%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU665^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:32:54 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of formulae : 83 ( 40 unt; 0 typ; 2 def)
% Number of atoms : 749 ( 155 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 1101 ( 33 ~; 63 |; 59 &; 815 @)
% ( 2 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 30 usr; 13 con; 0-4 aty)
% ( 40 !!; 17 ??; 0 @@+; 0 @@-)
% Number of variables : 223 ( 0 sgn 96 !; 14 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrI: $o ).
thf(func_def_4,type,
setext: $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
cartprodpairin: $o ).
thf(func_def_8,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_9,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vIMP: $o > $o > $o ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
sK2: $i > $i > $o ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_28,type,
sK5: $i > $i > $i ).
thf(func_def_29,type,
sK6: $i > $i > $i ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f3,axiom,
( cartprodpairin
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
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 ) )
& ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 ) )
& ( in @ X4 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstr) ).
thf(f5,conjecture,
( dsetconstrI
=> ( setext
=> ( cartprodpairin
=> ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(f6,negated_conjecture,
~ ( dsetconstrI
=> ( setext
=> ( cartprodpairin
=> ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f11,plain,
( cartprodpairin
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( cartprodpairin
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y3 ) @ ( cartprod @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
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 ) )
& ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 ) )
& ( 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] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( dsetconstrI
=> ( setext
=> ( cartprodpairin
=> ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
~ ( ( dsetconstrI = $true )
=> ( ( setext = $true )
=> ( ( cartprodpairin = $true )
=> ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( ( X2 @ X3 @ X4 )
= $true )
=> ( $true
= ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) )
& ( ( X2 @ X3 @ X4 )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( cartprodpairin = $true )
& ( setext = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) )
& ( ( X2 @ X3 @ X4 )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( cartprodpairin = $true )
& ( setext = $true )
& ( dsetconstrI = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( $true
!= ( in @ ( kpair @ sK3 @ sK4 )
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK2 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( sK2 @ sK3 @ sK4 ) )
& ( $true
= ( in @ sK4 @ sK1 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( cartprodpairin = $true )
& ( setext = $true )
& ( dsetconstrI = $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)],[f18]) ).
thf(f20,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f22,plain,
( cartprodpairin
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y3 ) @ ( cartprod @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f23,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
cartprodpairin = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f28,plain,
( $true
= ( in @ sK4 @ sK1 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f29,plain,
( $true
= ( sK2 @ sK3 @ sK4 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f30,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 )
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK2 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f33,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f20,f24]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y3 ) @ ( cartprod @ Y2 @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f22,f26]) ).
thf(f36,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) )
@ sK0
@ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK2 @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f30,f23]) ).
thf(f37,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 )
@ ( dsetconstr @ ( cartprod @ sK0 @ sK1 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( sK2 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y3 ) @ ( cartprod @ Y2 @ Y1 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f39,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( kpair @ X1 @ Y2 ) @ ( cartprod @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( kpair @ X1 @ Y2 ) @ ( cartprod @ Y1 @ Y0 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( kpair @ X1 @ Y1 ) @ ( cartprod @ Y0 @ X2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( kpair @ X1 @ Y1 ) @ ( cartprod @ Y0 @ X2 ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ X1 @ Y0 ) @ ( cartprod @ X3 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ X1 @ Y0 ) @ ( cartprod @ X3 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ X1 @ Y0 ) @ ( cartprod @ X3 @ X2 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( in @ ( kpair @ X1 @ X4 ) @ ( cartprod @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ X1 @ X4 ) @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f64,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f89,plain,
( ( $true != $true )
| ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( sK2 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) )
@ ( kpair @ sK3 @ sK4 ) ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f37,f71]) ).
thf(f92,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( sK2 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) )
@ ( kpair @ sK3 @ sK4 ) ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f93,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK1 )
& ( sK2 @ Y0 @ Y1 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK3 @ sK4 ) ) ) ) ) ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK1 )
& ( sK2 @ Y0 @ Y1 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK3 @ sK4 ) ) ) ) )
@ X1 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(pi_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X1: $i] :
( ( $false
= ( ( in @ X1 @ sK0 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
& ( sK2 @ X1 @ Y0 )
& ( ( kpair @ X1 @ Y0 )
= ( kpair @ sK3 @ sK4 ) ) ) ) ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
& ( sK2 @ X1 @ Y0 )
& ( ( kpair @ X1 @ Y0 )
= ( kpair @ sK3 @ sK4 ) ) ) ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
& ( sK2 @ X1 @ Y0 )
& ( ( kpair @ X1 @ Y0 )
= ( kpair @ sK3 @ sK4 ) ) )
@ X2 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(pi_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ X2 @ sK1 )
& ( sK2 @ X1 @ X2 )
& ( ( kpair @ X1 @ X2 )
= ( kpair @ sK3 @ sK4 ) ) ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( kpair @ X1 @ X2 )
= ( kpair @ sK3 @ sK4 ) ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( ( in @ X2 @ sK1 )
& ( sK2 @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X1: $i] :
( ( ( kpair @ sK3 @ sK4 )
!= ( kpair @ X1 @ X2 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( ( in @ X2 @ sK1 )
& ( sK2 @ X1 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X1: $i] :
( ( ( kpair @ sK3 @ sK4 )
!= ( kpair @ X1 @ X2 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( sK2 @ X1 @ X2 ) )
| ( $false
= ( in @ X2 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f100]) ).
thf(f103,definition,
( spl7_1
<=> ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f105,plain,
( ( $false
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( cartprod @ sK0 @ sK1 ) ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f107,definition,
( spl7_2
<=> ! [X2: $i,X1: $i] :
( ( ( kpair @ sK3 @ sK4 )
!= ( kpair @ X1 @ X2 ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $false
= ( sK2 @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f108,plain,
( ! [X2: $i,X1: $i] :
( ( ( kpair @ sK3 @ sK4 )
!= ( kpair @ X1 @ X2 ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $false
= ( sK2 @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ sK0 ) ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f107]) ).
thf(f109,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f101,f107,f103]) ).
thf(f122,plain,
( ( ( in @ sK4 @ sK1 )
= $false )
| ( ( sK2 @ sK3 @ sK4 )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl7_2 ),
inference(equality_resolution,[],[f108]) ).
thf(f123,plain,
( ( $true = $false )
| ( ( sK2 @ sK3 @ sK4 )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl7_2 ),
inference(forward_demodulation,[],[f122,f28]) ).
thf(f124,plain,
( ( ( sK2 @ sK3 @ sK4 )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f125,plain,
( ( $true = $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl7_2 ),
inference(forward_demodulation,[],[f124,f29]) ).
thf(f126,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f127,plain,
( ( $true = $false )
| ~ spl7_2 ),
inference(constrained_superposition,[],[f126,f27]) ).
thf(f133,plain,
( $false
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f134,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f133]) ).
thf(f137,plain,
( ( $true = $false )
| ( ( in @ sK4 @ sK1 )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl7_1 ),
inference(constrained_superposition,[],[f47,f105]) ).
thf(f138,plain,
( ( ( in @ sK4 @ sK1 )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f137]) ).
thf(f141,plain,
( ( $true = $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl7_1 ),
inference(forward_demodulation,[],[f138,f28]) ).
thf(f142,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f141]) ).
thf(f145,plain,
( ( $true = $false )
| ~ spl7_1 ),
inference(constrained_superposition,[],[f142,f27]) ).
thf(f151,plain,
( $false
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f152,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f151]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f109]) ).
cnf(s3,plain,
~ spl7_2,
inference(sat_conversion,[],[f134]) ).
cnf(s5,plain,
~ spl7_1,
inference(sat_conversion,[],[f152]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f153,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU665^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n008.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:07:09 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.29 % (3209780)Will run a generic schedule for satisfiability detection.
% 0.21/0.29 % (3209795)dis+10_1_sil=32000:sp=arity:random_seed=2729979053:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.29 % (3209793)% WARNING: option uhcvi not known.
% 0.21/0.29 % (3209795) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3209780-3209795"...
% 0.21/0.29 % (3209795)...printing done.
% 0.21/0.29 % (3209794)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2278250235:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.29 % (3209795)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (3209795)------------------------------
% 0.21/0.29 % (3209795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3209795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3209795)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3209795)Termination reason: Refutation
% 0.21/0.29 % (3209795)Time elapsed: 0.006 s
% 0.21/0.29 % (3209795)Peak memory usage: 12 MB
% 0.21/0.29 % (3209795)Instructions burned: 18 (million)
% 0.21/0.29 % (3209780)Success in time 0.043 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------