%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU687^2 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:47 AM UTC 2026
% Result : Theorem 0.24s 0.36s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 751 ( 206 equ; 0 cnn)
% Maximal formula atoms : 12 ( 15 avg)
% Number of connectives : 992 ( 93 ~; 82 |; 56 &; 702 @)
% ( 5 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 19 con; 0-4 aty)
% Number of variables : 162 ( 0 ^; 126 !; 36 ?; 162 :)
% 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,
funcGraphProp1: $o ).
thf(func_def_14,type,
funcGraphProp2: $o ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_24,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vIMP: $o > $o > $o ).
thf(func_def_26,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
sK15: $i > $i ).
thf(f5,axiom,
( funcGraphProp1
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(f6,axiom,
! [X2: $i,X0: $i,X1: $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 ) ) ) ) )
= funcGraphProp2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(f7,conjecture,
( funcGraphProp1
=> ( funcGraphProp2
=> ! [X0: $i,X2: $i,X1: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( func @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcextLem) ).
thf(f8,negated_conjecture,
~ ( funcGraphProp1
=> ( funcGraphProp2
=> ! [X0: $i,X2: $i,X1: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( func @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X2 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f14,plain,
~ ( funcGraphProp1
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X2 @ X1 )
=> ! [X3: $i] :
( ( func @ X0 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X2 @ X3 @ X4 )
= ( ap @ X0 @ X2 @ X1 @ X4 ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f15,plain,
~ ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp2 = $true )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( func @ X0 @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( func @ X0 @ X2 @ X3 )
= $true )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ap @ X0 @ X2 @ X3 @ X4 )
= ( ap @ X0 @ X2 @ X1 @ X4 ) ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X0 )
= $true )
=> ! [X6: $i] :
( ( ( in @ X6 @ X2 )
= $true )
=> ( ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
= $true )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X1 )
= $true ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( funcGraphProp1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 )
= $true ) ) )
<=> ( funcGraphProp1 = $true ) ),
inference(fool_elimination,[],[f16]) ).
thf(f20,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) )
= funcGraphProp2 ),
inference(rectify,[],[f6]) ).
thf(f21,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( ( funcGraphProp1 = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( func @ X0 @ X2 @ X1 )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 )
= $true ) ) ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f23,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $i] :
( ? [X5: $i] :
( ? [X6: $i] :
( ( ( in @ ( kpair @ X5 @ X6 ) @ X1 )
!= $true )
& ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
= $true )
& ( ( in @ X6 @ X2 )
= $true ) )
& ( ( in @ X5 @ X0 )
= $true ) )
& ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( ( ap @ X0 @ X2 @ X3 @ X4 )
= ( ap @ X0 @ X2 @ X1 @ X4 ) ) )
& ( ( func @ X0 @ X2 @ X3 )
= $true ) )
& ( ( func @ X0 @ X2 @ X1 )
= $true ) )
& ( funcGraphProp2 = $true )
& ( funcGraphProp1 = $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f24,plain,
( ( funcGraphProp2 = $true )
& ( funcGraphProp1 = $true )
& ? [X2: $i,X0: $i,X1: $i] :
( ( ( func @ X0 @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( ( ap @ X0 @ X2 @ X3 @ X4 )
= ( ap @ X0 @ X2 @ X1 @ X4 ) ) )
& ? [X5: $i] :
( ? [X6: $i] :
( ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
= $true )
& ( ( in @ X6 @ X2 )
= $true )
& ( ( in @ ( kpair @ X5 @ X6 ) @ X1 )
!= $true ) )
& ( ( in @ X5 @ X0 )
= $true ) )
& ( ( func @ X0 @ X2 @ X3 )
= $true ) ) ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
| ( $true
!= ( in @ X4 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( func @ X1 @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f26,plain,
( ( funcGraphProp2 = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
!= $true )
| ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X2 ) )
| ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) ) ),
inference(flattening,[],[f25]) ).
thf(f27,plain,
( ( ( funcGraphProp1 = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( func @ X0 @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 )
!= $true ) ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( func @ X0 @ X2 @ X1 )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 )
= $true ) ) )
| ( funcGraphProp1 != $true ) ) ),
inference(nnf_transformation,[],[f22]) ).
thf(f28,plain,
( ( ( funcGraphProp1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ ( kpair @ X3 @ ( ap @ X2 @ X0 @ X1 @ X3 ) ) @ X1 )
!= $true ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ( ( func @ X6 @ X4 @ X5 )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( $true
= ( in @ ( kpair @ X7 @ ( ap @ X6 @ X4 @ X5 @ X7 ) ) @ X5 ) ) ) )
| ( funcGraphProp1 != $true ) ) ),
inference(rectify,[],[f27]) ).
thf(f29,plain,
( ( ( funcGraphProp1 = $true )
| ( ( ( func @ sK2 @ sK0 @ sK1 )
= $true )
& ( ( in @ sK3 @ sK2 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK3 @ ( ap @ sK2 @ sK0 @ sK1 @ sK3 ) ) @ sK1 ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ( ( func @ X6 @ X4 @ X5 )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( $true
= ( in @ ( kpair @ X7 @ ( ap @ X6 @ X4 @ X5 @ X7 ) ) @ X5 ) ) ) )
| ( funcGraphProp1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f28]) ).
thf(f30,plain,
( ( ( funcGraphProp2 = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( ( ap @ X1 @ X2 @ X0 @ X3 )
!= X4 )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) )
& ( ( in @ X3 @ X1 )
= $true ) ) ) )
& ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
!= $true )
| ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X2 ) )
| ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
| ( funcGraphProp2 != $true ) ) ),
inference(nnf_transformation,[],[f26]) ).
thf(f31,plain,
( ( ( funcGraphProp2 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( ( ap @ X0 @ X2 @ X1 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( ( func @ X5 @ X7 @ X6 )
!= $true )
| ! [X8: $i] :
( ! [X9: $i] :
( ( ( in @ X9 @ X7 )
!= $true )
| ( ( ap @ X5 @ X7 @ X6 @ X8 )
= X9 )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X6 ) ) )
| ( $true
!= ( in @ X8 @ X5 ) ) ) )
| ( funcGraphProp2 != $true ) ) ),
inference(rectify,[],[f30]) ).
thf(f32,plain,
( ( ( funcGraphProp2 = $true )
| ( ( $true
= ( func @ sK4 @ sK6 @ sK5 ) )
& ( ( in @ sK8 @ sK6 )
= $true )
& ( ( ap @ sK4 @ sK6 @ sK5 @ sK7 )
!= sK8 )
& ( ( in @ ( kpair @ sK7 @ sK8 ) @ sK5 )
= $true )
& ( ( in @ sK7 @ sK4 )
= $true ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( ( func @ X5 @ X7 @ X6 )
!= $true )
| ! [X8: $i] :
( ! [X9: $i] :
( ( ( in @ X9 @ X7 )
!= $true )
| ( ( ap @ X5 @ X7 @ X6 @ X8 )
= X9 )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X6 ) ) )
| ( $true
!= ( in @ X8 @ X5 ) ) ) )
| ( funcGraphProp2 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7),skolemize(X4,sK8)],[f31]) ).
thf(f33,plain,
( ( funcGraphProp2 = $true )
& ( funcGraphProp1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X1 @ X0 @ X2 ) )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( ap @ X1 @ X0 @ X2 @ X4 )
= ( ap @ X1 @ X0 @ X3 @ X4 ) ) )
& ? [X5: $i] :
( ? [X6: $i] :
( ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
= $true )
& ( $true
= ( in @ X6 @ X0 ) )
& ( ( in @ ( kpair @ X5 @ X6 ) @ X2 )
!= $true ) )
& ( ( in @ X5 @ X1 )
= $true ) )
& ( $true
= ( func @ X1 @ X0 @ X3 ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f34,plain,
( ( funcGraphProp2 = $true )
& ( funcGraphProp1 = $true )
& ( ( func @ sK10 @ sK9 @ sK11 )
= $true )
& ! [X4: $i] :
( ( ( in @ X4 @ sK10 )
!= $true )
| ( ( ap @ sK10 @ sK9 @ sK12 @ X4 )
= ( ap @ sK10 @ sK9 @ sK11 @ X4 ) ) )
& ( $true
= ( in @ ( kpair @ sK13 @ sK14 ) @ sK12 ) )
& ( ( in @ sK14 @ sK9 )
= $true )
& ( ( in @ ( kpair @ sK13 @ sK14 ) @ sK11 )
!= $true )
& ( ( in @ sK13 @ sK10 )
= $true )
& ( $true
= ( func @ sK10 @ sK9 @ sK12 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13,sK14]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12),skolemize(X5,sK13),skolemize(X6,sK14)],[f33]) ).
thf(f36,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( funcGraphProp1 != $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( $true
= ( in @ ( kpair @ X7 @ ( ap @ X6 @ X4 @ X5 @ X7 ) ) @ X5 ) )
| ( ( func @ X6 @ X4 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f41,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( ap @ X5 @ X7 @ X6 @ X8 )
= X9 )
| ( $true
!= ( in @ X8 @ X5 ) )
| ( ( in @ X9 @ X7 )
!= $true )
| ( funcGraphProp2 != $true )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X6 ) )
| ( ( func @ X5 @ X7 @ X6 )
!= $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f48,plain,
( $true
= ( func @ sK10 @ sK9 @ sK12 ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f49,plain,
( ( in @ sK13 @ sK10 )
= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f50,plain,
( ( in @ ( kpair @ sK13 @ sK14 ) @ sK11 )
!= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f51,plain,
( ( in @ sK14 @ sK9 )
= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f52,plain,
( $true
= ( in @ ( kpair @ sK13 @ sK14 ) @ sK12 ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f53,plain,
! [X4: $i] :
( ( ( ap @ sK10 @ sK9 @ sK12 @ X4 )
= ( ap @ sK10 @ sK9 @ sK11 @ X4 ) )
| ( ( in @ X4 @ sK10 )
!= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f54,plain,
( ( func @ sK10 @ sK9 @ sK11 )
= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f55,plain,
funcGraphProp1 = $true,
inference(cnf_transformation,[],[f34]) ).
thf(f56,plain,
funcGraphProp2 = $true,
inference(cnf_transformation,[],[f34]) ).
thf(f111,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( kpair @ X7 @ ( ap @ X6 @ X4 @ X5 @ X7 ) ) @ X5 ) )
| ( ( func @ X6 @ X4 @ X5 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f36,f55]) ).
thf(f112,plain,
! [X0: $i] :
( ( ( func @ sK10 @ sK9 @ sK11 )
!= $true )
| ( ( in @ X0 @ sK10 )
!= $true )
| ( ( in @ X0 @ sK10 )
!= $true )
| ( ( in @ ( kpair @ X0 @ ( ap @ sK10 @ sK9 @ sK12 @ X0 ) ) @ sK11 )
= $true ) ),
inference(superposition,[],[f111,f53]) ).
thf(f113,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK10 )
!= $true )
| ( ( in @ ( kpair @ X0 @ ( ap @ sK10 @ sK9 @ sK12 @ X0 ) ) @ sK11 )
= $true )
| ( ( func @ sK10 @ sK9 @ sK11 )
!= $true ) ),
inference(duplicate_literal_removal,[],[f112]) ).
thf(f114,plain,
! [X0: $i] :
( ( ( in @ ( kpair @ X0 @ ( ap @ sK10 @ sK9 @ sK12 @ X0 ) ) @ sK11 )
= $true )
| ( ( in @ X0 @ sK10 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f113,f54]) ).
thf(f118,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X6 ) )
| ( $true
!= ( in @ X8 @ X5 ) )
| ( ( func @ X5 @ X7 @ X6 )
!= $true )
| ( ( ap @ X5 @ X7 @ X6 @ X8 )
= X9 )
| ( ( in @ X9 @ X7 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f41,f56]) ).
thf(f121,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( sK14
= ( ap @ X0 @ X1 @ sK12 @ sK13 ) )
| ( ( in @ sK14 @ X1 )
!= $true )
| ( ( func @ X0 @ X1 @ sK12 )
!= $true )
| ( $true
!= ( in @ sK13 @ X0 ) ) ),
inference(superposition,[],[f118,f52]) ).
thf(f124,plain,
! [X0: $i,X1: $i] :
( ( sK14
= ( ap @ X0 @ X1 @ sK12 @ sK13 ) )
| ( ( in @ sK14 @ X1 )
!= $true )
| ( ( func @ X0 @ X1 @ sK12 )
!= $true )
| ( $true
!= ( in @ sK13 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f125,plain,
( ( $true
!= ( func @ sK10 @ sK9 @ sK12 ) )
| ( ( in @ sK13 @ sK10 )
!= $true )
| ( ( in @ ( kpair @ sK13 @ sK14 ) @ sK11 )
= $true )
| ( ( in @ sK13 @ sK10 )
!= $true )
| ( ( in @ sK14 @ sK9 )
!= $true ) ),
inference(superposition,[],[f114,f124]) ).
thf(f127,plain,
( ( ( in @ ( kpair @ sK13 @ sK14 ) @ sK11 )
= $true )
| ( $true
!= ( func @ sK10 @ sK9 @ sK12 ) )
| ( ( in @ sK14 @ sK9 )
!= $true )
| ( ( in @ sK13 @ sK10 )
!= $true ) ),
inference(duplicate_literal_removal,[],[f125]) ).
thf(f129,plain,
( ( ( in @ sK14 @ sK9 )
!= $true )
| ( ( in @ sK13 @ sK10 )
!= $true )
| ( $true
!= ( func @ sK10 @ sK9 @ sK12 ) ) ),
inference(forward_subsumption_resolution,[],[f127,f50]) ).
thf(f130,plain,
( ( ( in @ sK13 @ sK10 )
!= $true )
| ( $true
!= ( func @ sK10 @ sK9 @ sK12 ) ) ),
inference(forward_subsumption_resolution,[],[f129,f51]) ).
thf(f131,plain,
( $true
!= ( func @ sK10 @ sK9 @ sK12 ) ),
inference(forward_subsumption_resolution,[],[f130,f49]) ).
thf(f132,plain,
$false,
inference(forward_subsumption_resolution,[],[f131,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU687^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 % Computer : n010.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 14:09:19 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 Running higher-order theorem proving
% 0.24/0.28 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
% 0.24/0.36 % (2913618)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.36 % (2913624)lrs+10_16_si=on:nwc=1.5:random_seed=952564036:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.36 % (2913623)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1170574985:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.36 % (2913624)Instruction limit reached!
% 0.24/0.36 % (2913624)------------------------------
% 0.24/0.36 % (2913624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (2913624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (2913624)CaDiCaL version: 2.1.3
% 0.24/0.36 % (2913624)Termination reason: Instruction limit
% 0.24/0.36 % (2913624)Termination phase: Saturation
% 0.24/0.36 % (2913624)Time elapsed: 0.011 s
% 0.24/0.36 % (2913624)Peak memory usage: 12 MB
% 0.24/0.36 % (2913624)Instructions burned: 20 (million)
% 0.24/0.36 % (2913627)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=641264157:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.36 % (2913632)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=679823867:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.24/0.36 % (2913632)Instruction limit reached!
% 0.24/0.36 % (2913632)------------------------------
% 0.24/0.36 % (2913632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (2913632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (2913632)CaDiCaL version: 2.1.3
% 0.24/0.36 % (2913632)Termination reason: Instruction limit
% 0.24/0.36 % (2913632)Termination phase: Property scanning
% 0.24/0.36 % (2913632)Time elapsed: 0.002 s
% 0.24/0.36 % (2913632)Peak memory usage: 10 MB
% 0.24/0.36 % (2913632)Instructions burned: 3 (million)
% 0.24/0.36 % (2913627) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2913618-2913627"...
% 0.24/0.36 % (2913627)...printing done.
% 0.24/0.36 % (2913627)Refutation found. Thanks to Tanya!
% 0.24/0.36 % SZS status Theorem for theBenchmark
% 0.24/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.37 % (2913627)------------------------------
% 0.24/0.37 % (2913627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (2913627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (2913627)CaDiCaL version: 2.1.3
% 0.24/0.37 % (2913627)Termination reason: Refutation
% 0.24/0.37 % (2913627)Time elapsed: 0.018 s
% 0.24/0.37 % (2913627)Peak memory usage: 12 MB
% 0.24/0.37 % (2913627)Instructions burned: 17 (million)
% 0.24/0.37 % (2913618)Success in time 0.075 s
% 0.24/0.37 % Vampire exiting
%------------------------------------------------------------------------------