%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU671^2 : 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 08:30:39 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of formulae : 82 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 541 ( 181 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 864 ( 12 ~; 10 |; 56 &; 653 @)
% ( 0 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 28 usr; 13 con; 0-4 aty)
% ( 63 !!; 17 ??; 0 @@+; 0 @@-)
% Number of variables : 286 ( 142 ^; 125 !; 19 ?; 286 :)
% 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,
dsetconstrER: $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
cartprod: $i > $i > $i ).
thf(func_def_6,type,
setukpairinjL: $o ).
thf(func_def_7,type,
setukpairinjR: $o ).
thf(func_def_8,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_15,type,
vIMP: $o > $o > $o ).
thf(func_def_16,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
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,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
sK4: $i > $i > $o ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f2,axiom,
( setukpairinjL
= ( ! [X0: $i,X1: $i,X3: $i,X2: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL) ).
thf(f3,axiom,
! [X3: $i,X2: $i,X1: $i,X0: $i] :
( ( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) )
= setukpairinjR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).
thf(f4,axiom,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ? [X5: $i] :
( ( X3
= ( kpair @ X4 @ X5 ) )
& ( in @ X5 @ X1 )
& ( X2 @ X4 @ X5 ) )
& ( in @ X4 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstr) ).
thf(f5,conjecture,
( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [X2: $i > $i > $o,X1: $i,X0: $i,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) )
=> ( X2 @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(f6,negated_conjecture,
~ ( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [X2: $i > $i > $o,X1: $i,X0: $i,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) )
=> ( X2 @ X3 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X2 @ X1
@ ^ [X5: $i,X6: $i] : ( X0 @ X5 @ X6 ) ) )
=> ( X0 @ X3 @ X4 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
~ ( ( dsetconstrER = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR = $true )
=> ! [X4: $i,X3: $i,X1: $i,X2: $i,X0: $i > $i > $o] :
( ( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
= $true )
=> ( $true
= ( X0 @ X3 @ X4 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( ( kpair @ X3 @ X2 )
= ( kpair @ X1 @ X0 ) )
=> ( X0 = X2 ) )
= setukpairinjR ),
inference(rectify,[],[f3]) ).
thf(f10,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y0 @ Y1 )
= ( kpair @ Y2 @ Y3 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
inference(rectify,[],[f1]) ).
thf(f12,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ? [X5: $i] :
( ( X3
= ( kpair @ X4 @ X5 ) )
& ( in @ X5 @ X1 )
& ( X2 @ X4 @ X5 ) )
& ( in @ X4 @ X0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,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] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( setukpairinjL
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X3 @ X2 ) )
=> ( X0 = X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f16,plain,
( setukpairinjL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y3 @ Y2 )
= ( kpair @ Y0 @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ? [X2: $i,X4: $i,X3: $i,X1: $i,X0: $i > $i > $o] :
( ( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
= $true )
& ( $true
!= ( X0 @ X3 @ X4 ) ) )
& ( setukpairinjR = $true )
& ( setukpairinjL = $true )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f18,plain,
( ( setukpairinjL = $true )
& ? [X2: $i,X4: $i,X3: $i,X1: $i,X0: $i > $i > $o] :
( ( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
= $true )
& ( $true
!= ( X0 @ X3 @ X4 ) ) )
& ( setukpairinjR = $true )
& ( dsetconstrER = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( setukpairinjL = $true )
& ? [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i > $i > $o] :
( ( $true
= ( in @ ( kpair @ X2 @ X1 )
@ ( dpsetconstr @ X0 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X4 @ Y0 @ Y1 ) ) ) )
& ( ( X4 @ X2 @ X1 )
!= $true ) )
& ( setukpairinjR = $true )
& ( dsetconstrER = $true ) ),
inference(rectify,[],[f18]) ).
thf(f20,plain,
( ( setukpairinjL = $true )
& ( $true
= ( in @ ( kpair @ sK2 @ sK1 )
@ ( dpsetconstr @ sK0 @ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ Y1 ) ) ) )
& ( ( sK4 @ sK2 @ sK1 )
!= $true )
& ( setukpairinjR = $true )
& ( dsetconstrER = $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)],[f19]) ).
thf(f21,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y0 @ Y1 )
= ( kpair @ Y2 @ Y3 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f22,plain,
( setukpairinjL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y3 @ Y2 )
= ( kpair @ Y0 @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f24,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f25,plain,
setukpairinjR = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f26,plain,
( ( sK4 @ sK2 @ sK1 )
!= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f27,plain,
( $true
= ( in @ ( kpair @ sK2 @ sK1 )
@ ( dpsetconstr @ sK0 @ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f28,plain,
setukpairinjL = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f29,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] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f32,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y0 @ Y1 )
= ( kpair @ Y2 @ Y3 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f21,f25]) ).
thf(f33,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y3 @ Y2 )
= ( kpair @ Y0 @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f22,f28]) ).
thf(f34,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f23,f24]) ).
thf(f35,plain,
( $true
= ( in @ ( kpair @ sK2 @ sK1 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) )
@ sK0
@ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f27,f29]) ).
thf(f36,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
= $false )
| ( ( X2 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( $true
= ( in @ ( kpair @ sK2 @ sK1 )
@ ( dsetconstr @ ( cartprod @ sK0 @ sK3 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y1 @ Y2 )
& ( in @ Y2 @ sK3 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f44,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y3 @ Y2 )
= ( kpair @ Y0 @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f45,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( kpair @ Y2 @ Y1 )
= ( kpair @ X1 @ Y0 ) )
=> ( Y2 = X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( kpair @ Y2 @ Y1 )
= ( kpair @ X1 @ Y0 ) )
=> ( Y2 = X1 ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( kpair @ Y1 @ Y0 )
= ( kpair @ X1 @ X2 ) )
=> ( Y1 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( kpair @ Y1 @ Y0 )
= ( kpair @ X1 @ X2 ) )
=> ( Y1 = X1 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( kpair @ Y0 @ X3 )
= ( kpair @ X1 @ X2 ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( kpair @ Y0 @ X3 )
= ( kpair @ X1 @ X2 ) )
=> ( Y0 = X1 ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ( ( kpair @ X4 @ X3 )
= ( kpair @ X1 @ X2 ) )
=> ( X4 = X1 ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( X4 = X1 )
= $true )
| ( ( ( kpair @ X4 @ X3 )
= ( kpair @ X1 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( X1 = X4 )
| ( ( ( kpair @ X4 @ X3 )
= ( kpair @ X1 @ X2 ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( kpair @ X4 @ X3 )
!= ( kpair @ X1 @ X2 ) )
| ( X1 = X4 ) ),
inference(equality_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y0 @ Y1 )
= ( kpair @ Y2 @ Y3 ) )
=> ( Y3 = Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f56,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( kpair @ X1 @ Y0 )
= ( kpair @ Y1 @ Y2 ) )
=> ( Y2 = Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( kpair @ X1 @ Y0 )
= ( kpair @ Y1 @ Y2 ) )
=> ( Y2 = Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ Y0 @ Y1 ) )
=> ( Y1 = X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ Y0 @ Y1 ) )
=> ( Y1 = X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ Y0 ) )
=> ( Y0 = X2 ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ^ [Y0: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ Y0 ) )
=> ( Y0 = X2 ) )
@ X4 )
= $true ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ X4 ) )
=> ( X4 = X2 ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( X4 = X2 )
= $true )
| ( $false
= ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( X2 = X4 )
| ( $false
= ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ X4 ) ) ) ),
inference(equality_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= ( kpair @ X1 @ X2 ) )
| ( X2 = X4 ) ),
inference(equality_proxy_clausification,[],[f64]) ).
thf(f73,plain,
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y1 @ Y2 )
& ( in @ Y2 @ sK3 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) )
@ ( kpair @ sK2 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f42,f43]) ).
thf(f74,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y1 @ Y2 )
& ( in @ Y2 @ sK3 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) )
@ ( kpair @ sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f75,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y0 @ Y1 )
& ( in @ Y1 @ sK3 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK2 @ sK1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y0 @ Y1 )
& ( in @ Y1 @ sK3 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK2 @ sK1 ) ) ) ) )
@ sK5 )
= $true ),
inference(sigma_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( ( ( in @ sK5 @ sK0 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK4 @ sK5 @ Y0 )
& ( in @ Y0 @ sK3 )
& ( ( kpair @ sK5 @ Y0 )
= ( kpair @ sK2 @ sK1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK4 @ sK5 @ Y0 )
& ( in @ Y0 @ sK3 )
& ( ( kpair @ sK5 @ Y0 )
= ( kpair @ sK2 @ sK1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( ( ^ [Y0: $i] :
( ( sK4 @ sK5 @ Y0 )
& ( in @ Y0 @ sK3 )
& ( ( kpair @ sK5 @ Y0 )
= ( kpair @ sK2 @ sK1 ) ) )
@ sK6 )
= $true ),
inference(sigma_proxy_clausification,[],[f78]) ).
thf(f81,plain,
( ( ( sK4 @ sK5 @ sK6 )
& ( in @ sK6 @ sK3 )
& ( ( kpair @ sK5 @ sK6 )
= ( kpair @ sK2 @ sK1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
( $true
= ( ( kpair @ sK5 @ sK6 )
= ( kpair @ sK2 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f81]) ).
thf(f83,plain,
( ( ( sK4 @ sK5 @ sK6 )
& ( in @ sK6 @ sK3 ) )
= $true ),
inference(and_proxy_clausification,[],[f81]) ).
thf(f85,plain,
( $true
= ( sK4 @ sK5 @ sK6 ) ),
inference(and_proxy_clausification,[],[f83]) ).
thf(f86,plain,
( ( kpair @ sK5 @ sK6 )
= ( kpair @ sK2 @ sK1 ) ),
inference(equality_proxy_clausification,[],[f82]) ).
thf(f101,plain,
! [X0: $i,X1: $i] :
( ( ( kpair @ X0 @ X1 )
!= ( kpair @ sK2 @ sK1 ) )
| ( sK6 = X1 ) ),
inference(constrained_superposition,[],[f65,f86]) ).
thf(f102,plain,
! [X0: $i,X1: $i] :
( ( ( kpair @ X0 @ X1 )
!= ( kpair @ sK2 @ sK1 ) )
| ( sK5 = X0 ) ),
inference(constrained_superposition,[],[f54,f86]) ).
thf(f109,plain,
sK1 = sK6,
inference(equality_resolution,[],[f101]) ).
thf(f112,plain,
( $true
= ( sK4 @ sK5 @ sK1 ) ),
inference(constrained_superposition,[],[f85,f109]) ).
thf(f120,plain,
sK5 = sK2,
inference(equality_resolution,[],[f102]) ).
thf(f123,plain,
( ( sK4 @ sK2 @ sK1 )
= $true ),
inference(constrained_superposition,[],[f112,f120]) ).
thf(f127,plain,
$false,
inference(forward_subsumption_resolution,[],[f123,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU671^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:06:40 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.19/0.26 % (772013)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (772019)lrs+10_16_si=on:nwc=1.5:random_seed=4288812541:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.26 % (772019) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-772013-772019"...
% 0.19/0.26 % (772019)...printing done.
% 0.19/0.26 % (772019)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.26 % (772019)------------------------------
% 0.19/0.26 % (772019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (772019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (772019)CaDiCaL version: 2.1.3
% 0.19/0.26 % (772019)Termination reason: Refutation
% 0.19/0.26 % (772019)Time elapsed: 0.005 s
% 0.19/0.26 % (772019)Peak memory usage: 12 MB
% 0.19/0.26 % (772019)Instructions burned: 15 (million)
% 0.19/0.26 % (772013)Success in time 0.029 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------