%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU665^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : Wed Sep 30 08:30:36 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 122 ( 37 unt; 0 typ; 12 def)
% Number of atoms : 1041 ( 263 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 1446 ( 176 ~; 196 |; 97 &; 897 @)
% ( 17 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 45 usr; 28 con; 0-4 aty)
% ( 0 !!; 27 ??; 0 @@+; 0 @@-)
% Number of variables : 301 ( 0 sgn 169 !; 33 ?; 301 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrI: $o ).
thf(func_def_4,type,
setext: $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
cartprodpairin: $o ).
thf(func_def_8,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vAND: $o > $o > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
sK2: $i > $o ).
thf(func_def_27,type,
sK7: $i > $i > $o ).
thf(func_def_34,type,
sK14: $i > $i > $i ).
thf(func_def_35,type,
sK15: $i > $i > $i ).
thf(func_def_36,type,
vNOT: $o > $o ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f3,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) ) ) )
= cartprodpairin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
thf(f4,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ? [X5: $i] :
( ( X3
= ( kpair @ X4 @ X5 ) )
& ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 ) )
& ( in @ X4 @ X0 ) ) ) )
= dpsetconstr ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstr) ).
thf(f5,conjecture,
( dsetconstrI
=> ( setext
=> ( cartprodpairin
=> ! [X2: $i > $i > $o,X0: $i,X1: $i,X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(f6,negated_conjecture,
~ ( dsetconstrI
=> ( setext
=> ( cartprodpairin
=> ! [X2: $i > $i > $o,X0: $i,X1: $i,X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ? [X5: $i] :
( ( X3
= ( kpair @ X4 @ X5 ) )
& ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 ) )
& ( in @ X4 @ X0 ) ) ) )
= dpsetconstr ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( dsetconstrI = $true )
<=> ! [X1: $i,X2: $i > $o,X0: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( $true
= ( X2 @ X0 ) )
=> ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) ) ) )
= cartprodpairin ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
= $true ) ) )
<=> ( cartprodpairin = $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( dsetconstrI
=> ( setext
=> ( cartprodpairin
=> ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X0 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X5: $i,X6: $i] : ( X0 @ X5 @ X6 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
~ ( ( dsetconstrI = $true )
=> ( ( setext = $true )
=> ( ( cartprodpairin = $true )
=> ! [X2: $i,X1: $i,X3: $i,X0: $i > $i > $o] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ( ( $true
= ( X0 @ X3 @ X4 ) )
=> ( $true
= ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( dsetconstrI = $true )
<=> ! [X1: $i,X2: $i > $o,X0: $i] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( X2 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f18,plain,
( ! [X1: $i,X0: $i,X2: $i > $o] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( X2 @ X0 ) ) )
<=> ( dsetconstrI = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ X0 )
!= $true ) )
<=> ( cartprodpairin = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f22,plain,
( ? [X2: $i,X1: $i,X3: $i,X0: $i > $i > $o] :
( ? [X4: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( X0 @ X3 @ X4 ) )
& ( $true
= ( in @ X4 @ X2 ) ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( cartprodpairin = $true )
& ( setext = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f23,plain,
( ( cartprodpairin = $true )
& ( dsetconstrI = $true )
& ? [X0: $i > $i > $o,X1: $i,X3: $i,X2: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ? [X4: $i] :
( ( $true
= ( X0 @ X3 @ X4 ) )
& ( $true
= ( in @ X4 @ X2 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ) ) )
& ( setext = $true ) ),
inference(flattening,[],[f22]) ).
thf(f24,plain,
( ( ! [X1: $i,X0: $i,X2: $i > $o] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( X2 @ X0 ) ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X1: $i,X0: $i,X2: $i > $o] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
& ( $true
= ( in @ X0 @ X1 ) )
& ( $true
= ( X2 @ X0 ) ) ) ) ),
inference(nnf_transformation,[],[f18]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( X2 @ X1 ) ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
& ( $true
= ( in @ X4 @ X3 ) )
& ( ( X5 @ X4 )
= $true ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( X2 @ X1 ) ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ( ( ( in @ sK1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( $true
= ( sK2 @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f25]) ).
thf(f27,plain,
( ( ! [X1: $i,X0: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( cartprodpairin != $true ) )
& ( ( cartprodpairin = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f19]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X1 @ X0 ) ) )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( cartprodpairin != $true ) )
& ( ( cartprodpairin = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ ( cartprod @ X5 @ X4 ) ) )
& ( $true
= ( in @ X7 @ X4 ) ) )
& ( $true
= ( in @ X6 @ X5 ) ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X1 @ X0 ) ) )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( cartprodpairin != $true ) )
& ( ( cartprodpairin = $true )
| ( ( $true
!= ( in @ ( kpair @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK3 ) ) )
& ( $true
= ( in @ sK6 @ sK3 ) )
& ( $true
= ( in @ sK5 @ sK4 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X4,sK3),skolemize(X5,sK4),skolemize(X6,sK5),skolemize(X7,sK6)],[f28]) ).
thf(f30,plain,
( ( cartprodpairin = $true )
& ( dsetconstrI = $true )
& ? [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ? [X4: $i] :
( ( ( X0 @ X2 @ X4 )
= $true )
& ( $true
= ( in @ X4 @ X3 ) )
& ( $true
!= ( in @ ( kpair @ X2 @ X4 )
@ ( dpsetconstr @ X1 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ) ) )
& ( setext = $true ) ),
inference(rectify,[],[f23]) ).
thf(f31,plain,
( ( cartprodpairin = $true )
& ( dsetconstrI = $true )
& ( ( in @ sK9 @ sK8 )
= $true )
& ( $true
= ( sK7 @ sK9 @ sK11 ) )
& ( $true
= ( in @ sK11 @ sK10 ) )
& ( $true
!= ( in @ ( kpair @ sK9 @ sK11 )
@ ( dpsetconstr @ sK8 @ sK10
@ ^ [Y0: $i,Y1: $i] : ( sK7 @ Y0 @ Y1 ) ) ) )
& ( setext = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10),skolemize(X4,sK11)],[f30]) ).
thf(f38,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( dsetconstrI != $true )
| ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( X2 @ X1 ) )
| ( $true
!= ( in @ X1 @ X0 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( cartprodpairin != $true )
| ( $true
= ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f44,plain,
( $true
!= ( in @ ( kpair @ sK9 @ sK11 )
@ ( dpsetconstr @ sK8 @ sK10
@ ^ [Y0: $i,Y1: $i] : ( sK7 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f45,plain,
( $true
= ( in @ sK11 @ sK10 ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f46,plain,
( $true
= ( sK7 @ sK9 @ sK11 ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f47,plain,
( ( in @ sK9 @ sK8 )
= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f48,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f31]) ).
thf(f49,plain,
cartprodpairin = $true,
inference(cnf_transformation,[],[f31]) ).
thf(f50,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f59,plain,
( $true
!= ( in @ ( kpair @ sK9 @ sK11 ) @ ( dpsetconstr @ sK8 @ sK10 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f60,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( X2 @ X1 ) )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( dsetconstrI != $true )
| ( $true
= ( in @ X1 @ ( dsetconstr @ X0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f71,definition,
( spl16_3
<=> ( dsetconstrI = $true ) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
thf(f74,plain,
spl16_3,
inference(avatar_split_clause,[],[f48,f71]) ).
thf(f84,definition,
( spl16_6
<=> ( cartprodpairin = $true ) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
thf(f87,plain,
spl16_6,
inference(avatar_split_clause,[],[f49,f84]) ).
thf(f103,definition,
( spl16_10
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true
= ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X1 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
thf(f104,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X1 @ X0 ) ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f105,plain,
( spl16_10
| ~ spl16_6 ),
inference(avatar_split_clause,[],[f42,f84,f103]) ).
thf(f116,definition,
( spl16_13
<=> ( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition]) ).
thf(f118,plain,
( ( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) )
| ~ spl16_13 ),
inference(avatar_component_clause,[],[f116]) ).
thf(f119,plain,
spl16_13,
inference(avatar_split_clause,[],[f50,f116]) ).
thf(f131,definition,
( spl16_16
<=> ( $true
= ( sK7 @ sK9 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_16])],[avatar_definition]) ).
thf(f133,plain,
( ( $true
= ( sK7 @ sK9 @ sK11 ) )
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f131]) ).
thf(f134,plain,
spl16_16,
inference(avatar_split_clause,[],[f46,f131]) ).
thf(f136,definition,
( spl16_17
<=> ( $true
= ( in @ ( kpair @ sK9 @ sK11 ) @ ( dpsetconstr @ sK8 @ sK10 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_17])],[avatar_definition]) ).
thf(f138,plain,
( ( $true
!= ( in @ ( kpair @ sK9 @ sK11 ) @ ( dpsetconstr @ sK8 @ sK10 @ sK7 ) ) )
| spl16_17 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f139,plain,
~ spl16_17,
inference(avatar_split_clause,[],[f59,f136]) ).
thf(f146,definition,
( spl16_19
<=> ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( X2 @ X1 ) )
| ( $true
= ( in @ X1 @ ( dsetconstr @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_19])],[avatar_definition]) ).
thf(f147,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( dsetconstr @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( X2 @ X1 ) ) )
| ~ spl16_19 ),
inference(avatar_component_clause,[],[f146]) ).
thf(f148,plain,
( spl16_19
| ~ spl16_3 ),
inference(avatar_split_clause,[],[f60,f71,f146]) ).
thf(f155,definition,
( spl16_21
<=> ( ( in @ sK9 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_21])],[avatar_definition]) ).
thf(f157,plain,
( ( ( in @ sK9 @ sK8 )
= $true )
| ~ spl16_21 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f158,plain,
spl16_21,
inference(avatar_split_clause,[],[f47,f155]) ).
thf(f165,definition,
( spl16_23
<=> ( $true
= ( in @ sK11 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_23])],[avatar_definition]) ).
thf(f167,plain,
( ( $true
= ( in @ sK11 @ sK10 ) )
| ~ spl16_23 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f168,plain,
spl16_23,
inference(avatar_split_clause,[],[f45,f165]) ).
thf(f174,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) )
@ X1 )
= ( dpsetconstr @ X1 ) )
| ~ spl16_13 ),
inference(argument_congruence,[],[f118]) ).
thf(f175,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X1 @ Y0 )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( Y1 @ Y3 @ Y4 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) ) ) ) ) )
= ( dpsetconstr @ X1 ) )
| ~ spl16_13 ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f184,plain,
( ! [X2: $i,X1: $i] :
( ( dpsetconstr @ X1 @ X2 )
= ( ^ [Y0: $i,Y1: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X1 @ Y0 )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( Y1 @ Y3 @ Y4 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) ) ) ) )
@ X2 ) )
| ~ spl16_13 ),
inference(argument_congruence,[],[f175]) ).
thf(f185,plain,
( ! [X2: $i,X1: $i] :
( ( dpsetconstr @ X1 @ X2 )
= ( ^ [Y0: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
& ( Y0 @ Y2 @ Y3 )
& ( ( kpair @ Y2 @ Y3 )
= Y1 ) ) ) ) ) ) ) )
| ~ spl16_13 ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f188,plain,
( ! [X2: $i,X3: $i > $i > $o,X1: $i] :
( ( ^ [Y0: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
& ( Y0 @ Y2 @ Y3 )
& ( ( kpair @ Y2 @ Y3 )
= Y1 ) ) ) ) ) )
@ X3 )
= ( dpsetconstr @ X1 @ X2 @ X3 ) )
| ~ spl16_13 ),
inference(argument_congruence,[],[f185]) ).
thf(f189,plain,
( ! [X2: $i,X3: $i > $i > $o,X1: $i] :
( ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
& ( X3 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) ) )
= ( dpsetconstr @ X1 @ X2 @ X3 ) )
| ~ spl16_13 ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f201,plain,
( ! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X3 @ ( dpsetconstr @ X0 @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
& ( X2 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) )
@ X3 ) ) )
| ~ spl16_13
| ~ spl16_19 ),
inference(superposition,[],[f147,f189]) ).
thf(f211,plain,
( ! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X3 @ ( dpsetconstr @ X0 @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
& ( X2 @ Y0 @ Y1 )
& ( ( kpair @ Y0 @ Y1 )
= X3 ) ) ) ) ) ) )
| ~ spl16_13
| ~ spl16_19 ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f212,plain,
( ! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ X3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
& ( X2 @ Y0 @ Y1 )
& ( ( kpair @ Y0 @ Y1 )
= X3 ) ) ) )
@ X4 ) )
| ( $true
= ( in @ X3 @ ( dpsetconstr @ X0 @ X1 @ X2 ) ) ) )
| ~ spl16_13
| ~ spl16_19 ),
inference(pi_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X3 @ ( dpsetconstr @ X0 @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ ( cartprod @ X0 @ X1 ) ) )
| ( ( ( in @ X4 @ X0 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( X2 @ X4 @ Y0 )
& ( ( kpair @ X4 @ Y0 )
= X3 ) ) ) )
= $false ) )
| ~ spl16_13
| ~ spl16_19 ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f214,plain,
( ! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( X2 @ X4 @ Y0 )
& ( ( kpair @ X4 @ Y0 )
= X3 ) ) )
= $false )
| ( ( in @ X4 @ X0 )
= $false )
| ( $true
!= ( in @ X3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( in @ X3 @ ( dpsetconstr @ X0 @ X1 @ X2 ) ) ) )
| ~ spl16_13
| ~ spl16_19 ),
inference(and_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X0 )
= $false )
| ( $true
= ( in @ X3 @ ( dpsetconstr @ X0 @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( X2 @ X4 @ Y0 )
& ( ( kpair @ X4 @ Y0 )
= X3 ) )
@ X5 ) )
| ( $true
!= ( in @ X3 @ ( cartprod @ X0 @ X1 ) ) ) )
| ~ spl16_13
| ~ spl16_19 ),
inference(pi_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ( in @ X5 @ X1 )
& ( X2 @ X4 @ X5 )
& ( ( kpair @ X4 @ X5 )
= X3 ) ) )
| ( $true
= ( in @ X3 @ ( dpsetconstr @ X0 @ X1 @ X2 ) ) )
| ( ( in @ X4 @ X0 )
= $false )
| ( $true
!= ( in @ X3 @ ( cartprod @ X0 @ X1 ) ) ) )
| ~ spl16_13
| ~ spl16_19 ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
( ! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ( in @ X5 @ X1 )
& ( X2 @ X4 @ X5 ) )
= $false )
| ( $true
!= ( in @ X3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( in @ X3 @ ( dpsetconstr @ X0 @ X1 @ X2 ) ) )
| ( $false
= ( ( kpair @ X4 @ X5 )
= X3 ) )
| ( ( in @ X4 @ X0 )
= $false ) )
| ~ spl16_13
| ~ spl16_19 ),
inference(and_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X1 )
= $false )
| ( $false
= ( ( kpair @ X4 @ X5 )
= X3 ) )
| ( ( in @ X4 @ X0 )
= $false )
| ( $true
!= ( in @ X3 @ ( cartprod @ X0 @ X1 ) ) )
| ( ( X2 @ X4 @ X5 )
= $false )
| ( $true
= ( in @ X3 @ ( dpsetconstr @ X0 @ X1 @ X2 ) ) ) )
| ~ spl16_13
| ~ spl16_19 ),
inference(and_proxy_clausification,[],[f217]) ).
thf(f219,plain,
( ! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( dpsetconstr @ X0 @ X1 @ X2 ) ) )
| ( ( kpair @ X4 @ X5 )
!= X3 )
| ( ( in @ X5 @ X1 )
= $false )
| ( ( X2 @ X4 @ X5 )
= $false )
| ( ( in @ X4 @ X0 )
= $false )
| ( $true
!= ( in @ X3 @ ( cartprod @ X0 @ X1 ) ) ) )
| ~ spl16_13
| ~ spl16_19 ),
inference(equality_proxy_clausification,[],[f218]) ).
thf(f250,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X1 @ sK10 ) )
| ( $true != $true )
| ( $true
!= ( in @ ( kpair @ sK9 @ sK11 ) @ ( cartprod @ sK8 @ sK10 ) ) )
| ( $false
= ( in @ X0 @ sK8 ) )
| ( $false
= ( sK7 @ X0 @ X1 ) )
| ( ( kpair @ sK9 @ sK11 )
!= ( kpair @ X0 @ X1 ) ) )
| ~ spl16_13
| spl16_17
| ~ spl16_19 ),
inference(superposition,[],[f138,f219]) ).
thf(f257,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X1 @ sK10 ) )
| ( $true
!= ( in @ ( kpair @ sK9 @ sK11 ) @ ( cartprod @ sK8 @ sK10 ) ) )
| ( $false
= ( in @ X0 @ sK8 ) )
| ( $false
= ( sK7 @ X0 @ X1 ) )
| ( ( kpair @ sK9 @ sK11 )
!= ( kpair @ X0 @ X1 ) ) )
| ~ spl16_13
| spl16_17
| ~ spl16_19 ),
inference(trivial_inequality_removal,[],[f250]) ).
thf(f264,definition,
( spl16_24
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X1 @ sK10 ) )
| ( ( kpair @ sK9 @ sK11 )
!= ( kpair @ X0 @ X1 ) )
| ( $false
= ( in @ X0 @ sK8 ) )
| ( $false
= ( sK7 @ X0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_24])],[avatar_definition]) ).
thf(f265,plain,
( ! [X0: $i,X1: $i] :
( ( ( kpair @ sK9 @ sK11 )
!= ( kpair @ X0 @ X1 ) )
| ( $false
= ( in @ X0 @ sK8 ) )
| ( $false
= ( sK7 @ X0 @ X1 ) )
| ( $false
= ( in @ X1 @ sK10 ) ) )
| ~ spl16_24 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f267,definition,
( spl16_25
<=> ( $true
= ( in @ ( kpair @ sK9 @ sK11 ) @ ( cartprod @ sK8 @ sK10 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_25])],[avatar_definition]) ).
thf(f269,plain,
( ( $true
!= ( in @ ( kpair @ sK9 @ sK11 ) @ ( cartprod @ sK8 @ sK10 ) ) )
| spl16_25 ),
inference(avatar_component_clause,[],[f267]) ).
thf(f270,plain,
( spl16_24
| ~ spl16_25
| ~ spl16_13
| spl16_17
| ~ spl16_19 ),
inference(avatar_split_clause,[],[f257,f146,f136,f116,f267,f264]) ).
thf(f285,plain,
( ( $true
!= ( in @ sK11 @ sK10 ) )
| ( ( in @ sK9 @ sK8 )
!= $true )
| ( $true != $true )
| ~ spl16_10
| spl16_25 ),
inference(superposition,[],[f269,f104]) ).
thf(f286,plain,
( ( $true
!= ( in @ sK11 @ sK10 ) )
| ( ( in @ sK9 @ sK8 )
!= $true )
| ~ spl16_10
| spl16_25 ),
inference(trivial_inequality_removal,[],[f285]) ).
thf(f287,plain,
( ( ( in @ sK9 @ sK8 )
!= $true )
| ~ spl16_10
| ~ spl16_23
| spl16_25 ),
inference(forward_subsumption_resolution,[],[f286,f167]) ).
thf(f288,plain,
( $false
| ~ spl16_10
| ~ spl16_21
| ~ spl16_23
| spl16_25 ),
inference(forward_subsumption_resolution,[],[f287,f157]) ).
thf(f289,plain,
( ~ spl16_10
| ~ spl16_21
| ~ spl16_23
| spl16_25 ),
inference(avatar_contradiction_clause,[],[f288]) ).
thf(f290,plain,
( ( $false
= ( in @ sK11 @ sK10 ) )
| ( ( in @ sK9 @ sK8 )
= $false )
| ( $false
= ( sK7 @ sK9 @ sK11 ) )
| ~ spl16_24 ),
inference(equality_resolution,[],[f265]) ).
thf(f291,plain,
( ( $true = $false )
| ( $false
= ( sK7 @ sK9 @ sK11 ) )
| ( ( in @ sK9 @ sK8 )
= $false )
| ~ spl16_23
| ~ spl16_24 ),
inference(forward_demodulation,[],[f290,f167]) ).
thf(f292,plain,
( ( $false
= ( sK7 @ sK9 @ sK11 ) )
| ( ( in @ sK9 @ sK8 )
= $false )
| ~ spl16_23
| ~ spl16_24 ),
inference(trivial_inequality_removal,[],[f291]) ).
thf(f293,plain,
( ( $true = $false )
| ( ( in @ sK9 @ sK8 )
= $false )
| ~ spl16_16
| ~ spl16_23
| ~ spl16_24 ),
inference(forward_demodulation,[],[f292,f133]) ).
thf(f294,plain,
( ( ( in @ sK9 @ sK8 )
= $false )
| ~ spl16_16
| ~ spl16_23
| ~ spl16_24 ),
inference(trivial_inequality_removal,[],[f293]) ).
thf(f296,definition,
( spl16_26
<=> ( ( in @ sK9 @ sK8 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl16_26])],[avatar_definition]) ).
thf(f298,plain,
( ( ( in @ sK9 @ sK8 )
= $false )
| ~ spl16_26 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f299,plain,
( spl16_26
| ~ spl16_16
| ~ spl16_23
| ~ spl16_24 ),
inference(avatar_split_clause,[],[f294,f264,f165,f131,f296]) ).
thf(f300,plain,
( ( $true = $false )
| ~ spl16_21
| ~ spl16_26 ),
inference(superposition,[],[f298,f157]) ).
thf(f304,plain,
( $false
| ~ spl16_21
| ~ spl16_26 ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f305,plain,
( ~ spl16_21
| ~ spl16_26 ),
inference(avatar_contradiction_clause,[],[f304]) ).
cnf(s2,plain,
spl16_3,
inference(sat_conversion,[],[f74]) ).
cnf(s5,plain,
spl16_6,
inference(sat_conversion,[],[f87]) ).
cnf(s9,plain,
( ~ spl16_6
| spl16_10 ),
inference(sat_conversion,[],[f105]) ).
cnf(s12,plain,
spl16_13,
inference(sat_conversion,[],[f119]) ).
cnf(s16,plain,
spl16_16,
inference(sat_conversion,[],[f134]) ).
cnf(s17,plain,
~ spl16_17,
inference(sat_conversion,[],[f139]) ).
cnf(s19,plain,
( ~ spl16_3
| spl16_19 ),
inference(sat_conversion,[],[f148]) ).
cnf(s21,plain,
spl16_21,
inference(sat_conversion,[],[f158]) ).
cnf(s23,plain,
spl16_23,
inference(sat_conversion,[],[f168]) ).
cnf(s24,plain,
( ~ spl16_13
| spl16_17
| ~ spl16_19
| spl16_24
| ~ spl16_25 ),
inference(sat_conversion,[],[f270]) ).
cnf(s25,plain,
( ~ spl16_10
| ~ spl16_21
| ~ spl16_23
| spl16_25 ),
inference(sat_conversion,[],[f289]) ).
cnf(s26,plain,
( ~ spl16_16
| ~ spl16_23
| ~ spl16_24
| spl16_26 ),
inference(sat_conversion,[],[f299]) ).
cnf(s28,plain,
( ~ spl16_21
| ~ spl16_26 ),
inference(sat_conversion,[],[f305]) ).
cnf(s29,plain,
~ spl16_26,
inference(rat,[],[s28,s21]) ).
cnf(s30,plain,
~ spl16_24,
inference(rat,[],[s26,s29,s23,s16]) ).
cnf(s33,plain,
spl16_10,
inference(rat,[],[s9,s5]) ).
cnf(s34,plain,
spl16_25,
inference(rat,[],[s25,s21,s23,s33]) ).
cnf(s35,plain,
~ spl16_19,
inference(rat,[],[s24,s12,s30,s17,s34]) ).
cnf(s36,plain,
~ spl16_3,
inference(rat,[],[s19,s35]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s2,s36]) ).
thf(f306,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU665^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:06:20 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 higher-order theorem proving
% 0.09/0.23 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
% 0.20/0.28 % (770023)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (770031)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2400737394:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.28 % (770029)lrs+10_16_si=on:nwc=1.5:random_seed=1331907590:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (770028)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2092681595:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (770032)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3312273268:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (770031) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-770023-770031"...
% 0.20/0.28 % (770030)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=25864243:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (770031)...printing done.
% 0.20/0.28 % (770031)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (770031)------------------------------
% 0.20/0.28 % (770031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (770031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (770031)CaDiCaL version: 2.1.3
% 0.20/0.28 % (770031)Termination reason: Refutation
% 0.20/0.28 % (770031)Time elapsed: 0.011 s
% 0.20/0.28 % (770031)Peak memory usage: 13 MB
% 0.20/0.28 % (770031)Instructions burned: 31 (million)
% 0.20/0.28 % (770023)Success in time 0.043 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------