%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU779^2 : 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 : n014.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 08:31:19 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 3
% Syntax : Number of formulae : 55 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 648 ( 125 equ; 0 cnn)
% Maximal formula atoms : 9 ( 11 avg)
% Number of connectives : 1009 ( 10 ~; 42 |; 47 &; 789 @)
% ( 0 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 28 usr; 11 con; 0-4 aty)
% ( 36 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 192 ( 92 ^; 86 !; 14 ?; 192 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
cartprod: $i > $i > $i ).
thf(func_def_4,type,
breln: $i > $i > $i > $o ).
thf(func_def_6,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_7,type,
dpsetconstrI: $o ).
thf(func_def_8,type,
breln1: $i > $i > $o ).
thf(func_def_9,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_29,type,
vNOT: $o > $o ).
thf(f2,axiom,
( dpsetconstrI
= ( ! [X3: $i,X2: $i > $i > $o,X0: $i,X1: $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/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(f4,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X3: $i,X4: $i] :
? [X5: $i] :
( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
& ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ X5 @ X0 ) ) ) )
= breln1compset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compset) ).
thf(f5,conjecture,
( dpsetconstrI
=> ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
=> ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compI) ).
thf(f6,negated_conjecture,
~ ( dpsetconstrI
=> ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
=> ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( dpsetconstrI
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X5 ) @ X0 )
=> ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
~ ( ( dpsetconstrI = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ! [X5: $i] :
( ( $true
= ( in @ X5 @ X1 ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
=> ( ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true )
=> ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f10,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X3: $i,X4: $i] :
? [X5: $i] :
( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
& ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ X5 @ X0 ) ) ) )
= breln1compset ),
inference(rectify,[],[f4]) ).
thf(f11,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f13,plain,
( dpsetconstrI
= ( ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ X0 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( ( X1 @ X0 @ X4 )
=> ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X2 @ X3
@ ^ [X5: $i,X6: $i] : ( X1 @ X5 @ X6 ) ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f14,plain,
( dpsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) ) )
& ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
& ( $true
= ( in @ X5 @ X1 ) ) )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( dpsetconstrI = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f16,plain,
( ( dpsetconstrI = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ? [X4: $i] :
( ? [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) ) )
& ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
& ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true )
& ( $true
= ( in @ X5 @ X1 ) ) )
& ( ( in @ X4 @ X1 )
= $true ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ( dpsetconstrI = $true )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) )
& ( $true
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
& ( ( in @ sK5 @ sK1 )
= $true )
& ( $true
= ( in @ sK4 @ sK1 ) )
& ( $true
= ( breln1 @ sK1 @ sK2 ) )
& ( $true
= ( breln1 @ sK1 @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f16]) ).
thf(f20,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f21,plain,
( dpsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
( $true
= ( in @ sK4 @ sK1 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f25,plain,
( ( in @ sK5 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f26,plain,
( $true
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
( $true
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f28,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f29,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f30,plain,
dpsetconstrI = $true,
inference(cnf_transformation,[],[f17]) ).
thf(f34,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f21,f30]) ).
thf(f35,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) ) )
@ sK1
@ sK0
@ sK2 ) ) ),
inference(definition_unfolding,[],[f28,f20]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f41,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( Y1 @ Y2 @ Y3 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ ( dpsetconstr @ Y0 @ X1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( Y1 @ Y2 @ Y3 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ ( dpsetconstr @ Y0 @ X1 @ Y1 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y0 @ Y1 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ ( dpsetconstr @ X2 @ X1 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y0 @ Y1 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ ( dpsetconstr @ X2 @ X1 @ Y0 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( X3 @ Y0 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( X3 @ Y0 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) ) ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i] :
( $true
= ( ( in @ X4 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ X4 @ Y0 )
=> ( in @ ( kpair @ X4 @ Y0 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ X4 @ Y0 )
=> ( in @ ( kpair @ X4 @ Y0 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) ) )
= $true )
| ( ( in @ X4 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ X4 @ Y0 )
=> ( in @ ( kpair @ X4 @ Y0 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X2 )
= $false )
| ( $true
= ( ( in @ X5 @ X1 )
=> ( ( X3 @ X4 @ X5 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ( X3 @ X4 @ X5 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( ( in @ X5 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) )
| ( ( in @ X5 @ X1 )
= $false )
| ( ( X3 @ X4 @ X5 )
= $false )
| ( ( in @ X4 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 )
@ ( dpsetconstr @ sK1 @ sK1
@ ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f58,plain,
( ( ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 ) ) )
@ sK3
@ sK4 )
= $false )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( ( in @ sK3 @ sK1 )
= $false )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f53,f52]) ).
thf(f59,plain,
( ( ( in @ sK3 @ sK1 )
= $false )
| ( ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 ) ) )
@ sK3
@ sK4 )
= $false )
| ( $false
= ( in @ sK4 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f60,plain,
( ( $false
= ( in @ sK4 @ sK1 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
& ( in @ ( kpair @ Y0 @ sK4 ) @ sK2 )
& ( in @ ( kpair @ sK3 @ Y0 ) @ sK0 ) ) )
= $false )
| ( ( in @ sK3 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X1: $i] :
( ( ( in @ sK3 @ sK1 )
= $false )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
& ( in @ ( kpair @ Y0 @ sK4 ) @ sK2 )
& ( in @ ( kpair @ sK3 @ Y0 ) @ sK0 ) )
@ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X1: $i] :
( ( $false
= ( in @ sK4 @ sK1 ) )
| ( ( ( in @ X1 @ sK1 )
& ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
& ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) )
= $false )
| ( ( in @ sK3 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X1: $i] :
( ( ( ( in @ X1 @ sK1 )
& ( in @ ( kpair @ X1 @ sK4 ) @ sK2 ) )
= $false )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( ( in @ ( kpair @ sK3 @ X1 ) @ sK0 )
= $false )
| ( ( in @ sK3 @ sK1 )
= $false ) ),
inference(and_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X1: $i] :
( ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
= $false )
| ( ( in @ ( kpair @ sK3 @ X1 ) @ sK0 )
= $false )
| ( ( in @ sK3 @ sK1 )
= $false )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X1: $i] :
( ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $true = $false )
| ( ( in @ ( kpair @ sK3 @ X1 ) @ sK0 )
= $false )
| ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
= $false ) ),
inference(forward_demodulation,[],[f64,f29]) ).
thf(f66,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK1 ) )
| ( ( in @ ( kpair @ sK3 @ X1 ) @ sK0 )
= $false )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f67,plain,
! [X1: $i] :
( ( $true = $false )
| ( ( in @ ( kpair @ sK3 @ X1 ) @ sK0 )
= $false )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
= $false ) ),
inference(forward_demodulation,[],[f66,f24]) ).
thf(f68,plain,
! [X1: $i] :
( ( ( in @ ( kpair @ sK3 @ X1 ) @ sK0 )
= $false )
| ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
= $false )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f70,plain,
( ( $false
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) )
| ( $true = $false )
| ( ( in @ sK5 @ sK1 )
= $false ) ),
inference(constrained_superposition,[],[f26,f68]) ).
thf(f71,plain,
( ( ( in @ sK5 @ sK1 )
= $false )
| ( $false
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f73,plain,
( ( $true = $false )
| ( $false
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) ) ),
inference(forward_demodulation,[],[f71,f25]) ).
thf(f74,plain,
( $false
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f77,plain,
$true = $false,
inference(constrained_superposition,[],[f74,f27]) ).
thf(f79,plain,
$false,
inference(trivial_inequality_removal,[],[f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU779^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:27:45 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.27 % (2741238)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (2741244)lrs+10_16_si=on:nwc=1.5:random_seed=1939034595:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (2741244) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2741238-2741244"...
% 0.21/0.27 % (2741249)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (2741249)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
% 0.21/0.27 % (2741244)...printing done.
% 0.21/0.27 % (2741244)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (2741244)------------------------------
% 0.21/0.27 % (2741244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2741244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2741244)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2741244)Termination reason: Refutation
% 0.21/0.27 % (2741244)Time elapsed: 0.004 s
% 0.21/0.27 % (2741244)Peak memory usage: 12 MB
% 0.21/0.27 % (2741244)Instructions burned: 13 (million)
% 0.21/0.27 % (2741238)Success in time 0.032 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------