%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU692^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:30:48 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 27
% Syntax : Number of formulae : 181 ( 52 unt; 0 typ; 24 def)
% Number of atoms : 1238 ( 299 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 1717 ( 141 ~; 221 |; 20 &;1141 @)
% ( 16 <=>; 105 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 49 ( 45 usr; 30 con; 0-4 aty)
% ( 73 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 243 ( 0 sgn 149 !; 12 ?; 243 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
func: $i > $i > $i > $o ).
thf(func_def_2,type,
funcSet: $i > $i > $i ).
thf(func_def_3,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_4,type,
infuncsetfunc: $o ).
thf(func_def_6,type,
funcext: $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
sF5: $o ).
thf(func_def_24,type,
sF6: $o ).
thf(func_def_25,type,
sF7: $i > $i ).
thf(func_def_26,type,
sF8: $i > $i ).
thf(func_def_27,type,
sF9: $i > $o ).
thf(func_def_28,type,
sF10: $o ).
thf(func_def_29,type,
sF11: $o ).
thf(func_def_33,type,
sK15: $i > $i > $i > $i > $i ).
thf(f1,axiom,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(f2,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( func @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) )
= funcext ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext) ).
thf(f3,conjecture,
( infuncsetfunc
=> ( funcext
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext2) ).
thf(f4,negated_conjecture,
~ ( infuncsetfunc
=> ( funcext
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( infuncsetfunc
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( func @ X1 @ X0 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( ap @ X1 @ X0 @ X3 @ X4 )
= ( ap @ X1 @ X0 @ X2 @ X4 ) ) )
=> ( X2 = X3 ) ) ) )
= funcext ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( funcext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y1 @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ap @ Y1 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y1 @ Y2 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( infuncsetfunc
=> ( funcext
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( infuncsetfunc = $true )
=> ( ( funcext = $true )
=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X1: $i,X2: $i,X0: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ! [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( funcext = $true )
& ( infuncsetfunc = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
= $true )
& ( X2 != X3 )
& ! [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) )
| ( ( in @ X4 @ X0 )
!= $true ) ) ) )
& ( funcext = $true )
& ( infuncsetfunc = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( funcSet @ X2 @ X0 ) ) )
& ( X1 != X3 )
& ! [X4: $i] :
( ( ( ap @ X2 @ X0 @ X3 @ X4 )
= ( ap @ X2 @ X0 @ X1 @ X4 ) )
| ( $true
!= ( in @ X4 @ X2 ) ) ) ) )
& ( funcext = $true )
& ( infuncsetfunc = $true ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) )
= $true )
& ( ( in @ sK3 @ ( funcSet @ sK2 @ sK0 ) )
= $true )
& ( sK3 != sK1 )
& ! [X4: $i] :
( ( ( ap @ sK2 @ sK0 @ sK3 @ X4 )
= ( ap @ sK2 @ sK0 @ sK1 @ X4 ) )
| ( ( in @ X4 @ sK2 )
!= $true ) )
& ( funcext = $true )
& ( infuncsetfunc = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f13]) ).
thf(f15,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f16,plain,
funcext = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f17,plain,
! [X4: $i] :
( ( ( ap @ sK2 @ sK0 @ sK3 @ X4 )
= ( ap @ sK2 @ sK0 @ sK1 @ X4 ) )
| ( ( in @ X4 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
sK3 != sK1,
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( ( in @ sK3 @ ( funcSet @ sK2 @ sK0 ) )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
( ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( infuncsetfunc
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f22,plain,
( funcext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y1 @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ap @ Y1 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y1 @ Y2 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f25,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f21,f15]) ).
thf(f26,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y1 @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ap @ Y1 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y1 @ Y2 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f22,f16]) ).
thf(f27,definition,
( sF4
= ( funcSet @ sK2 @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f28,definition,
( sF5
= ( in @ sK1 @ sF4 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f29,plain,
sF5 = $true,
inference(definition_folding,[],[f20,f28,f27]) ).
thf(f30,definition,
( sF6
= ( in @ sK3 @ sF4 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f31,plain,
( ( in @ sK3 @ sF4 )
= sF6 ),
inference(reorient_equations,[],[f30]) ).
thf(f32,plain,
$true = sF6,
inference(definition_folding,[],[f19,f31,f27]) ).
thf(f33,definition,
! [X4: $i] :
( ( sF7 @ X4 )
= ( ap @ sK2 @ sK0 @ sK3 @ X4 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f34,plain,
! [X4: $i] :
( ( ap @ sK2 @ sK0 @ sK3 @ X4 )
= ( sF7 @ X4 ) ),
inference(reorient_equations,[],[f33]) ).
thf(f35,definition,
! [X4: $i] :
( ( sF8 @ X4 )
= ( ap @ sK2 @ sK0 @ sK1 @ X4 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f36,definition,
! [X4: $i] :
( ( sF9 @ X4 )
= ( in @ X4 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f37,plain,
! [X4: $i] :
( ( ( sF8 @ X4 )
= ( sF7 @ X4 ) )
| ( ( sF9 @ X4 )
!= $true ) ),
inference(definition_folding,[],[f17,f36,f35,f34]) ).
thf(f38,definition,
( sF10
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
thf(f39,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) )
= sF10 ),
inference(reorient_equations,[],[f38]) ).
thf(f40,plain,
$true = sF10,
inference(definition_folding,[],[f25,f39]) ).
thf(f41,definition,
( sF11
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y1 @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ap @ Y1 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y1 @ Y2 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
thf(f42,plain,
sF11 = $true,
inference(definition_folding,[],[f26,f41]) ).
thf(f43,plain,
( ( $false = sF10 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f39]) ).
thf(f53,plain,
! [X1: $i] :
( ( $false = sF10 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f54,plain,
! [X1: $i] :
( ( $false = sF10 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( funcSet @ Y1 @ Y0 ) )
=> ( func @ Y1 @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( $false = sF10 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( funcSet @ Y1 @ Y0 ) )
=> ( func @ Y1 @ Y0 @ X1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( funcSet @ Y0 @ X2 ) )
=> ( func @ Y0 @ X2 @ X1 ) ) ) )
| ( $false = sF10 ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( funcSet @ Y0 @ X2 ) )
=> ( func @ Y0 @ X2 @ X1 ) )
@ X3 ) )
| ( $false = sF10 ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF10 )
| ( ( ( in @ X1 @ ( funcSet @ X3 @ X2 ) )
=> ( func @ X3 @ X2 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( funcSet @ X3 @ X2 ) ) )
| ( $false = sF10 )
| ( ( func @ X3 @ X2 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f61,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y1 @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ap @ Y1 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y1 @ Y2 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) ) )
| ( $false = sF11 ) ),
inference(iff_proxy_clausification,[],[f41]) ).
thf(f62,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y1 @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ap @ Y1 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y1 @ Y2 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) )
@ X1 )
= $true )
| ( $false = sF11 ) ),
inference(pi_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y0 @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 @ X1 @ Y3 ) ) ) )
=> ( X1 = Y2 ) ) ) ) ) ) )
= $true )
| ( $false = sF11 ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y0 @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 @ X1 @ Y3 ) ) ) )
=> ( X1 = Y2 ) ) ) ) ) )
@ X2 )
= $true )
| ( $false = sF11 ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( $false = sF11 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ X2 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( func @ X2 @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ap @ X2 @ Y0 @ Y1 @ Y2 )
= ( ap @ X2 @ Y0 @ X1 @ Y2 ) ) ) )
=> ( X1 = Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( func @ X2 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( func @ X2 @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ap @ X2 @ Y0 @ Y1 @ Y2 )
= ( ap @ X2 @ Y0 @ X1 @ Y2 ) ) ) )
=> ( X1 = Y1 ) ) ) ) )
@ X3 ) )
| ( $false = sF11 ) ),
inference(pi_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF11 )
| ( ( ( func @ X2 @ X3 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ X2 @ X3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( ap @ X2 @ X3 @ Y0 @ Y1 )
= ( ap @ X2 @ X3 @ X1 @ Y1 ) ) ) )
=> ( X1 = Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ X2 @ X3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( ap @ X2 @ X3 @ Y0 @ Y1 )
= ( ap @ X2 @ X3 @ X1 @ Y1 ) ) ) )
=> ( X1 = Y0 ) ) ) ) )
| ( $false = sF11 )
| ( ( func @ X2 @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( func @ X2 @ X3 @ X1 )
= $false )
| ( $false = sF11 )
| ( $true
= ( ^ [Y0: $i] :
( ( func @ X2 @ X3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( ap @ X2 @ X3 @ Y0 @ Y1 )
= ( ap @ X2 @ X3 @ X1 @ Y1 ) ) ) )
=> ( X1 = Y0 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( func @ X2 @ X3 @ X1 )
= $false )
| ( $false = sF11 )
| ( $true
= ( ( func @ X2 @ X3 @ X4 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( ap @ X2 @ X3 @ X4 @ Y0 )
= ( ap @ X2 @ X3 @ X1 @ Y0 ) ) ) )
=> ( X1 = X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false = sF11 )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( ap @ X2 @ X3 @ X4 @ Y0 )
= ( ap @ X2 @ X3 @ X1 @ Y0 ) ) ) )
=> ( X1 = X4 ) )
= $true )
| ( $false
= ( func @ X2 @ X3 @ X4 ) )
| ( ( func @ X2 @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( func @ X2 @ X3 @ X1 )
= $false )
| ( $false
= ( func @ X2 @ X3 @ X4 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( ap @ X2 @ X3 @ X4 @ Y0 )
= ( ap @ X2 @ X3 @ X1 @ Y0 ) ) ) )
= $false )
| ( ( X1 = X4 )
= $true )
| ( $false = sF11 ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( ap @ X2 @ X3 @ X4 @ Y0 )
= ( ap @ X2 @ X3 @ X1 @ Y0 ) ) )
@ ( sK15 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( func @ X2 @ X3 @ X4 ) )
| ( $false = sF11 )
| ( ( X1 = X4 )
= $true )
| ( ( func @ X2 @ X3 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( func @ X2 @ X3 @ X1 )
= $false )
| ( $false = sF11 )
| ( X1 = X4 )
| ( $false
= ( func @ X2 @ X3 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( ap @ X2 @ X3 @ X4 @ Y0 )
= ( ap @ X2 @ X3 @ X1 @ Y0 ) ) )
@ ( sK15 @ X3 @ X1 @ X4 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( func @ X2 @ X3 @ X1 )
= $false )
| ( $false = sF11 )
| ( $false
= ( func @ X2 @ X3 @ X4 ) )
| ( ( ( in @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) @ X2 )
=> ( ( ap @ X2 @ X3 @ X4 @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) )
= ( ap @ X2 @ X3 @ X1 @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) ) ) )
= $false )
| ( X1 = X4 ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( func @ X2 @ X3 @ X1 )
= $false )
| ( ( ( ap @ X2 @ X3 @ X4 @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) )
= ( ap @ X2 @ X3 @ X1 @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) ) )
= $false )
| ( $false = sF11 )
| ( X1 = X4 )
| ( $false
= ( func @ X2 @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( func @ X2 @ X3 @ X1 )
= $false )
| ( $false = sF11 )
| ( X1 = X4 )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) @ X2 ) )
| ( $false
= ( func @ X2 @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false = sF11 )
| ( ( ap @ X2 @ X3 @ X1 @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) )
!= ( ap @ X2 @ X3 @ X4 @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( func @ X2 @ X3 @ X4 ) )
| ( X1 = X4 )
| ( ( func @ X2 @ X3 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f76]) ).
thf(f99,plain,
( ( sF5 = $false )
| ( $true
= ( in @ sK1 @ sF4 ) ) ),
inference(iff_proxy_clausification,[],[f28]) ).
thf(f100,plain,
( ( ( in @ sK3 @ sF4 )
= $true )
| ( $false = sF6 ) ),
inference(iff_proxy_clausification,[],[f31]) ).
thf(f102,plain,
! [X4: $i] :
( ( ( in @ X4 @ sK2 )
= $false )
| ( ( sF9 @ X4 )
= $true ) ),
inference(iff_proxy_clausification,[],[f36]) ).
thf(f109,definition,
( spl20_2
<=> ( $true = sF10 ) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
thf(f111,plain,
( ( $true = sF10 )
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f119,definition,
( spl20_4
<=> ( $false = sF10 ) ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
thf(f121,plain,
( ( $false = sF10 )
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f123,definition,
( spl20_5
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X1 @ ( funcSet @ X3 @ X2 ) ) )
| ( ( func @ X3 @ X2 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl20_5])],[avatar_definition]) ).
thf(f124,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( funcSet @ X3 @ X2 ) ) )
| ( ( func @ X3 @ X2 @ X1 )
= $true ) )
| ~ spl20_5 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f125,plain,
( spl20_4
| spl20_5 ),
inference(avatar_split_clause,[],[f59,f123,f119]) ).
thf(f127,definition,
( spl20_6
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( ( func @ X2 @ X3 @ X1 )
= $false )
| ( $false
= ( func @ X2 @ X3 @ X4 ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) @ X2 ) )
| ( X1 = X4 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
thf(f128,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) @ X2 ) )
| ( $false
= ( func @ X2 @ X3 @ X4 ) )
| ( X1 = X4 )
| ( ( func @ X2 @ X3 @ X1 )
= $false ) )
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f130,definition,
( spl20_7
<=> ( $false = sF11 ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
thf(f132,plain,
( ( $false = sF11 )
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f130]) ).
thf(f133,plain,
( spl20_6
| spl20_7 ),
inference(avatar_split_clause,[],[f77,f130,f127]) ).
thf(f135,definition,
( spl20_8
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( ( ap @ X2 @ X3 @ X1 @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) )
!= ( ap @ X2 @ X3 @ X4 @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( ( func @ X2 @ X3 @ X1 )
= $false )
| ( X1 = X4 )
| ( $false
= ( func @ X2 @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
thf(f136,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ap @ X2 @ X3 @ X1 @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) )
!= ( ap @ X2 @ X3 @ X4 @ ( sK15 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( ( func @ X2 @ X3 @ X1 )
= $false )
| ( $false
= ( func @ X2 @ X3 @ X4 ) )
| ( X1 = X4 ) )
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f135]) ).
thf(f137,plain,
( spl20_8
| spl20_7 ),
inference(avatar_split_clause,[],[f78,f130,f135]) ).
thf(f143,definition,
( spl20_10
<=> ( sF11 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_10])],[avatar_definition]) ).
thf(f145,plain,
( ( sF11 = $true )
| ~ spl20_10 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f161,plain,
spl20_2,
inference(avatar_split_clause,[],[f40,f109]) ).
thf(f163,definition,
( spl20_14
<=> ( $true
= ( in @ sK1 @ sF4 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_14])],[avatar_definition]) ).
thf(f165,plain,
( ( $true
= ( in @ sK1 @ sF4 ) )
| ~ spl20_14 ),
inference(avatar_component_clause,[],[f163]) ).
thf(f167,definition,
( spl20_15
<=> ( sF5 = $false ) ),
introduced(definition,[new_symbols(definition,[spl20_15])],[avatar_definition]) ).
thf(f169,plain,
( ( sF5 = $false )
| ~ spl20_15 ),
inference(avatar_component_clause,[],[f167]) ).
thf(f170,plain,
( spl20_14
| spl20_15 ),
inference(avatar_split_clause,[],[f99,f167,f163]) ).
thf(f176,definition,
( spl20_17
<=> ( sF5 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_17])],[avatar_definition]) ).
thf(f178,plain,
( ( sF5 = $true )
| ~ spl20_17 ),
inference(avatar_component_clause,[],[f176]) ).
thf(f181,definition,
( spl20_18
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl20_18])],[avatar_definition]) ).
thf(f183,plain,
( ( $true = sF6 )
| ~ spl20_18 ),
inference(avatar_component_clause,[],[f181]) ).
thf(f190,definition,
( spl20_20
<=> ( ( in @ sK3 @ sF4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_20])],[avatar_definition]) ).
thf(f192,plain,
( ( ( in @ sK3 @ sF4 )
= $true )
| ~ spl20_20 ),
inference(avatar_component_clause,[],[f190]) ).
thf(f194,definition,
( spl20_21
<=> ( $false = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl20_21])],[avatar_definition]) ).
thf(f196,plain,
( ( $false = sF6 )
| ~ spl20_21 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f197,plain,
( spl20_20
| spl20_21 ),
inference(avatar_split_clause,[],[f100,f194,f190]) ).
thf(f198,plain,
spl20_17,
inference(avatar_split_clause,[],[f29,f176]) ).
thf(f199,plain,
spl20_18,
inference(avatar_split_clause,[],[f32,f181]) ).
thf(f200,plain,
spl20_10,
inference(avatar_split_clause,[],[f42,f143]) ).
thf(f201,plain,
( ( $false = $true )
| ~ spl20_2
| ~ spl20_4 ),
inference(forward_demodulation,[],[f111,f121]) ).
thf(f202,plain,
( $false
| ~ spl20_2
| ~ spl20_4 ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f203,plain,
( ~ spl20_2
| ~ spl20_4 ),
inference(avatar_contradiction_clause,[],[f202]) ).
thf(f215,plain,
( ( $false = $true )
| ~ spl20_7
| ~ spl20_10 ),
inference(forward_demodulation,[],[f145,f132]) ).
thf(f216,plain,
( $false
| ~ spl20_7
| ~ spl20_10 ),
inference(trivial_inequality_removal,[],[f215]) ).
thf(f217,plain,
( ~ spl20_7
| ~ spl20_10 ),
inference(avatar_contradiction_clause,[],[f216]) ).
thf(f226,plain,
( ! [X0: $i] :
( ( ( func @ sK2 @ sK0 @ X0 )
= $true )
| ( $false
= ( in @ X0 @ sF4 ) ) )
| ~ spl20_5 ),
inference(constrained_superposition,[],[f124,f27]) ).
thf(f232,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( func @ sK2 @ X0 @ X2 )
= $false )
| ( $false = $true )
| ( ( sF9 @ ( sK15 @ X0 @ X1 @ X2 @ sK2 ) )
= $true )
| ( X1 = X2 )
| ( ( func @ sK2 @ X0 @ X1 )
= $false ) )
| ~ spl20_6 ),
inference(constrained_superposition,[],[f102,f128]) ).
thf(f234,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sF9 @ ( sK15 @ X0 @ X1 @ X2 @ sK2 ) )
= $true )
| ( ( func @ sK2 @ X0 @ X2 )
= $false )
| ( X1 = X2 )
| ( ( func @ sK2 @ X0 @ X1 )
= $false ) )
| ~ spl20_6 ),
inference(trivial_inequality_removal,[],[f232]) ).
thf(f241,plain,
( ! [X0: $i] :
( ( ( sF8 @ ( sK15 @ sK0 @ X0 @ sK1 @ sK2 ) )
!= ( ap @ sK2 @ sK0 @ X0 @ ( sK15 @ sK0 @ X0 @ sK1 @ sK2 ) ) )
| ( sK1 = X0 )
| ( ( func @ sK2 @ sK0 @ sK1 )
= $false )
| ( ( func @ sK2 @ sK0 @ X0 )
= $false ) )
| ~ spl20_8 ),
inference(constrained_superposition,[],[f136,f35]) ).
thf(f245,definition,
( spl20_22
<=> ( ( func @ sK2 @ sK0 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl20_22])],[avatar_definition]) ).
thf(f246,plain,
( ( ( func @ sK2 @ sK0 @ sK1 )
!= $false )
| spl20_22 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f247,plain,
( ( ( func @ sK2 @ sK0 @ sK1 )
= $false )
| ~ spl20_22 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f249,definition,
( spl20_23
<=> ! [X0: $i] :
( ( ( sF8 @ ( sK15 @ sK0 @ X0 @ sK1 @ sK2 ) )
!= ( ap @ sK2 @ sK0 @ X0 @ ( sK15 @ sK0 @ X0 @ sK1 @ sK2 ) ) )
| ( ( func @ sK2 @ sK0 @ X0 )
= $false )
| ( sK1 = X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_23])],[avatar_definition]) ).
thf(f250,plain,
( ! [X0: $i] :
( ( ( sF8 @ ( sK15 @ sK0 @ X0 @ sK1 @ sK2 ) )
!= ( ap @ sK2 @ sK0 @ X0 @ ( sK15 @ sK0 @ X0 @ sK1 @ sK2 ) ) )
| ( ( func @ sK2 @ sK0 @ X0 )
= $false )
| ( sK1 = X0 ) )
| ~ spl20_23 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f251,plain,
( spl20_22
| spl20_23
| ~ spl20_8 ),
inference(avatar_split_clause,[],[f241,f135,f249,f245]) ).
thf(f257,definition,
( spl20_25
<=> ( ( func @ sK2 @ sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl20_25])],[avatar_definition]) ).
thf(f258,plain,
( ( ( func @ sK2 @ sK0 @ sK3 )
!= $false )
| spl20_25 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f259,plain,
( ( ( func @ sK2 @ sK0 @ sK3 )
= $false )
| ~ spl20_25 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f268,plain,
( ( $false = $true )
| ( $false
= ( in @ sK1 @ sF4 ) )
| ~ spl20_5
| ~ spl20_22 ),
inference(constrained_superposition,[],[f247,f226]) ).
thf(f273,plain,
( ( $false
= ( in @ sK1 @ sF4 ) )
| ~ spl20_5
| ~ spl20_22 ),
inference(trivial_inequality_removal,[],[f268]) ).
thf(f277,plain,
( ( $false = $true )
| ~ spl20_5
| ~ spl20_14
| ~ spl20_22 ),
inference(forward_demodulation,[],[f273,f165]) ).
thf(f278,plain,
( $false
| ~ spl20_5
| ~ spl20_14
| ~ spl20_22 ),
inference(trivial_inequality_removal,[],[f277]) ).
thf(f279,plain,
( ~ spl20_5
| ~ spl20_14
| ~ spl20_22 ),
inference(avatar_contradiction_clause,[],[f278]) ).
thf(f280,plain,
( ( $false = $true )
| ~ spl20_15
| ~ spl20_17 ),
inference(forward_demodulation,[],[f169,f178]) ).
thf(f281,plain,
( $false
| ~ spl20_15
| ~ spl20_17 ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f282,plain,
( ~ spl20_15
| ~ spl20_17 ),
inference(avatar_contradiction_clause,[],[f281]) ).
thf(f289,plain,
( ( $false = $true )
| ( ( in @ sK3 @ sF4 )
= $false )
| ~ spl20_5
| ~ spl20_25 ),
inference(constrained_superposition,[],[f226,f259]) ).
thf(f291,plain,
( ( ( in @ sK3 @ sF4 )
= $false )
| ~ spl20_5
| ~ spl20_25 ),
inference(trivial_inequality_removal,[],[f289]) ).
thf(f296,plain,
( ( $false = $true )
| ~ spl20_5
| ~ spl20_20
| ~ spl20_25 ),
inference(forward_demodulation,[],[f291,f192]) ).
thf(f297,plain,
( $false
| ~ spl20_5
| ~ spl20_20
| ~ spl20_25 ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f298,plain,
( ~ spl20_5
| ~ spl20_20
| ~ spl20_25 ),
inference(avatar_contradiction_clause,[],[f297]) ).
thf(f300,plain,
( ( $false = $true )
| ~ spl20_18
| ~ spl20_21 ),
inference(forward_demodulation,[],[f196,f183]) ).
thf(f301,plain,
( $false
| ~ spl20_18
| ~ spl20_21 ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f302,plain,
( ~ spl20_18
| ~ spl20_21 ),
inference(avatar_contradiction_clause,[],[f301]) ).
thf(f306,plain,
( ( ( sF8 @ ( sK15 @ sK0 @ sK3 @ sK1 @ sK2 ) )
!= ( sF7 @ ( sK15 @ sK0 @ sK3 @ sK1 @ sK2 ) ) )
| ( sK3 = sK1 )
| ( ( func @ sK2 @ sK0 @ sK3 )
= $false )
| ~ spl20_23 ),
inference(constrained_superposition,[],[f250,f34]) ).
thf(f307,plain,
( ( ( sF8 @ ( sK15 @ sK0 @ sK3 @ sK1 @ sK2 ) )
!= ( sF7 @ ( sK15 @ sK0 @ sK3 @ sK1 @ sK2 ) ) )
| ( ( func @ sK2 @ sK0 @ sK3 )
= $false )
| ~ spl20_23 ),
inference(forward_subsumption_resolution,[],[f306,f18]) ).
thf(f308,plain,
( ( ( sF8 @ ( sK15 @ sK0 @ sK3 @ sK1 @ sK2 ) )
!= ( sF7 @ ( sK15 @ sK0 @ sK3 @ sK1 @ sK2 ) ) )
| ~ spl20_23
| spl20_25 ),
inference(forward_subsumption_resolution,[],[f307,f258]) ).
thf(f309,plain,
( ( ( sF8 @ ( sK15 @ sK0 @ sK3 @ sK1 @ sK2 ) )
!= ( sF8 @ ( sK15 @ sK0 @ sK3 @ sK1 @ sK2 ) ) )
| ( ( sF9 @ ( sK15 @ sK0 @ sK3 @ sK1 @ sK2 ) )
!= $true )
| ~ spl20_23
| spl20_25 ),
inference(constrained_superposition,[],[f308,f37]) ).
thf(f310,plain,
( ( ( sF9 @ ( sK15 @ sK0 @ sK3 @ sK1 @ sK2 ) )
!= $true )
| ~ spl20_23
| spl20_25 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f314,plain,
( ( sK3 = sK1 )
| ( $true != $true )
| ( ( func @ sK2 @ sK0 @ sK1 )
= $false )
| ( ( func @ sK2 @ sK0 @ sK3 )
= $false )
| ~ spl20_6
| ~ spl20_23
| spl20_25 ),
inference(constrained_superposition,[],[f310,f234]) ).
thf(f316,plain,
( ( sK3 = sK1 )
| ( ( func @ sK2 @ sK0 @ sK3 )
= $false )
| ( ( func @ sK2 @ sK0 @ sK1 )
= $false )
| ~ spl20_6
| ~ spl20_23
| spl20_25 ),
inference(trivial_inequality_removal,[],[f314]) ).
thf(f318,plain,
( ( ( func @ sK2 @ sK0 @ sK3 )
= $false )
| ( ( func @ sK2 @ sK0 @ sK1 )
= $false )
| ~ spl20_6
| ~ spl20_23
| spl20_25 ),
inference(forward_subsumption_resolution,[],[f316,f18]) ).
thf(f319,plain,
( ( ( func @ sK2 @ sK0 @ sK1 )
= $false )
| ~ spl20_6
| ~ spl20_23
| spl20_25 ),
inference(forward_subsumption_resolution,[],[f318,f258]) ).
thf(f320,plain,
( $false
| ~ spl20_6
| spl20_22
| ~ spl20_23
| spl20_25 ),
inference(forward_subsumption_resolution,[],[f319,f246]) ).
thf(f321,plain,
( ~ spl20_6
| spl20_22
| ~ spl20_23
| spl20_25 ),
inference(avatar_contradiction_clause,[],[f320]) ).
cnf(s3,plain,
( spl20_4
| spl20_5 ),
inference(sat_conversion,[],[f125]) ).
cnf(s4,plain,
( spl20_6
| spl20_7 ),
inference(sat_conversion,[],[f133]) ).
cnf(s5,plain,
( spl20_7
| spl20_8 ),
inference(sat_conversion,[],[f137]) ).
cnf(s10,plain,
spl20_2,
inference(sat_conversion,[],[f161]) ).
cnf(s11,plain,
( spl20_14
| spl20_15 ),
inference(sat_conversion,[],[f170]) ).
cnf(s14,plain,
( spl20_20
| spl20_21 ),
inference(sat_conversion,[],[f197]) ).
cnf(s15,plain,
spl20_17,
inference(sat_conversion,[],[f198]) ).
cnf(s16,plain,
spl20_18,
inference(sat_conversion,[],[f199]) ).
cnf(s17,plain,
spl20_10,
inference(sat_conversion,[],[f200]) ).
cnf(s18,plain,
( ~ spl20_2
| ~ spl20_4 ),
inference(sat_conversion,[],[f203]) ).
cnf(s19,plain,
( ~ spl20_7
| ~ spl20_10 ),
inference(sat_conversion,[],[f217]) ).
cnf(s20,plain,
( ~ spl20_8
| spl20_22
| spl20_23 ),
inference(sat_conversion,[],[f251]) ).
cnf(s25,plain,
( ~ spl20_5
| ~ spl20_14
| ~ spl20_22 ),
inference(sat_conversion,[],[f279]) ).
cnf(s26,plain,
( ~ spl20_15
| ~ spl20_17 ),
inference(sat_conversion,[],[f282]) ).
cnf(s30,plain,
( ~ spl20_5
| ~ spl20_20
| ~ spl20_25 ),
inference(sat_conversion,[],[f298]) ).
cnf(s32,plain,
( ~ spl20_18
| ~ spl20_21 ),
inference(sat_conversion,[],[f302]) ).
cnf(s34,plain,
( ~ spl20_6
| spl20_22
| ~ spl20_23
| spl20_25 ),
inference(sat_conversion,[],[f321]) ).
cnf(s35,plain,
~ spl20_7,
inference(rat,[],[s19,s17]) ).
cnf(s36,plain,
~ spl20_21,
inference(rat,[],[s32,s16]) ).
cnf(s37,plain,
~ spl20_15,
inference(rat,[],[s26,s15]) ).
cnf(s38,plain,
spl20_20,
inference(rat,[],[s14,s36]) ).
cnf(s39,plain,
spl20_14,
inference(rat,[],[s11,s37]) ).
cnf(s40,plain,
~ spl20_4,
inference(rat,[],[s18,s10]) ).
cnf(s41,plain,
spl20_8,
inference(rat,[],[s5,s35]) ).
cnf(s42,plain,
spl20_6,
inference(rat,[],[s4,s35]) ).
cnf(s43,plain,
spl20_5,
inference(rat,[],[s3,s40]) ).
cnf(s44,plain,
~ spl20_25,
inference(rat,[],[s30,s38,s43]) ).
cnf(s45,plain,
~ spl20_22,
inference(rat,[],[s25,s39,s43]) ).
cnf(s48,plain,
~ spl20_23,
inference(rat,[],[s34,s44,s42,s45]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s20,s41,s48,s45]) ).
thf(f322,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU692^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n013.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 14:10:54 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.30 % (2177093)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (2177104)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (2177104)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
% 0.23/0.30 % (2177104)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=2345303783:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (2177104) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2177093-2177104"...
% 0.23/0.30 % (2177098)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3828045808:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (2177099)lrs+10_16_si=on:nwc=1.5:random_seed=3809127795:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (2177100)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1398463377:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (2177102)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2142944205:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (2177101)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=2451364526: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)
% 0.23/0.30 % (2177103)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3261837840:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (2177104)...printing done.
% 0.23/0.30 % (2177100)Instruction limit reached!
% 0.23/0.30 % (2177100)------------------------------
% 0.23/0.30 % (2177100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (2177100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (2177100)CaDiCaL version: 2.1.3
% 0.23/0.30 % (2177100)Termination reason: Instruction limit
% 0.23/0.30 % (2177100)Termination phase: Saturation
% 0.23/0.30 % (2177100)Time elapsed: 0.002 s
% 0.23/0.30 % (2177100)Peak memory usage: 12 MB
% 0.23/0.30 % (2177100)Instructions burned: 3 (million)
% 0.23/0.30 % (2177104)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.30 % (2177104)------------------------------
% 0.23/0.30 % (2177104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (2177104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (2177104)CaDiCaL version: 2.1.3
% 0.23/0.30 % (2177104)Termination reason: Refutation
% 0.23/0.30 % (2177104)Time elapsed: 0.008 s
% 0.23/0.30 % (2177104)Peak memory usage: 13 MB
% 0.23/0.30 % (2177104)Instructions burned: 26 (million)
% 0.23/0.30 % (2177093)Success in time 0.042 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------