 )
= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( ? [X7: $i] :
( ( ( cR @ X7 )
!= $true )
& ( ( cP @ X7 )
= $true ) )
& ! [X6: $i] :
( ( ( cS @ X6 )
= $true )
| ( ( cQ @ X6 )
!= $true ) ) )
| ( ? [X9: $i] :
( ( ( cS @ X9 )
!= $true )
& ( ( cQ @ X9 )
= $true ) )
& ! [X8: $i] :
( ( ( cR @ X8 )
= $true )
| ( ( cP @ X8 )
!= $true ) ) ) )
& ! [X0: $i,X1: $i] :
( ( ( ( ( cR @ X0 )
= $true )
| ( ( cS @ X1 )
!= $true ) )
& ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X0 )
!= $true ) ) )
| ( ( cQ @ X1 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ! [X2: $i] :
( ( cQ @ X2 )
!= $true ) )
& ( ? [X5: $i] :
( ( cQ @ X5 )
= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,definition,
( ( ? [X9: $i] :
( ( ( cS @ X9 )
!= $true )
& ( ( cQ @ X9 )
= $true ) )
& ! [X8: $i] :
( ( ( cR @ X8 )
= $true )
| ( ( cP @ X8 )
!= $true ) ) )
| ( $true != sP0 ) ),
introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction]) ).
thf(f8,plain,
( ( ( ? [X7: $i] :
( ( ( cR @ X7 )
!= $true )
& ( ( cP @ X7 )
= $true ) )
& ! [X6: $i] :
( ( ( cS @ X6 )
= $true )
| ( ( cQ @ X6 )
!= $true ) ) )
| ( $true = sP0 ) )
& ! [X0: $i,X1: $i] :
( ( ( ( ( cR @ X0 )
= $true )
| ( ( cS @ X1 )
!= $true ) )
& ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X0 )
!= $true ) ) )
| ( ( cQ @ X1 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ! [X2: $i] :
( ( cQ @ X2 )
!= $true ) )
& ( ? [X5: $i] :
( ( cQ @ X5 )
= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) ) ),
inference(definition_folding,[],[f6,f7]) ).
thf(f9,plain,
( ( ? [X9: $i] :
( ( ( cS @ X9 )
!= $true )
& ( ( cQ @ X9 )
= $true ) )
& ! [X8: $i] :
( ( ( cR @ X8 )
= $true )
| ( ( cP @ X8 )
!= $true ) ) )
| ( $true != sP0 ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cQ @ X0 )
= $true ) )
& ! [X1: $i] :
( ( $true
= ( cR @ X1 ) )
| ( $true
!= ( cP @ X1 ) ) ) )
| ( $true != sP0 ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( ( $true
!= ( cS @ sK1 ) )
& ( $true
= ( cQ @ sK1 ) )
& ! [X1: $i] :
( ( $true
= ( cR @ X1 ) )
| ( $true
!= ( cP @ X1 ) ) ) )
| ( $true != sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f10]) ).
thf(f12,plain,
( ( ( ? [X0: $i] :
( ( ( cR @ X0 )
!= $true )
& ( ( cP @ X0 )
= $true ) )
& ! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( ( cQ @ X1 )
!= $true ) ) )
| ( $true = sP0 ) )
& ! [X2: $i,X3: $i] :
( ( ( ( $true
= ( cR @ X2 ) )
| ( $true
!= ( cS @ X3 ) ) )
& ( ( $true
= ( cS @ X3 ) )
| ( $true
!= ( cR @ X2 ) ) ) )
| ( $true
!= ( cQ @ X3 ) )
| ( $true
!= ( cP @ X2 ) ) )
& ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
| ! [X5: $i] :
( ( cQ @ X5 )
!= $true ) )
& ( ? [X6: $i] :
( ( cQ @ X6 )
= $true )
| ! [X7: $i] :
( ( cP @ X7 )
!= $true ) ) ),
inference(rectify,[],[f8]) ).
thf(f13,plain,
( ( ( ( $true
!= ( cR @ sK2 ) )
& ( $true
= ( cP @ sK2 ) )
& ! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( ( cQ @ X1 )
!= $true ) ) )
| ( $true = sP0 ) )
& ! [X2: $i,X3: $i] :
( ( ( ( $true
= ( cR @ X2 ) )
| ( $true
!= ( cS @ X3 ) ) )
& ( ( $true
= ( cS @ X3 ) )
| ( $true
!= ( cR @ X2 ) ) ) )
| ( $true
!= ( cQ @ X3 ) )
| ( $true
!= ( cP @ X2 ) ) )
& ( ( $true
= ( cP @ sK3 ) )
| ! [X5: $i] :
( ( cQ @ X5 )
!= $true ) )
& ( ( $true
= ( cQ @ sK4 ) )
| ! [X7: $i] :
( ( cP @ X7 )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X4,sK3),skolemize(X6,sK4)],[f12]) ).
thf(f14,plain,
! [X1: $i] :
( ( $true
= ( cR @ X1 ) )
| ( $true
!= ( cP @ X1 ) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( ( $true
= ( cQ @ sK1 ) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( ( $true
!= ( cS @ sK1 ) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f17,plain,
! [X7: $i] :
( ( $true
= ( cQ @ sK4 ) )
| ( ( cP @ X7 )
!= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
! [X5: $i] :
( ( $true
= ( cP @ sK3 ) )
| ( ( cQ @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( cS @ X3 ) )
| ( $true
!= ( cR @ X2 ) )
| ( $true
!= ( cQ @ X3 ) )
| ( $true
!= ( cP @ X2 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( cR @ X2 ) )
| ( $true
!= ( cS @ X3 ) )
| ( $true
!= ( cQ @ X3 ) )
| ( $true
!= ( cP @ X2 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( ( cQ @ X1 )
!= $true )
| ( $true = sP0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f22,plain,
( ( $true
= ( cP @ sK2 ) )
| ( $true = sP0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f23,plain,
( ( $true
!= ( cR @ sK2 ) )
| ( $true = sP0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f27,definition,
( spl5_1
<=> ! [X7: $i] :
( ( cP @ X7 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f28,plain,
( ! [X7: $i] :
( ( cP @ X7 )
!= $true )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f30,definition,
( spl5_2
<=> ( $true
= ( cQ @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f32,plain,
( ( $true
= ( cQ @ sK4 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f17,f30,f27]) ).
thf(f35,definition,
( spl5_3
<=> ! [X5: $i] :
( ( cQ @ X5 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f36,plain,
( ! [X5: $i] :
( ( cQ @ X5 )
!= $true )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,definition,
( spl5_4
<=> ( $true
= ( cP @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f40,plain,
( ( $true
= ( cP @ sK3 ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f41,plain,
( spl5_3
| spl5_4 ),
inference(avatar_split_clause,[],[f18,f38,f35]) ).
thf(f43,definition,
( spl5_5
<=> ! [X2: $i] :
( ( $true
!= ( cR @ X2 ) )
| ( $true
!= ( cP @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f44,plain,
( ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( $true
!= ( cR @ X2 ) ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f46,definition,
( spl5_6
<=> ! [X3: $i] :
( ( $true
= ( cS @ X3 ) )
| ( $true
!= ( cQ @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f47,plain,
( ! [X3: $i] :
( ( $true
!= ( cQ @ X3 ) )
| ( $true
= ( cS @ X3 ) ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f48,plain,
( spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f19,f46,f43]) ).
thf(f50,definition,
( spl5_7
<=> ! [X3: $i] :
( ( $true
!= ( cS @ X3 ) )
| ( $true
!= ( cQ @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f51,plain,
( ! [X3: $i] :
( ( $true
!= ( cQ @ X3 ) )
| ( $true
!= ( cS @ X3 ) ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,definition,
( spl5_8
<=> ! [X2: $i] :
( ( $true
= ( cR @ X2 ) )
| ( $true
!= ( cP @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f54,plain,
( ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( $true
= ( cR @ X2 ) ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f55,plain,
( spl5_7
| spl5_8 ),
inference(avatar_split_clause,[],[f20,f53,f50]) ).
thf(f57,definition,
( spl5_9
<=> ( $true = sP0 ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f60,plain,
( spl5_9
| spl5_6 ),
inference(avatar_split_clause,[],[f21,f46,f57]) ).
thf(f62,definition,
( spl5_10
<=> ( $true
= ( cP @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
thf(f64,plain,
( ( $true
= ( cP @ sK2 ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f65,plain,
( spl5_9
| spl5_10 ),
inference(avatar_split_clause,[],[f22,f62,f57]) ).
thf(f67,definition,
( spl5_11
<=> ( $true
= ( cR @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
thf(f69,plain,
( ( $true
!= ( cR @ sK2 ) )
| spl5_11 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f70,plain,
( spl5_9
| ~ spl5_11 ),
inference(avatar_split_clause,[],[f23,f67,f57]) ).
thf(f71,plain,
( ~ spl5_9
| spl5_8 ),
inference(avatar_split_clause,[],[f14,f53,f57]) ).
thf(f73,definition,
( spl5_12
<=> ( $true
= ( cQ @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
thf(f75,plain,
( ( $true
= ( cQ @ sK1 ) )
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f76,plain,
( ~ spl5_9
| spl5_12 ),
inference(avatar_split_clause,[],[f15,f73,f57]) ).
thf(f78,definition,
( spl5_13
<=> ( $true
= ( cS @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_13])],[avatar_definition]) ).
thf(f81,plain,
( ~ spl5_9
| ~ spl5_13 ),
inference(avatar_split_clause,[],[f16,f78,f57]) ).
thf(f82,plain,
( ( $true != $true )
| ~ spl5_2
| ~ spl5_3 ),
inference(constrained_superposition,[],[f36,f32]) ).
thf(f83,plain,
( $false
| ~ spl5_2
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f84,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f83]) ).
thf(f85,plain,
( $false
| ~ spl5_1
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f64,f28]) ).
thf(f86,plain,
( ~ spl5_1
| ~ spl5_10 ),
inference(avatar_contradiction_clause,[],[f85]) ).
thf(f87,plain,
( $false
| ~ spl5_3
| ~ spl5_12 ),
inference(forward_subsumption_resolution,[],[f75,f36]) ).
thf(f88,plain,
( ~ spl5_3
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f87]) ).
thf(f89,plain,
( $false
| ~ spl5_1
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f40,f28]) ).
thf(f90,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f89]) ).
thf(f93,plain,
( ! [X3: $i] :
( $true
!= ( cQ @ X3 ) )
| ~ spl5_6
| ~ spl5_7 ),
inference(forward_subsumption_resolution,[],[f51,f47]) ).
thf(f94,plain,
( spl5_3
| ~ spl5_6
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f93,f50,f46,f35]) ).
thf(f99,plain,
( ! [X2: $i] :
( $true
!= ( cP @ X2 ) )
| ~ spl5_5
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f54,f44]) ).
thf(f100,plain,
( spl5_1
| ~ spl5_5
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f99,f53,f43,f27]) ).
thf(f121,plain,
( ( $true != $true )
| ( $true
= ( cS @ sK1 ) )
| ~ spl5_6
| ~ spl5_12 ),
inference(constrained_superposition,[],[f47,f75]) ).
thf(f122,plain,
( ( $true
= ( cS @ sK1 ) )
| ~ spl5_6
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f123,plain,
( spl5_13
| ~ spl5_6
| ~ spl5_12 ),
inference(avatar_split_clause,[],[f122,f73,f46,f78]) ).
thf(f126,plain,
( ( $true != $true )
| ( $true
= ( cR @ sK2 ) )
| ~ spl5_8
| ~ spl5_10 ),
inference(constrained_superposition,[],[f54,f64]) ).
thf(f127,plain,
( ( $true
= ( cR @ sK2 ) )
| ~ spl5_8
| ~ spl5_10 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f128,plain,
( $false
| ~ spl5_8
| ~ spl5_10
| spl5_11 ),
inference(forward_subsumption_resolution,[],[f127,f69]) ).
thf(f129,plain,
( ~ spl5_8
| ~ spl5_10
| spl5_11 ),
inference(avatar_contradiction_clause,[],[f128]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f41]) ).
cnf(s3,plain,
( spl5_5
| spl5_6 ),
inference(sat_conversion,[],[f48]) ).
cnf(s4,plain,
( spl5_7
| spl5_8 ),
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
( spl5_6
| spl5_9 ),
inference(sat_conversion,[],[f60]) ).
cnf(s6,plain,
( spl5_9
| spl5_10 ),
inference(sat_conversion,[],[f65]) ).
cnf(s7,plain,
( spl5_9
| ~ spl5_11 ),
inference(sat_conversion,[],[f70]) ).
cnf(s8,plain,
( spl5_8
| ~ spl5_9 ),
inference(sat_conversion,[],[f71]) ).
cnf(s9,plain,
( ~ spl5_9
| spl5_12 ),
inference(sat_conversion,[],[f76]) ).
cnf(s10,plain,
( ~ spl5_9
| ~ spl5_13 ),
inference(sat_conversion,[],[f81]) ).
cnf(s11,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f84]) ).
cnf(s12,plain,
( ~ spl5_1
| ~ spl5_10 ),
inference(sat_conversion,[],[f86]) ).
cnf(s13,plain,
( ~ spl5_3
| ~ spl5_12 ),
inference(sat_conversion,[],[f88]) ).
cnf(s14,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f90]) ).
cnf(s15,plain,
( spl5_3
| ~ spl5_6
| ~ spl5_7 ),
inference(sat_conversion,[],[f94]) ).
cnf(s16,plain,
( spl5_1
| ~ spl5_5
| ~ spl5_8 ),
inference(sat_conversion,[],[f100]) ).
cnf(s17,plain,
( ~ spl5_6
| ~ spl5_12
| spl5_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s18,plain,
( ~ spl5_8
| ~ spl5_10
| spl5_11 ),
inference(sat_conversion,[],[f129]) ).
cnf(s19,plain,
( spl5_9
| ~ spl5_8 ),
inference(rat,[],[s18,s6,s7]) ).
cnf(s20,plain,
( ~ spl5_6
| spl5_3 ),
inference(rat,[],[s17,s9,s10,s19,s4,s15]) ).
cnf(s21,plain,
spl5_1,
inference(rat,[],[s16,s8,s3,s5,s20,s11,s1]) ).
cnf(s22,plain,
~ spl5_4,
inference(rat,[],[s14,s21]) ).
cnf(s23,plain,
~ spl5_10,
inference(rat,[],[s12,s21]) ).
cnf(s24,plain,
spl5_3,
inference(rat,[],[s2,s22]) ).
cnf(s25,plain,
spl5_9,
inference(rat,[],[s6,s23]) ).
cnf(s26,plain,
~ spl5_12,
inference(rat,[],[s13,s24]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s9,s26,s25]) ).
thf(f130,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN056^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n005.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 : Tue Sep 29 16:14:01 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.26 % (1861797)Will run a generic schedule for satisfiability detection.
% 0.21/0.26 % (1861814)dis+10_1_sil=32000:sp=arity:random_seed=620678812:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.26 % (1861814) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1861797-1861814"...
% 0.21/0.26 % (1861812)% WARNING: option uhcvi not known.
% 0.21/0.26 % (1861814)...printing done.
% 0.21/0.26 % (1861814)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.26 % (1861814)------------------------------
% 0.21/0.26 % (1861814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (1861814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (1861814)CaDiCaL version: 2.1.3
% 0.21/0.26 % (1861814)Termination reason: Refutation
% 0.21/0.26 % (1861814)Time elapsed: 0.003 s
% 0.21/0.26 % (1861814)Peak memory usage: 12 MB
% 0.21/0.26 % (1861814)Instructions burned: 7 (million)
% 0.21/0.26 % (1861797)Success in time 0.03 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------