%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU704^2 : 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 : n018.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 08:33:02 AM UTC 2026
% Result : Theorem 0.21s 0.33s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 12
% Syntax : Number of formulae : 141 ( 58 unt; 0 typ; 7 def)
% Number of atoms : 1237 ( 405 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 1669 ( 177 ~; 214 |; 166 &; 882 @)
% ( 7 <=>; 144 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 38 usr; 20 con; 0-4 aty)
% ( 75 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 389 ( 20 sgn 192 !; 10 ?; 389 :)
% 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,
singleton: $i > $o ).
thf(func_def_6,type,
iffalseProp1: $o ).
thf(func_def_7,type,
iffalseProp2: $o ).
thf(func_def_8,type,
iftrueProp1: $o ).
thf(func_def_9,type,
iftrueProp2: $o ).
thf(func_def_10,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vAND: $o > $o > $o ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vIMP: $o > $o > $o ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
sK1: $o ).
thf(func_def_30,type,
sK5: $i > $i ).
thf(func_def_32,type,
sK7: $o > $i ).
thf(func_def_33,type,
sK8: $i > $i ).
thf(func_def_34,type,
sK9: $i > $i ).
thf(f1,axiom,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(f3,axiom,
( iffalseProp2
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X4 = X3 )
& ~ X1 )
| ( ( X4 = X2 )
& X1 ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalseProp2) ).
thf(f4,axiom,
( iftrueProp1
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X4 = X3 )
& ~ X1 )
| ( ( X4 = X2 )
& X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp1) ).
thf(f5,axiom,
( iftrueProp2
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X4 = X3 )
& ~ X1 )
| ( ( X4 = X2 )
& X1 ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp2) ).
thf(f6,conjecture,
( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X4 = X3 )
& ~ X1 )
| ( ( X4 = X2 )
& X1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifSingleton) ).
thf(f7,negated_conjecture,
~ ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X4 = X3 )
& ~ X1 )
| ( ( X4 = X2 )
& X1 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f12,plain,
( iffalseProp2
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X4 = X3 )
& ~ X1 )
| ( ( X4 = X2 )
& X1 ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( iffalseProp2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ~ Y1
=> ( ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( iftrueProp1
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X4 = X3 )
& ~ X1 )
| ( ( X4 = X2 )
& X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( iftrueProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( iftrueProp2
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X4 = X3 )
& ~ X1 )
| ( ( X4 = X2 )
& X1 ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( iftrueProp2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X4 = X3 )
& ~ X1 )
| ( ( X4 = X2 )
& X1 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
~ ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ! [X0: $i,X1: $o,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( $true
= ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X1
& ( X2 = Y0 ) )
| ( ~ X1
& ( X3 = Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i,X1: $o,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X1
& ( X2 = Y0 ) )
| ( ~ X1
& ( X3 = Y0 ) ) ) ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f21,plain,
( ? [X0: $i,X1: $o,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X1
& ( X2 = Y0 ) )
| ( ~ X1
& ( X3 = Y0 ) ) ) ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( $true
!= ( singleton
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] :
( ( sK1
& ( sK2 = Y0 ) )
| ( ~ sK1
& ( sK3 = Y0 ) ) ) ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f21]) ).
thf(f23,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f25,plain,
( iffalseProp2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ~ Y1
=> ( ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f26,plain,
( iftrueProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
( iftrueProp2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f29,plain,
iffalseProp2 = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
iftrueProp1 = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f31,plain,
iftrueProp2 = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
( $true
!= ( singleton
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] :
( ( sK1
& ( sK2 = Y0 ) )
| ( ~ sK1
& ( sK3 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ~ Y1
=> ( ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f25,f29]) ).
thf(f39,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f26,f30]) ).
thf(f40,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f27,f31]) ).
thf(f41,plain,
( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] :
( ( sK1
& ( sK2 = Y0 ) )
| ( ~ sK1
& ( sK3 = Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f34,f23]) ).
thf(f42,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] :
( ( sK1
& ( sK2 = Y1 ) )
| ( ~ sK1
& ( sK3 = Y1 ) ) ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] :
( ( sK1
& ( sK2 = Y1 ) )
| ( ~ sK1
& ( sK3 = Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] :
( ( sK1
& ( sK2 = Y1 ) )
| ( ~ sK1
& ( sK3 = Y1 ) ) ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] :
( ( sK1
& ( sK2 = Y1 ) )
| ( ~ sK1
& ( sK3 = Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X1: $i] :
( $false
= ( ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] :
( ( sK1
& ( sK2 = Y0 ) )
| ( ~ sK1
& ( sK3 = Y0 ) ) ) ) )
& ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] :
( ( sK1
& ( sK2 = Y0 ) )
| ( ~ sK1
& ( sK3 = Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X1: $i] :
( ( $false
= ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] :
( ( sK1
& ( sK2 = Y0 ) )
| ( ~ sK1
& ( sK3 = Y0 ) ) ) ) ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] :
( ( sK1
& ( sK2 = Y0 ) )
| ( ~ sK1
& ( sK3 = Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ sK0
@ ^ [Y0: $i] :
( ( sK1
& ( sK2 = Y0 ) )
| ( ~ sK1
& ( sK3 = Y0 ) ) ) ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] :
( ( sK1
& ( sK2 = Y0 ) )
| ( ~ sK1
& ( sK3 = Y0 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( Y0
=> ( ( dsetconstr @ Y1
@ ^ [Y3: $i] :
( ( Y0
& ( X1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $o,X1: $i] :
( $true
= ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( Y0
=> ( ( dsetconstr @ Y1
@ ^ [Y3: $i] :
( ( Y0
& ( X1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( X2
=> ( ( dsetconstr @ Y0
@ ^ [Y2: $i] :
( ( X2
& ( X1 = Y2 ) )
| ( ~ X2
& ( Y1 = Y2 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( X2
=> ( ( dsetconstr @ Y0
@ ^ [Y2: $i] :
( ( X2
& ( X1 = Y2 ) )
| ( ~ X2
& ( Y1 = Y2 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X2
=> ( ( dsetconstr @ X3
@ ^ [Y1: $i] :
( ( X2
& ( X1 = Y1 ) )
| ( ~ X2
& ( Y0 = Y1 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
! [X2: $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X2
=> ( ( dsetconstr @ X3
@ ^ [Y1: $i] :
( ( X2
& ( X1 = Y1 ) )
| ( ~ X2
& ( Y0 = Y1 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X2
=> ( ( dsetconstr @ X3
@ ^ [Y1: $i] :
( ( X2
& ( X1 = Y1 ) )
| ( ~ X2
& ( Y0 = Y1 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( X2
=> ( ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( X2
=> ( ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false = X2 )
| ( $true
= ( ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false = X2 )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(equality_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f60,plain,
! [X1: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( Y0
=> ( in @ X1
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] :
( ( Y0
& ( X1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $o,X1: $i] :
( $true
= ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( Y0
=> ( in @ X1
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] :
( ( Y0
& ( X1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( X2
=> ( in @ X1
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] :
( ( X2
& ( X1 = Y2 ) )
| ( ~ X2
& ( Y1 = Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( X2
=> ( in @ X1
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] :
( ( X2
& ( X1 = Y2 ) )
| ( ~ X2
& ( Y1 = Y2 ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X2
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y1: $i] :
( ( X2
& ( X1 = Y1 ) )
| ( ~ X2
& ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
! [X2: $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X2
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y1: $i] :
( ( X2
& ( X1 = Y1 ) )
| ( ~ X2
& ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f66,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X2
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y1: $i] :
( ( X2
& ( X1 = Y1 ) )
| ( ~ X2
& ( Y0 = Y1 ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( X2
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( X2
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false = X2 )
| ( $true
= ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ~ Y1
=> ( ( dsetconstr @ Y2
@ ^ [Y4: $i] :
( ( Y1
& ( Y0 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f71,plain,
! [X1: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ~ Y0
=> ( ( dsetconstr @ Y1
@ ^ [Y3: $i] :
( ( Y0
& ( X1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
! [X2: $o,X1: $i] :
( $true
= ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ~ Y0
=> ( ( dsetconstr @ Y1
@ ^ [Y3: $i] :
( ( Y0
& ( X1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ~ X2
=> ( ( dsetconstr @ Y0
@ ^ [Y2: $i] :
( ( X2
& ( X1 = Y2 ) )
| ( ~ X2
& ( Y1 = Y2 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ~ X2
=> ( ( dsetconstr @ Y0
@ ^ [Y2: $i] :
( ( X2
& ( X1 = Y2 ) )
| ( ~ X2
& ( Y1 = Y2 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ~ X2
=> ( ( dsetconstr @ X3
@ ^ [Y1: $i] :
( ( X2
& ( X1 = Y1 ) )
| ( ~ X2
& ( Y0 = Y1 ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X2: $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ~ X2
=> ( ( dsetconstr @ X3
@ ^ [Y1: $i] :
( ( X2
& ( X1 = Y1 ) )
| ( ~ X2
& ( Y0 = Y1 ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ~ X2
=> ( ( dsetconstr @ X3
@ ^ [Y1: $i] :
( ( X2
& ( X1 = Y1 ) )
| ( ~ X2
& ( Y0 = Y1 ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( ~ X2
=> ( ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( ~ X2
=> ( ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ) ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false = ( ~ X2 ) )
| ( $true
= ( ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true = X2 )
| ( $true
= ( ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ),
inference(not_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X4 = Y0 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true = X2 )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(equality_proxy_clausification,[],[f81]) ).
thf(f95,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false = X2 )
| ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(forward_subsumption_demodulation,[],[f69,f58]) ).
thf(f98,definition,
( spl4_1
<=> ! [X2: $o] : ( $false = X2 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f99,plain,
( ! [X2: $o] : ( $false = X2 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f98]) ).
thf(f101,definition,
( spl4_2
<=> ! [X4: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( $false
= ( in @ X4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f102,plain,
( ! [X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( $false
= ( in @ X4 @ X3 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f103,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f95,f101,f98]) ).
thf(f113,plain,
( ! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ~ spl4_2 ),
inference(equality_factoring,[],[f102]) ).
thf(f114,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f210,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f32,f99]) ).
thf(f221,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f210]) ).
thf(f222,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f221]) ).
thf(f265,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true = sK1 )
| ( ( in @ sK2 @ sK0 )
= $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(constrained_superposition,[],[f46,f82]) ).
thf(f266,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ sK2 @ emptyset ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ sK2 @ emptyset ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( sK1 = $false )
| ( ( in @ sK2 @ sK0 )
= $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(constrained_superposition,[],[f46,f58]) ).
thf(f267,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ sK2 @ emptyset ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ sK2 @ emptyset ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( sK1 = $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(forward_demodulation,[],[f266,f32]) ).
thf(f268,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ sK2 @ emptyset ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ sK2 @ emptyset ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( sK1 = $false )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f269,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true = sK1 )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(forward_demodulation,[],[f265,f32]) ).
thf(f270,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true = sK1 )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f272,definition,
( spl4_9
<=> ( sK1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
thf(f274,plain,
( ( sK1 = $false )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f276,definition,
( spl4_10
<=> ! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
thf(f277,plain,
( ! [X1: $i] :
( ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK3 ) )
| ( $false
= ( in @ X1 @ sK0 ) ) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f279,definition,
( spl4_11
<=> ! [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ sK2 @ emptyset ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
thf(f280,plain,
( ! [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ sK2 @ emptyset ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f279]) ).
thf(f281,plain,
( spl4_9
| spl4_10
| spl4_11 ),
inference(avatar_split_clause,[],[f268,f279,f276,f272]) ).
thf(f283,definition,
( spl4_12
<=> ( $true = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
thf(f285,plain,
( ( $true = sK1 )
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f283]) ).
thf(f287,definition,
( spl4_13
<=> ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK3 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition]) ).
thf(f288,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK3 ) )
| ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f287]) ).
thf(f289,plain,
( spl4_12
| spl4_13 ),
inference(avatar_split_clause,[],[f270,f287,f283]) ).
thf(f290,plain,
( ( $true = $false )
| ~ spl4_9
| ~ spl4_12 ),
inference(forward_demodulation,[],[f285,f274]) ).
thf(f291,plain,
( $false
| ~ spl4_9
| ~ spl4_12 ),
inference(trivial_inequality_removal,[],[f290]) ).
thf(f292,plain,
( ~ spl4_9
| ~ spl4_12 ),
inference(avatar_contradiction_clause,[],[f291]) ).
thf(f295,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_10 ),
inference(equality_resolution,[],[f277]) ).
thf(f297,plain,
( ( $true = $false )
| ~ spl4_10 ),
inference(backward_demodulation,[],[f33,f295]) ).
thf(f298,plain,
( $false
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f297]) ).
thf(f299,plain,
~ spl4_10,
inference(avatar_contradiction_clause,[],[f298]) ).
thf(f300,plain,
( ( $false
= ( in @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
| ~ spl4_11 ),
inference(equality_resolution,[],[f280]) ).
thf(f436,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK2 @ X0 ) ) )
| ~ spl4_2
| ~ spl4_11 ),
inference(constrained_superposition,[],[f114,f300]) ).
thf(f437,plain,
( ! [X0: $i] :
( $false
= ( in @ sK2 @ X0 ) )
| ~ spl4_2
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f436]) ).
thf(f440,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_11 ),
inference(backward_demodulation,[],[f32,f437]) ).
thf(f441,plain,
( $false
| ~ spl4_2
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f440]) ).
thf(f442,plain,
( ~ spl4_2
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f441]) ).
thf(f477,plain,
( ! [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ sK3 @ emptyset ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( in @ X0 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
| ~ spl4_13 ),
inference(equality_resolution,[],[f288]) ).
thf(f479,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ sK3 @ emptyset ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
| ~ spl4_13 ),
inference(forward_demodulation,[],[f477,f33]) ).
thf(f480,plain,
( ! [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ sK3 @ emptyset ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
| ~ spl4_13 ),
inference(trivial_inequality_removal,[],[f479]) ).
thf(f481,plain,
( ( $false
= ( in @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl4_13 ),
inference(equality_resolution,[],[f480]) ).
thf(f487,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK3 @ X0 ) ) )
| ~ spl4_2
| ~ spl4_13 ),
inference(constrained_superposition,[],[f114,f481]) ).
thf(f488,plain,
( ! [X0: $i] :
( $false
= ( in @ sK3 @ X0 ) )
| ~ spl4_2
| ~ spl4_13 ),
inference(trivial_inequality_removal,[],[f487]) ).
thf(f491,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_13 ),
inference(backward_demodulation,[],[f33,f488]) ).
thf(f492,plain,
( $false
| ~ spl4_2
| ~ spl4_13 ),
inference(trivial_inequality_removal,[],[f491]) ).
thf(f493,plain,
( ~ spl4_2
| ~ spl4_13 ),
inference(avatar_contradiction_clause,[],[f492]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f103]) ).
cnf(s11,plain,
~ spl4_1,
inference(sat_conversion,[],[f222]) ).
cnf(s12,plain,
( spl4_9
| spl4_10
| spl4_11 ),
inference(sat_conversion,[],[f281]) ).
cnf(s13,plain,
( spl4_12
| spl4_13 ),
inference(sat_conversion,[],[f289]) ).
cnf(s14,plain,
( ~ spl4_9
| ~ spl4_12 ),
inference(sat_conversion,[],[f292]) ).
cnf(s15,plain,
~ spl4_10,
inference(sat_conversion,[],[f299]) ).
cnf(s24,plain,
( ~ spl4_2
| ~ spl4_11 ),
inference(sat_conversion,[],[f442]) ).
cnf(s27,plain,
( ~ spl4_2
| ~ spl4_13 ),
inference(sat_conversion,[],[f493]) ).
cnf(s36,plain,
( spl4_9
| spl4_11 ),
inference(rat,[],[s12,s15]) ).
cnf(s41,plain,
spl4_2,
inference(rat,[],[s1,s11]) ).
cnf(s42,plain,
~ spl4_13,
inference(rat,[],[s27,s41]) ).
cnf(s43,plain,
~ spl4_11,
inference(rat,[],[s24,s41]) ).
cnf(s44,plain,
spl4_12,
inference(rat,[],[s13,s42]) ).
cnf(s45,plain,
spl4_9,
inference(rat,[],[s36,s43]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s14,s44,s45]) ).
thf(f494,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU704^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:14:41 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.21/0.33 % (137386)Will run a generic schedule for satisfiability detection.
% 0.21/0.33 % (137392)% WARNING: option uhcvi not known.
% 0.21/0.33 % (137394)dis+10_1_sil=32000:sp=arity:random_seed=526872379:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.33 % (137393)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=165008189:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.33 % (137392)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1211516043:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.33 % (137392)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.33 % (137392)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.33 % (137391)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3237078522_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.33 % Exception at run slice level
% 0.21/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.33 % (137395)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3147576457:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.33 % (137395)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.33 % (137396)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=721746000:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.33 % (137397)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3540932570:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.33 % (137402)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=576336814:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.33 % Exception at run slice level
% 0.21/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.33 % (137407)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1500828755:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.33 % (137394)Instruction limit reached!
% 0.21/0.33 % (137394)------------------------------
% 0.21/0.33 % (137394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (137394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (137394)CaDiCaL version: 2.1.3
% 0.21/0.33 % (137394)Termination reason: Instruction limit
% 0.21/0.33 % (137394)Termination phase: Saturation
% 0.21/0.33 % (137394)Time elapsed: 0.049 s
% 0.21/0.33 % (137394)Peak memory usage: 12 MB
% 0.21/0.33 % (137394)Instructions burned: 105 (million)
% 0.21/0.33 % (137407) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-137386-137407"...
% 0.21/0.33 % (137407)...printing done.
% 0.21/0.33 % (137407)Refutation found. Thanks to Tanya!
% 0.21/0.33 % SZS status Theorem for theBenchmark
% 0.21/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.33 % (137407)------------------------------
% 0.21/0.33 % (137407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (137407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (137407)CaDiCaL version: 2.1.3
% 0.21/0.33 % (137407)Termination reason: Refutation
% 0.21/0.33 % (137407)Time elapsed: 0.020 s
% 0.21/0.33 % (137407)Peak memory usage: 13 MB
% 0.21/0.33 % (137407)Instructions burned: 75 (million)
% 0.21/0.33 % (137386)Success in time 0.084 s
% 0.21/0.33 % Vampire exiting
%------------------------------------------------------------------------------