%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU672^2 : 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 : n002.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 08:30:40 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 7
% Syntax : Number of formulae : 77 ( 34 unt; 0 typ; 2 def)
% Number of atoms : 735 ( 134 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 989 ( 30 ~; 57 |; 31 &; 833 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 33 usr; 11 con; 0-4 aty)
% ( 6 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 200 ( 0 sgn 37 !; 10 ?; 200 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_21,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
sK4: $i > $i ).
thf(func_def_30,type,
sK5: $i > $i > $i ).
thf(func_def_31,type,
sK6: $i > $i > $i ).
thf(func_def_32,type,
sK7: $i > $i ).
thf(f1,axiom,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(f2,axiom,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(f3,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
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,conjecture,
! [X2: $i,X1: $i,X0: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(f6,negated_conjecture,
~ ! [X2: $i,X1: $i,X0: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f8,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f11,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( $true
= ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,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(f13,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,[],[f12]) ).
thf(f14,plain,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
inference(rectify,[],[f2]) ).
thf(f15,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true
!= ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f17,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) )
!= $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ( func @ sK0 @ sK2 @ sK1 )
= $true )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f17]) ).
thf(f19,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f20,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f21,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f22,plain,
( $true
!= ( singleton
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f23,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f24,plain,
( ( func @ sK0 @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f25,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,[],[f13]) ).
thf(f28,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f19,f20]) ).
thf(f29,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f25,f21,f28]) ).
thf(f30,plain,
( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
@ sK0
@ sK2
@ sK1 )
= $true ),
inference(definition_unfolding,[],[f24,f29]) ).
thf(f31,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
!= $true ),
inference(definition_unfolding,[],[f22,f20]) ).
thf(f32,plain,
( $true
= ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f33,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f35,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f36,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X1: $i] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) ) ) ) )
| ( ( in @ X1 @ sK0 )
= $false ) ),
inference(imp_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $false )
| ( $true
= ( ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK1 ) ) )
& ( in @ ( sK4 @ X1 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X1: $i] :
( ( $true
= ( in @ ( sK4 @ X1 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK1 ) ) ) )
| ( ( in @ X1 @ sK0 )
= $false ) ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X1: $i] :
( ( ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK1 ) ) )
= $true )
| ( ( in @ X1 @ sK0 )
= $false ) ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f42,plain,
! [X1: $i] :
( ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK1 ) ) )
| ( ( in @ X1 @ sK0 )
= $false ) ),
inference(equality_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ sK3 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ sK3 @ Y1 ) @ sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f44,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ sK3 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ sK3 @ Y1 ) @ sK1 ) ) ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X1: $i] :
( ( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
& ( in @ X1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X1: $i] :
( ( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( ( in @ X1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
| ( ( in @ X1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f46]) ).
thf(f49,plain,
! [X0: $i] :
( ( ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK1 ) )
!= ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
| ( ( in @ ( sK4 @ X0 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( ( in @ X0 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f47,f42]) ).
thf(f69,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) )
!= ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK1 ) ) )
| ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ ( sK4 @ X0 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false ) ),
inference(equality_resolution,[],[f49]) ).
thf(f70,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 )
@ ( sK7 @ X0 ) )
!= ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK1 )
@ ( sK7 @ X0 ) ) )
| ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ ( sK4 @ X0 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false ) ),
inference(negative_extensionality,[],[f69]) ).
thf(f71,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK0 )
= $false )
| ( $true
= ( ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 )
@ ( sK7 @ X0 ) ) )
| ( ( in @ ( sK4 @ X0 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK1 )
@ ( sK7 @ X0 ) ) ) ),
inference(xor_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 )
@ ( sK7 @ X0 ) )
= $false )
| ( ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK1 )
@ ( sK7 @ X0 ) )
= $false )
| ( ( in @ ( sK4 @ X0 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( ( in @ X0 @ sK0 )
= $false ) ),
inference(xor_proxy_clausification,[],[f70]) ).
thf(f73,plain,
! [X0: $i] :
( ( ( in @ ( kpair @ sK3 @ ( sK7 @ X0 ) ) @ sK1 )
= $false )
| ( ( in @ ( kpair @ X0 @ ( sK7 @ X0 ) ) @ sK1 )
= $false )
| ( ( in @ ( sK4 @ X0 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( ( in @ X0 @ sK0 )
= $false ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X0: $i] :
( ( $true
= ( in @ ( kpair @ sK3 @ ( sK7 @ X0 ) ) @ sK1 ) )
| ( $true
= ( in @ ( kpair @ X0 @ ( sK7 @ X0 ) ) @ sK1 ) )
| ( ( in @ ( sK4 @ X0 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( ( in @ X0 @ sK0 )
= $false ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f80,plain,
( ( ( in @ ( kpair @ sK3 @ ( sK7 @ sK3 ) ) @ sK1 )
= $false )
| ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( $false != $false )
| ( ( in @ sK3 @ sK0 )
= $false ) ),
inference(equality_factoring,[],[f73]) ).
thf(f84,plain,
( ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( ( in @ ( kpair @ sK3 @ ( sK7 @ sK3 ) ) @ sK1 )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f87,plain,
( ( $true = $false )
| ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( ( in @ ( kpair @ sK3 @ ( sK7 @ sK3 ) ) @ sK1 )
= $false ) ),
inference(forward_demodulation,[],[f84,f23]) ).
thf(f88,plain,
( ( ( in @ ( kpair @ sK3 @ ( sK7 @ sK3 ) ) @ sK1 )
= $false )
| ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f90,definition,
( spl8_1
<=> ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f91,plain,
( ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f93,definition,
( spl8_2
<=> ( ( in @ ( kpair @ sK3 @ ( sK7 @ sK3 ) ) @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f94,plain,
( ( ( in @ ( kpair @ sK3 @ ( sK7 @ sK3 ) ) @ sK1 )
= $false )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f96,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f88,f93,f90]) ).
thf(f124,plain,
( ( $true = $false )
| ( $true = $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ~ spl8_2 ),
inference(constrained_superposition,[],[f74,f94]) ).
thf(f136,plain,
( ( $true = $false )
| ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl8_2 ),
inference(duplicate_literal_removal,[],[f124]) ).
thf(f137,plain,
( ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f147,plain,
( ( $true = $false )
| ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ~ spl8_2 ),
inference(forward_demodulation,[],[f137,f23]) ).
thf(f148,plain,
( ( ( in @ ( sK4 @ sK3 )
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) )
= $false )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f155,plain,
( spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f148,f93,f90]) ).
thf(f170,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( $true = $false )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f40,f91]) ).
thf(f171,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f170]) ).
thf(f174,plain,
( ( $true = $false )
| ~ spl8_1 ),
inference(backward_demodulation,[],[f23,f171]) ).
thf(f175,plain,
( $false
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f176,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f175]) ).
cnf(s2,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f96]) ).
cnf(s3,plain,
( spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f155]) ).
cnf(s7,plain,
~ spl8_1,
inference(sat_conversion,[],[f176]) ).
cnf(s8,plain,
~ spl8_2,
inference(rat,[],[s3,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s8,s7]) ).
thf(f177,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU672^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:09:37 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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
% 0.20/0.29 % (1343793)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (1343798)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2207144974:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (1343798)Refutation not found, incomplete strategy
% 0.20/0.29 % (1343798)------------------------------
% 0.20/0.29 % (1343798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1343798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1343798)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1343798)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1343798)Time elapsed: 0.002 s
% 0.20/0.29 % (1343798)Peak memory usage: 12 MB
% 0.20/0.29 % (1343798)Instructions burned: 4 (million)
% 0.20/0.29 % (1343798)------------------------------
% 0.20/0.29 % (1343798)------------------------------
% 0.20/0.29 % (1343800)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3055514668:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (1343801)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=487558935: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)
% 0.20/0.29 % (1343799)lrs+10_16_si=on:nwc=1.5:random_seed=2323750780:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (1343800)Refutation not found, incomplete strategy
% 0.20/0.29 % (1343800)------------------------------
% 0.20/0.29 % (1343800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1343800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1343800)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1343800)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1343800)Time elapsed: 0.002 s
% 0.20/0.29 % (1343800)Peak memory usage: 12 MB
% 0.20/0.29 % (1343800)Instructions burned: 3 (million)
% 0.20/0.29 % (1343800)------------------------------
% 0.20/0.29 % (1343800)------------------------------
% 0.20/0.29 % (1343806)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3035585724:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.29 % (1343801)Refutation not found, incomplete strategy
% 0.20/0.29 % (1343801)------------------------------
% 0.20/0.29 % (1343801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1343801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1343801)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1343801)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1343801)Time elapsed: 0.007 s
% 0.20/0.29 % (1343801)Peak memory usage: 12 MB
% 0.20/0.29 % (1343801)Instructions burned: 10 (million)
% 0.20/0.29 % (1343801)------------------------------
% 0.20/0.29 % (1343801)------------------------------
% 0.20/0.29 % (1343806)Instruction limit reached!
% 0.20/0.29 % (1343806)------------------------------
% 0.20/0.29 % (1343806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1343806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1343806)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1343806)Termination reason: Instruction limit
% 0.20/0.29 % (1343806)Termination phase: Saturation
% 0.20/0.29 % (1343806)Time elapsed: 0.002 s
% 0.20/0.29 % (1343806)Peak memory usage: 12 MB
% 0.20/0.29 % (1343806)Instructions burned: 6 (million)
% 0.20/0.29 % (1343799)Instruction limit reached!
% 0.20/0.29 % (1343799)------------------------------
% 0.20/0.29 % (1343799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1343804)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (1343799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1343799)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1343799)Termination reason: Instruction limit
% 0.20/0.29 % (1343799)Termination phase: Saturation
% 0.20/0.29 % (1343799)Time elapsed: 0.010 s
% 0.20/0.29 % (1343804)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
% 0.20/0.29 % (1343799)Peak memory usage: 12 MB
% 0.20/0.29 % (1343799)Instructions burned: 18 (million)
% 0.20/0.29 % (1343804)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=3200694682:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (1343803)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1929634068:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (1343804)Refutation not found, incomplete strategy
% 0.20/0.29 % (1343804)------------------------------
% 0.20/0.29 % (1343804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1343804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1343804)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1343804)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1343804)Time elapsed: 0.004 s
% 0.20/0.29 % (1343804)Peak memory usage: 12 MB
% 0.20/0.29 % (1343804)Instructions burned: 6 (million)
% 0.20/0.29 % (1343804)------------------------------
% 0.20/0.29 % (1343804)------------------------------
% 0.20/0.29 % (1343803) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1343793-1343803"...
% 0.20/0.29 % (1343810)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2624766563:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.29 % (1343803)...printing done.
% 0.20/0.29 % (1343812)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.29 % (1343803)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1343803)------------------------------
% 0.20/0.29 % (1343803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1343803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1343803)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1343803)Termination reason: Refutation
% 0.20/0.29 % (1343803)Time elapsed: 0.008 s
% 0.20/0.29 % (1343803)Peak memory usage: 13 MB
% 0.20/0.29 % (1343803)Instructions burned: 28 (million)
% 0.20/0.29 % (1343793)Success in time 0.071 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------