%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU686^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:30:46 AM UTC 2026
% Result : Theorem 0.51s 0.40s
% Output : Refutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 19
% Syntax : Number of formulae : 140 ( 44 unt; 0 typ; 14 def)
% Number of atoms : 1508 ( 378 equ; 0 cnn)
% Maximal formula atoms : 14 ( 10 avg)
% Number of connectives : 1878 ( 287 ~; 313 |; 77 &;1091 @)
% ( 22 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 36 con; 0-4 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 346 ( 0 sgn 232 !; 39 ?; 346 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
breln: $i > $i > $i > $o ).
thf(func_def_11,type,
func: $i > $i > $i > $o ).
thf(func_def_12,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_13,type,
app: $o ).
thf(func_def_14,type,
ex1E2: $o ).
thf(func_def_15,type,
funcGraphProp1: $o ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_21,type,
vAND: $o > $o > $o ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
sK14: $i > $o ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_47,type,
sK18: $i > $i ).
thf(func_def_48,type,
sK19: $i > $i > $i > $i ).
thf(f4,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) )
= func ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',func) ).
thf(f5,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) )
= app ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(f6,axiom,
( ex1E2
= ( ! [X0: $i,X1: $i > $o] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(f7,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) )
= funcGraphProp1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(f8,conjecture,
( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X1: $i,X2: $i,X0: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(f9,negated_conjecture,
~ ( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X1: $i,X2: $i,X0: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f13,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) )
= func ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) )
= app ),
inference(rectify,[],[f5]) ).
thf(f16,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
= $true ) ) )
<=> ( app = $true ) ),
inference(fool_elimination,[],[f15]) ).
thf(f19,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 ) ) )
= funcGraphProp1 ),
inference(rectify,[],[f7]) ).
thf(f20,plain,
( ( funcGraphProp1 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
( ex1E2
= ( ! [X0: $i,X1: $i > $o] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( X1 @ X3 )
=> ( ( X1 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f22,plain,
( ( ex1E2 = $true )
<=> ! [X0: $i,X1: $i > $o] :
( ( ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( X1 @ X3 )
= $true )
=> ( ( ( X1 @ X4 )
= $true )
=> ( X3 = X4 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
~ ( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( ( ap @ X2 @ X0 @ X1 @ X3 )
= X4 ) ) ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f24,plain,
~ ( ( app = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
=> ( ( ap @ X2 @ X0 @ X1 @ X3 )
= X4 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( ( ex1E2 = $true )
<=> ! [X1: $i > $o,X0: $i] :
( ( ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( X1 @ X2 )
= $true )
=> ( ( ( X1 @ X3 )
= $true )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f26,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X2 @ X0 @ X1 @ X3 )
!= X4 )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( func @ X2 @ X0 @ X1 )
= $true ) )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( app = $true ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f27,plain,
( ( app = $true )
& ( ex1E2 = $true )
& ( funcGraphProp1 = $true )
& ? [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X2 @ X0 @ X1 @ X3 )
!= X4 )
& ( ( in @ X4 @ X0 )
= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) )
& ( ( in @ X3 @ X2 )
= $true ) ) ) ),
inference(flattening,[],[f26]) ).
thf(f28,plain,
( ( funcGraphProp1 = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 )
= $true ) )
| ( ( func @ X1 @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f29,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
<=> ( app = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f30,plain,
( ( ex1E2 = $true )
<=> ! [X1: $i > $o,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( X2 = X3 )
| ( ( X1 @ X3 )
!= $true )
| ( ( X1 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f31,plain,
( ! [X0: $i,X1: $i > $o] :
( ( ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ! [X3: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X3 )
!= $true )
| ( X2 = X3 ) ) ) )
<=> ( ex1E2 = $true ) ),
inference(flattening,[],[f30]) ).
thf(f32,plain,
( ( app = $true )
& ( ex1E2 = $true )
& ( funcGraphProp1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
!= X4 )
& ( $true
= ( in @ X4 @ X2 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f33,plain,
( ( app = $true )
& ( ex1E2 = $true )
& ( funcGraphProp1 = $true )
& ( ( func @ sK1 @ sK2 @ sK0 )
= $true )
& ( sK4
!= ( ap @ sK1 @ sK2 @ sK0 @ sK3 ) )
& ( $true
= ( in @ sK4 @ sK2 ) )
& ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 )
= $true )
& ( ( in @ sK3 @ sK1 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f32]) ).
thf(f34,plain,
( ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ( app != $true ) )
& ( ( app = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ) ),
inference(nnf_transformation,[],[f29]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X0 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( in @ ( ap @ X1 @ X0 @ X2 @ X3 ) @ X0 )
= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ) )
| ( app != $true ) )
& ( ( app = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ( ( func @ X5 @ X4 @ X6 )
= $true )
& ? [X7: $i] :
( ( ( in @ ( ap @ X5 @ X4 @ X6 @ X7 ) @ X4 )
!= $true )
& ( ( in @ X7 @ X5 )
= $true ) ) ) ) ),
inference(rectify,[],[f34]) ).
thf(f36,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X0 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( in @ ( ap @ X1 @ X0 @ X2 @ X3 ) @ X0 )
= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ) )
| ( app != $true ) )
& ( ( app = $true )
| ( ( ( func @ sK6 @ sK5 @ sK7 )
= $true )
& ( ( in @ ( ap @ sK6 @ sK5 @ sK7 @ sK8 ) @ sK5 )
!= $true )
& ( ( in @ sK8 @ sK6 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X4,sK5),skolemize(X5,sK6),skolemize(X6,sK7),skolemize(X7,sK8)],[f35]) ).
thf(f37,plain,
( ( ( funcGraphProp1 = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 )
!= $true ) )
& ( ( func @ X1 @ X2 @ X0 )
= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 )
= $true ) )
| ( ( func @ X1 @ X2 @ X0 )
!= $true ) )
| ( funcGraphProp1 != $true ) ) ),
inference(nnf_transformation,[],[f28]) ).
thf(f38,plain,
( ( ( funcGraphProp1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) ) )
& ( ( func @ X1 @ X0 @ X2 )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
| ( $true
= ( in @ ( kpair @ X7 @ ( ap @ X5 @ X4 @ X6 @ X7 ) ) @ X6 ) ) )
| ( ( func @ X5 @ X4 @ X6 )
!= $true ) )
| ( funcGraphProp1 != $true ) ) ),
inference(rectify,[],[f37]) ).
thf(f39,plain,
( ( ( funcGraphProp1 = $true )
| ( ( ( in @ sK12 @ sK10 )
= $true )
& ( ( in @ ( kpair @ sK12 @ ( ap @ sK10 @ sK9 @ sK11 @ sK12 ) ) @ sK11 )
!= $true )
& ( ( func @ sK10 @ sK9 @ sK11 )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
| ( $true
= ( in @ ( kpair @ X7 @ ( ap @ X5 @ X4 @ X6 @ X7 ) ) @ X6 ) ) )
| ( ( func @ X5 @ X4 @ X6 )
!= $true ) )
| ( funcGraphProp1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f38]) ).
thf(f40,plain,
( ( ! [X0: $i,X1: $i > $o] :
( ( ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ! [X3: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X3 )
!= $true )
| ( X2 = X3 ) ) ) )
| ( ex1E2 != $true ) )
& ( ( ex1E2 = $true )
| ? [X0: $i,X1: $i > $o] :
( ( ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( X1 @ X3 )
= $true )
& ( X2 != X3 ) ) ) ) ) ),
inference(nnf_transformation,[],[f31]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i > $o] :
( ( ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ! [X3: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X3 )
!= $true )
| ( X2 = X3 ) ) ) )
| ( ex1E2 != $true ) )
& ( ( ex1E2 = $true )
| ? [X4: $i,X5: $i > $o] :
( ( ( ex1 @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) )
= $true )
& ? [X6: $i] :
( ( $true
= ( in @ X6 @ X4 ) )
& ? [X7: $i] :
( ( $true
= ( X5 @ X6 ) )
& ( ( in @ X7 @ X4 )
= $true )
& ( $true
= ( X5 @ X7 ) )
& ( X6 != X7 ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f42,plain,
( ( ! [X0: $i,X1: $i > $o] :
( ( ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ! [X3: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X3 )
!= $true )
| ( X2 = X3 ) ) ) )
| ( ex1E2 != $true ) )
& ( ( ex1E2 = $true )
| ( ( ( ex1 @ sK13
@ ^ [Y0: $i] : ( sK14 @ Y0 ) )
= $true )
& ( ( in @ sK15 @ sK13 )
= $true )
& ( ( sK14 @ sK15 )
= $true )
& ( ( in @ sK16 @ sK13 )
= $true )
& ( ( sK14 @ sK16 )
= $true )
& ( sK15 != sK16 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16]),skolemize(X4,sK13),skolemize(X5,sK14),skolemize(X6,sK15),skolemize(X7,sK16)],[f41]) ).
thf(f44,plain,
( ( in @ sK3 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f45,plain,
( ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 )
= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f46,plain,
( $true
= ( in @ sK4 @ sK2 ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f47,plain,
( sK4
!= ( ap @ sK1 @ sK2 @ sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f48,plain,
( ( func @ sK1 @ sK2 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f49,plain,
funcGraphProp1 = $true,
inference(cnf_transformation,[],[f33]) ).
thf(f50,plain,
ex1E2 = $true,
inference(cnf_transformation,[],[f33]) ).
thf(f51,plain,
app = $true,
inference(cnf_transformation,[],[f33]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( app != $true )
| ( ( func @ X1 @ X0 @ X2 )
!= $true )
| ( ( in @ ( ap @ X1 @ X0 @ X2 @ X3 ) @ X0 )
= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f56,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f58,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( func @ X5 @ X4 @ X6 )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( $true
= ( in @ ( kpair @ X7 @ ( ap @ X5 @ X4 @ X6 @ X7 ) ) @ X6 ) )
| ( funcGraphProp1 != $true ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= $true )
| ( X2 = X3 )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X2 )
!= $true )
| ( ( X1 @ X3 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ex1E2 != $true ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( ex1E2 != $true )
| ( ( X1 @ X2 )
!= $true )
| ( ( ex1 @ X0 @ X1 )
!= $true )
| ( ( X1 @ X3 )
!= $true )
| ( X2 = X3 )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f75,definition,
( spl17_1
<=> ( app = $true ) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
thf(f78,plain,
spl17_1,
inference(avatar_split_clause,[],[f51,f75]) ).
thf(f89,definition,
( spl17_4
<=> ( ex1E2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
thf(f103,definition,
( spl17_7
<=> ( funcGraphProp1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
thf(f108,definition,
( spl17_8
<=> ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_8])],[avatar_definition]) ).
thf(f110,plain,
( ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 )
= $true )
| ~ spl17_8 ),
inference(avatar_component_clause,[],[f108]) ).
thf(f111,plain,
spl17_8,
inference(avatar_split_clause,[],[f45,f108]) ).
thf(f123,definition,
( spl17_11
<=> ( $true
= ( in @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_11])],[avatar_definition]) ).
thf(f125,plain,
( ( $true
= ( in @ sK4 @ sK2 ) )
| ~ spl17_11 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f126,plain,
spl17_11,
inference(avatar_split_clause,[],[f46,f123]) ).
thf(f128,definition,
( spl17_12
<=> ( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_12])],[avatar_definition]) ).
thf(f130,plain,
( ( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) )
| ~ spl17_12 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f131,plain,
spl17_12,
inference(avatar_split_clause,[],[f56,f128]) ).
thf(f133,definition,
( spl17_13
<=> ( sK4
= ( ap @ sK1 @ sK2 @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_13])],[avatar_definition]) ).
thf(f135,plain,
( ( sK4
!= ( ap @ sK1 @ sK2 @ sK0 @ sK3 ) )
| spl17_13 ),
inference(avatar_component_clause,[],[f133]) ).
thf(f136,plain,
~ spl17_13,
inference(avatar_split_clause,[],[f47,f133]) ).
thf(f137,plain,
spl17_4,
inference(avatar_split_clause,[],[f50,f89]) ).
thf(f153,plain,
spl17_7,
inference(avatar_split_clause,[],[f49,f103]) ).
thf(f160,definition,
( spl17_18
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( ( func @ X5 @ X4 @ X6 )
!= $true )
| ( $true
= ( in @ ( kpair @ X7 @ ( ap @ X5 @ X4 @ X6 @ X7 ) ) @ X6 ) )
| ( ( in @ X7 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl17_18])],[avatar_definition]) ).
thf(f161,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( kpair @ X7 @ ( ap @ X5 @ X4 @ X6 @ X7 ) ) @ X6 ) )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( func @ X5 @ X4 @ X6 )
!= $true ) )
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f160]) ).
thf(f162,plain,
( spl17_18
| ~ spl17_7 ),
inference(avatar_split_clause,[],[f58,f103,f160]) ).
thf(f164,definition,
( spl17_19
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( func @ X1 @ X0 @ X2 )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ ( ap @ X1 @ X0 @ X2 @ X3 ) @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl17_19])],[avatar_definition]) ).
thf(f165,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( ap @ X1 @ X0 @ X2 @ X3 ) @ X0 )
= $true )
| ( ( func @ X1 @ X0 @ X2 )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ~ spl17_19 ),
inference(avatar_component_clause,[],[f164]) ).
thf(f166,plain,
( spl17_19
| ~ spl17_1 ),
inference(avatar_split_clause,[],[f55,f75,f164]) ).
thf(f183,definition,
( spl17_23
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( X2 = X3 )
| ( ( X1 @ X3 )
!= $true )
| ( ( ex1 @ X0 @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl17_23])],[avatar_definition]) ).
thf(f184,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( ( ex1 @ X0 @ X1 )
!= $true )
| ( ( X1 @ X3 )
!= $true )
| ( ( X1 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f183]) ).
thf(f185,plain,
( spl17_23
| ~ spl17_4 ),
inference(avatar_split_clause,[],[f73,f89,f183]) ).
thf(f197,definition,
( spl17_26
<=> ( ( func @ sK1 @ sK2 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_26])],[avatar_definition]) ).
thf(f199,plain,
( ( ( func @ sK1 @ sK2 @ sK0 )
= $true )
| ~ spl17_26 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f200,plain,
spl17_26,
inference(avatar_split_clause,[],[f48,f197]) ).
thf(f202,definition,
( spl17_27
<=> ( ( in @ sK3 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_27])],[avatar_definition]) ).
thf(f204,plain,
( ( ( in @ sK3 @ sK1 )
= $true )
| ~ spl17_27 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f205,plain,
spl17_27,
inference(avatar_split_clause,[],[f44,f202]) ).
thf(f288,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
@ X1 )
= ( func @ X1 ) )
| ~ spl17_12 ),
inference(argument_congruence,[],[f130]) ).
thf(f289,plain,
( ! [X1: $i] :
( ( func @ X1 )
= ( ^ [Y0: $i,Y1: $i] :
( ( breln @ X1 @ Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ex1 @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) )
| ~ spl17_12 ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f292,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i,Y1: $i] :
( ( breln @ X1 @ Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ex1 @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
@ X2 )
= ( func @ X1 @ X2 ) )
| ~ spl17_12 ),
inference(argument_congruence,[],[f289]) ).
thf(f293,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( breln @ X1 @ X2 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ex1 @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
= ( func @ X1 @ X2 ) )
| ~ spl17_12 ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f301,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( func @ X1 @ X2 @ X3 )
= ( ^ [Y0: $i] :
( ( breln @ X1 @ X2 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ex1 @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
@ X3 ) )
| ~ spl17_12 ),
inference(argument_congruence,[],[f293]) ).
thf(f303,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( breln @ X1 @ X2 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ex1 @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
@ X3 ) )
| ( ( func @ X1 @ X2 @ X3 )
= $false ) )
| ~ spl17_12 ),
inference(iff_proxy_clausification,[],[f301]) ).
thf(f304,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( ( breln @ X1 @ X2 @ X3 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ex1 @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) )
= $true )
| ( ( func @ X1 @ X2 @ X3 )
= $false ) )
| ~ spl17_12 ),
inference(beta-eta_normalization,[],[f303]) ).
thf(f305,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ex1 @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) )
= $true )
| ( ( func @ X1 @ X2 @ X3 )
= $false ) )
| ~ spl17_12 ),
inference(and_proxy_clausification,[],[f304]) ).
thf(f307,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ex1 @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) )
@ X4 ) )
| ( ( func @ X1 @ X2 @ X3 )
= $false ) )
| ~ spl17_12 ),
inference(pi_proxy_clausification,[],[f305]) ).
thf(f308,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( in @ X4 @ X1 )
=> ( ex1 @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X3 ) ) ) )
| ( ( func @ X1 @ X2 @ X3 )
= $false ) )
| ~ spl17_12 ),
inference(beta-eta_normalization,[],[f307]) ).
thf(f309,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ex1 @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X3 ) )
= $true )
| ( ( in @ X4 @ X1 )
= $false )
| ( ( func @ X1 @ X2 @ X3 )
= $false ) )
| ~ spl17_12 ),
inference(imp_proxy_clausification,[],[f308]) ).
thf(f330,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( X3 = X4 )
| ( $true
!= ( ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ X2 )
@ X3 ) )
| ( ( in @ X4 @ X0 )
!= $true )
| ( $true != $true )
| ( $true
!= ( ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ X2 )
@ X4 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X1 @ X5 )
= $false )
| ( ( func @ X5 @ X0 @ X2 )
= $false ) )
| ~ spl17_12
| ~ spl17_23 ),
inference(superposition,[],[f184,f309]) ).
thf(f331,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( X3 = X4 )
| ( ( func @ X5 @ X0 @ X2 )
= $false )
| ( $true
!= ( ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ X2 )
@ X4 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X1 @ X5 )
= $false )
| ( ( in @ X4 @ X0 )
!= $true )
| ( $true
!= ( ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ X2 )
@ X3 ) ) )
| ~ spl17_12
| ~ spl17_23 ),
inference(trivial_inequality_removal,[],[f330]) ).
thf(f332,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ ( kpair @ X1 @ X3 ) @ X2 ) )
| ( X3 = X4 )
| ( ( in @ ( kpair @ X1 @ X4 ) @ X2 )
!= $true )
| ( ( func @ X5 @ X0 @ X2 )
= $false )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X1 @ X5 )
= $false )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ~ spl17_12
| ~ spl17_23 ),
inference(beta-eta_normalization,[],[f331]) ).
thf(f333,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ sK3 @ X1 )
= $false )
| ( ( in @ sK4 @ X2 )
!= $true )
| ( sK4 = X0 )
| ( $true
!= ( in @ ( kpair @ sK3 @ X0 ) @ sK0 ) )
| ( ( func @ X1 @ X2 @ sK0 )
= $false )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true != $true ) )
| ~ spl17_8
| ~ spl17_12
| ~ spl17_23 ),
inference(superposition,[],[f332,f110]) ).
thf(f337,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ sK3 @ X0 ) @ sK0 ) )
| ( ( func @ X1 @ X2 @ sK0 )
= $false )
| ( ( in @ sK3 @ X1 )
= $false )
| ( ( in @ sK4 @ X2 )
!= $true )
| ( sK4 = X0 )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ~ spl17_8
| ~ spl17_12
| ~ spl17_23 ),
inference(trivial_inequality_removal,[],[f333]) ).
thf(f338,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( func @ X2 @ X3 @ sK0 )
= $false )
| ( $false
= ( in @ sK3 @ X2 ) )
| ( ( in @ sK3 @ X0 )
!= $true )
| ( ( func @ X0 @ X1 @ sK0 )
!= $true )
| ( $true
!= ( in @ sK4 @ X3 ) )
| ( ( in @ ( ap @ X0 @ X1 @ sK0 @ sK3 ) @ X3 )
!= $true )
| ( sK4
= ( ap @ X0 @ X1 @ sK0 @ sK3 ) )
| ( $true != $true ) )
| ~ spl17_8
| ~ spl17_12
| ~ spl17_18
| ~ spl17_23 ),
inference(superposition,[],[f337,f161]) ).
thf(f340,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( ap @ X0 @ X1 @ sK0 @ sK3 ) @ X3 )
!= $true )
| ( $false
= ( in @ sK3 @ X2 ) )
| ( sK4
= ( ap @ X0 @ X1 @ sK0 @ sK3 ) )
| ( ( in @ sK3 @ X0 )
!= $true )
| ( ( func @ X2 @ X3 @ sK0 )
= $false )
| ( ( func @ X0 @ X1 @ sK0 )
!= $true )
| ( $true
!= ( in @ sK4 @ X3 ) ) )
| ~ spl17_8
| ~ spl17_12
| ~ spl17_18
| ~ spl17_23 ),
inference(trivial_inequality_removal,[],[f338]) ).
thf(f345,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ sK3 @ X0 )
!= $true )
| ( ( in @ sK3 @ X0 )
!= $true )
| ( $false
= ( in @ sK3 @ X2 ) )
| ( $true != $true )
| ( sK4
= ( ap @ X0 @ X1 @ sK0 @ sK3 ) )
| ( ( in @ sK4 @ X1 )
!= $true )
| ( ( func @ X0 @ X1 @ sK0 )
!= $true )
| ( ( func @ X2 @ X1 @ sK0 )
= $false )
| ( ( func @ X0 @ X1 @ sK0 )
!= $true ) )
| ~ spl17_8
| ~ spl17_12
| ~ spl17_18
| ~ spl17_19
| ~ spl17_23 ),
inference(superposition,[],[f340,f165]) ).
thf(f347,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ sK4 @ X1 )
!= $true )
| ( sK4
= ( ap @ X0 @ X1 @ sK0 @ sK3 ) )
| ( ( func @ X2 @ X1 @ sK0 )
= $false )
| ( $true != $true )
| ( $false
= ( in @ sK3 @ X2 ) )
| ( ( func @ X0 @ X1 @ sK0 )
!= $true )
| ( ( in @ sK3 @ X0 )
!= $true ) )
| ~ spl17_8
| ~ spl17_12
| ~ spl17_18
| ~ spl17_19
| ~ spl17_23 ),
inference(duplicate_literal_removal,[],[f345]) ).
thf(f348,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( sK4
= ( ap @ X0 @ X1 @ sK0 @ sK3 ) )
| ( ( func @ X2 @ X1 @ sK0 )
= $false )
| ( ( func @ X0 @ X1 @ sK0 )
!= $true )
| ( $false
= ( in @ sK3 @ X2 ) )
| ( ( in @ sK4 @ X1 )
!= $true )
| ( ( in @ sK3 @ X0 )
!= $true ) )
| ~ spl17_8
| ~ spl17_12
| ~ spl17_18
| ~ spl17_19
| ~ spl17_23 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f367,definition,
( spl17_35
<=> ! [X1: $i] :
( ( ( in @ sK3 @ X1 )
= $false )
| ( $false
= ( func @ X1 @ sK2 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_35])],[avatar_definition]) ).
thf(f368,plain,
( ! [X1: $i] :
( ( $false
= ( func @ X1 @ sK2 @ sK0 ) )
| ( ( in @ sK3 @ X1 )
= $false ) )
| ~ spl17_35 ),
inference(avatar_component_clause,[],[f367]) ).
thf(f373,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false = $true )
| ~ spl17_26
| ~ spl17_35 ),
inference(superposition,[],[f368,f199]) ).
thf(f375,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ~ spl17_26
| ~ spl17_35 ),
inference(trivial_inequality_removal,[],[f373]) ).
thf(f378,definition,
( spl17_37
<=> ( $false
= ( in @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_37])],[avatar_definition]) ).
thf(f380,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ~ spl17_37 ),
inference(avatar_component_clause,[],[f378]) ).
thf(f381,plain,
( spl17_37
| ~ spl17_26
| ~ spl17_35 ),
inference(avatar_split_clause,[],[f375,f367,f197,f378]) ).
thf(f383,plain,
( ! [X0: $i] :
( ( ( in @ sK3 @ sK1 )
!= $true )
| ( ( func @ X0 @ sK2 @ sK0 )
= $false )
| ( $true
!= ( in @ sK4 @ sK2 ) )
| ( ( func @ sK1 @ sK2 @ sK0 )
!= $true )
| ( sK4 != sK4 )
| ( $false
= ( in @ sK3 @ X0 ) ) )
| ~ spl17_8
| ~ spl17_12
| spl17_13
| ~ spl17_18
| ~ spl17_19
| ~ spl17_23 ),
inference(superposition,[],[f135,f348]) ).
thf(f397,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ sK2 ) )
| ( ( func @ sK1 @ sK2 @ sK0 )
!= $true )
| ( ( func @ X0 @ sK2 @ sK0 )
= $false )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( ( in @ sK3 @ sK1 )
!= $true ) )
| ~ spl17_8
| ~ spl17_12
| spl17_13
| ~ spl17_18
| ~ spl17_19
| ~ spl17_23 ),
inference(trivial_inequality_removal,[],[f383]) ).
thf(f398,plain,
( ! [X0: $i] :
( ( ( func @ sK1 @ sK2 @ sK0 )
!= $true )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( ( in @ sK3 @ sK1 )
!= $true )
| ( ( func @ X0 @ sK2 @ sK0 )
= $false ) )
| ~ spl17_8
| ~ spl17_11
| ~ spl17_12
| spl17_13
| ~ spl17_18
| ~ spl17_19
| ~ spl17_23 ),
inference(forward_subsumption_resolution,[],[f397,f125]) ).
thf(f399,plain,
( ! [X0: $i] :
( ( ( func @ X0 @ sK2 @ sK0 )
= $false )
| ( ( in @ sK3 @ sK1 )
!= $true )
| ( $false
= ( in @ sK3 @ X0 ) ) )
| ~ spl17_8
| ~ spl17_11
| ~ spl17_12
| spl17_13
| ~ spl17_18
| ~ spl17_19
| ~ spl17_23
| ~ spl17_26 ),
inference(forward_subsumption_resolution,[],[f398,f199]) ).
thf(f400,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( ( func @ X0 @ sK2 @ sK0 )
= $false ) )
| ~ spl17_8
| ~ spl17_11
| ~ spl17_12
| spl17_13
| ~ spl17_18
| ~ spl17_19
| ~ spl17_23
| ~ spl17_26
| ~ spl17_27 ),
inference(forward_subsumption_resolution,[],[f399,f204]) ).
thf(f401,plain,
( spl17_35
| ~ spl17_8
| ~ spl17_11
| ~ spl17_12
| spl17_13
| ~ spl17_18
| ~ spl17_19
| ~ spl17_23
| ~ spl17_26
| ~ spl17_27 ),
inference(avatar_split_clause,[],[f400,f202,f197,f183,f164,f160,f133,f128,f123,f108,f367]) ).
thf(f426,plain,
( ( $false = $true )
| ~ spl17_27
| ~ spl17_37 ),
inference(superposition,[],[f204,f380]) ).
thf(f429,plain,
( $false
| ~ spl17_27
| ~ spl17_37 ),
inference(trivial_inequality_removal,[],[f426]) ).
thf(f430,plain,
( ~ spl17_27
| ~ spl17_37 ),
inference(avatar_contradiction_clause,[],[f429]) ).
cnf(s1,plain,
spl17_1,
inference(sat_conversion,[],[f78]) ).
cnf(s6,plain,
spl17_8,
inference(sat_conversion,[],[f111]) ).
cnf(s9,plain,
spl17_11,
inference(sat_conversion,[],[f126]) ).
cnf(s10,plain,
spl17_12,
inference(sat_conversion,[],[f131]) ).
cnf(s11,plain,
~ spl17_13,
inference(sat_conversion,[],[f136]) ).
cnf(s12,plain,
spl17_4,
inference(sat_conversion,[],[f137]) ).
cnf(s16,plain,
spl17_7,
inference(sat_conversion,[],[f153]) ).
cnf(s18,plain,
( ~ spl17_7
| spl17_18 ),
inference(sat_conversion,[],[f162]) ).
cnf(s19,plain,
( ~ spl17_1
| spl17_19 ),
inference(sat_conversion,[],[f166]) ).
cnf(s23,plain,
( ~ spl17_4
| spl17_23 ),
inference(sat_conversion,[],[f185]) ).
cnf(s26,plain,
spl17_26,
inference(sat_conversion,[],[f200]) ).
cnf(s27,plain,
spl17_27,
inference(sat_conversion,[],[f205]) ).
cnf(s37,plain,
( ~ spl17_26
| ~ spl17_35
| spl17_37 ),
inference(sat_conversion,[],[f381]) ).
cnf(s39,plain,
( ~ spl17_8
| ~ spl17_11
| ~ spl17_12
| spl17_13
| ~ spl17_18
| ~ spl17_19
| ~ spl17_23
| ~ spl17_26
| ~ spl17_27
| spl17_35 ),
inference(sat_conversion,[],[f401]) ).
cnf(s44,plain,
( ~ spl17_27
| ~ spl17_37 ),
inference(sat_conversion,[],[f430]) ).
cnf(s45,plain,
~ spl17_37,
inference(rat,[],[s44,s27]) ).
cnf(s46,plain,
~ spl17_35,
inference(rat,[],[s37,s45,s26]) ).
cnf(s47,plain,
spl17_18,
inference(rat,[],[s18,s16]) ).
cnf(s48,plain,
spl17_23,
inference(rat,[],[s23,s12]) ).
cnf(s51,plain,
~ spl17_19,
inference(rat,[],[s39,s46,s27,s26,s48,s9,s47,s11,s10,s6]) ).
cnf(s52,plain,
~ spl17_1,
inference(rat,[],[s19,s51]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s1,s52]) ).
thf(f431,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU686^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n018.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 14:11:11 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.30 Running higher-order theorem proving
% 0.23/0.31 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.40 % (133665)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.51/0.40 % (133674)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2586085050:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.51/0.40 % (133670)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2639372266:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.51/0.40 % (133676)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.51/0.40 % (133676)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
% 0.51/0.40 % (133674)Instruction limit reached!
% 0.51/0.40 % (133674)------------------------------
% 0.51/0.40 % (133674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (133674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (133674)CaDiCaL version: 2.1.3
% 0.51/0.40 % (133674)Termination reason: Instruction limit
% 0.51/0.40 % (133674)Termination phase: Saturation
% 0.51/0.40 % (133674)Time elapsed: 0.012 s
% 0.51/0.40 % (133674)Peak memory usage: 11 MB
% 0.51/0.40 % (133674)Instructions burned: 24 (million)
% 0.51/0.40 % (133671)lrs+10_16_si=on:nwc=1.5:random_seed=3429167420:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.51/0.40 % (133672)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2469562095:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.51/0.40 % (133673)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=331703868: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)
% 0.51/0.40 % (133675)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3336554220:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.51/0.40 % (133676)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3408484594:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.51/0.40 % (133672)Instruction limit reached!
% 0.51/0.40 % (133672)------------------------------
% 0.51/0.40 % (133672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (133672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (133672)CaDiCaL version: 2.1.3
% 0.51/0.40 % (133672)Termination reason: Instruction limit
% 0.51/0.40 % (133672)Termination phase: Function definition elimination
% 0.51/0.40 % (133672)Time elapsed: 0.003 s
% 0.51/0.40 % (133672)Peak memory usage: 10 MB
% 0.51/0.40 % (133672)Instructions burned: 3 (million)
% 0.51/0.40 % (133680)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2776207482:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.51/0.40 % (133671)Instruction limit reached!
% 0.51/0.40 % (133671)------------------------------
% 0.51/0.40 % (133671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (133671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (133671)CaDiCaL version: 2.1.3
% 0.51/0.40 % (133671)Termination reason: Instruction limit
% 0.51/0.40 % (133671)Termination phase: Saturation
% 0.51/0.40 % (133671)Time elapsed: 0.017 s
% 0.51/0.40 % (133671)Peak memory usage: 12 MB
% 0.51/0.40 % (133671)Instructions burned: 18 (million)
% 0.51/0.40 % (133680)Instruction limit reached!
% 0.51/0.40 % (133680)------------------------------
% 0.51/0.40 % (133680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (133680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (133680)CaDiCaL version: 2.1.3
% 0.51/0.40 % (133680)Termination reason: Instruction limit
% 0.51/0.40 % (133680)Termination phase: Property scanning
% 0.51/0.40 % (133680)Time elapsed: 0.001 s
% 0.51/0.40 % (133680)Peak memory usage: 10 MB
% 0.51/0.40 % (133680)Instructions burned: 2 (million)
% 0.51/0.40 % (133673) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-133665-133673"...
% 0.51/0.40 % (133685)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3935928679:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.51/0.40 % (133687)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.51/0.40 % (133688)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2623122227:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.51/0.40 % (133685)Instruction limit reached!
% 0.51/0.40 % (133685)------------------------------
% 0.51/0.40 % (133685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (133685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (133685)CaDiCaL version: 2.1.3
% 0.51/0.40 % (133685)Termination reason: Instruction limit
% 0.51/0.40 % (133685)Termination phase: Saturation
% 0.51/0.40 % (133685)Time elapsed: 0.005 s
% 0.51/0.40 % (133685)Peak memory usage: 12 MB
% 0.51/0.40 % (133685)Instructions burned: 5 (million)
% 0.51/0.40 % (133687)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3532794236:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.51/0.40 % (133673)...printing done.
% 0.51/0.40 % (133673)Refutation found. Thanks to Tanya!
% 0.51/0.40 % SZS status Theorem for theBenchmark
% 0.51/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.51/0.40 % (133673)------------------------------
% 0.51/0.40 % (133673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (133673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (133673)CaDiCaL version: 2.1.3
% 0.51/0.40 % (133673)Termination reason: Refutation
% 0.51/0.40 % (133673)Time elapsed: 0.041 s
% 0.51/0.40 % (133673)Peak memory usage: 13 MB
% 0.51/0.40 % (133673)Instructions burned: 40 (million)
% 0.51/0.40 % (133665)Success in time 0.079 s
% 0.51/0.40 % Vampire exiting
%------------------------------------------------------------------------------