%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU782^2 : 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 : n009.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 08:31:21 AM UTC 2026
% Result : Theorem 0.25s 0.35s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 32
% Syntax : Number of formulae : 217 ( 72 unt; 0 typ; 26 def)
% Number of atoms : 1387 ( 274 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 1657 ( 179 ~; 261 |; 20 &; 941 @)
% ( 19 <=>; 159 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 52 ( 48 usr; 36 con; 0-4 aty)
% ( 78 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 301 ( 0 sgn 139 !; 9 ?; 301 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
subsetI1: $o ).
thf(func_def_4,type,
subsetE: $o ).
thf(func_def_5,type,
binunion: $i > $i > $i ).
thf(func_def_6,type,
binunionEcases: $o ).
thf(func_def_7,type,
cartprod: $i > $i > $i ).
thf(func_def_8,type,
breln: $i > $i > $i > $o ).
thf(func_def_9,type,
breln1: $i > $i > $o ).
thf(func_def_12,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sF3: $o ).
thf(func_def_24,type,
sF5: $o ).
thf(func_def_25,type,
sF6: $o ).
thf(func_def_26,type,
sF7: $o ).
thf(func_def_27,type,
sF8: $o ).
thf(func_def_28,type,
sF9: $o ).
thf(func_def_34,type,
sK15: $o ).
thf(func_def_38,type,
sK19: $i > $i > $i ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(f2,axiom,
( subsetE
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(f3,axiom,
! [X0: $i,X3: $o,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
= binunionEcases ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(f4,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(f5,axiom,
( breln1
= ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1) ).
thf(f6,conjecture,
( subsetI1
=> ( subsetE
=> ( binunionEcases
=> ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionprop) ).
thf(f7,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( binunionEcases
=> ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
~ ( subsetI1
=> ( subsetE
=> ( binunionEcases
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ( breln1 @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
~ ( ( subsetI1 = $true )
=> ( ( subsetE = $true )
=> ( ( binunionEcases = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X1 @ X2 )
= $true )
=> ( ( breln1 @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f13,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f14,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f16,plain,
! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X3 ) )
=> ( ( ( in @ X2 @ X0 )
=> X1 )
=> ( ( ( in @ X2 @ X3 )
=> X1 )
=> X1 ) ) )
= binunionEcases ),
inference(rectify,[],[f3]) ).
thf(f17,plain,
( binunionEcases
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ ( binunion @ Y3 @ Y0 ) )
=> ( ( ( in @ Y1 @ Y3 )
=> Y2 )
=> ( ( ( in @ Y1 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( breln1 @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( breln1 @ X1 @ X2 )
= $true ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( binunionEcases = $true )
& ( subsetE = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f19,plain,
( ( subsetI1 = $true )
& ( subsetE = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( breln1 @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( breln1 @ X1 @ X2 )
= $true ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( binunionEcases = $true ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
( ( subsetI1 = $true )
& ( subsetE = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( breln1 @ X0 @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( binunionEcases = $true ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( subsetI1 = $true )
& ( subsetE = $true )
& ( ( breln1 @ sK0 @ ( binunion @ sK1 @ sK2 ) )
!= $true )
& ( $true
= ( breln1 @ sK0 @ sK2 ) )
& ( ( breln1 @ sK0 @ sK1 )
= $true )
& ( binunionEcases = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f20]) ).
thf(f22,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f23,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f25,plain,
binunionEcases = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f26,plain,
( ( breln1 @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f27,plain,
( $true
= ( breln1 @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
( ( breln1 @ sK0 @ ( binunion @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f29,plain,
subsetE = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f30,plain,
subsetI1 = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f31,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f32,plain,
( binunionEcases
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ ( binunion @ Y3 @ Y0 ) )
=> ( ( ( in @ Y1 @ Y3 )
=> Y2 )
=> ( ( ( in @ Y1 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f35,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f24,f22]) ).
thf(f36,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f23,f29]) ).
thf(f37,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ ( binunion @ sK1 @ sK2 ) )
!= $true ),
inference(definition_unfolding,[],[f28,f35]) ).
thf(f38,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sK2 )
= $true ),
inference(definition_unfolding,[],[f27,f35]) ).
thf(f39,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f26,f35]) ).
thf(f40,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f31,f30]) ).
thf(f41,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ ( binunion @ Y3 @ Y0 ) )
=> ( ( ( in @ Y1 @ Y3 )
=> Y2 )
=> ( ( ( in @ Y1 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f32,f25]) ).
thf(f42,definition,
( sF3
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f43,plain,
sF3 = $true,
inference(definition_folding,[],[f36,f42]) ).
thf(f44,definition,
( sF4
= ( binunion @ sK1 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f45,definition,
( sF5
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sF4 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f46,plain,
sF5 != $true,
inference(definition_folding,[],[f37,f45,f44]) ).
thf(f47,definition,
( sF6
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f48,plain,
sF6 = $true,
inference(definition_folding,[],[f38,f47]) ).
thf(f49,definition,
( sF7
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f50,plain,
sF7 = $true,
inference(definition_folding,[],[f39,f49]) ).
thf(f51,definition,
( sF8
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f52,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= sF8 ),
inference(reorient_equations,[],[f51]) ).
thf(f53,plain,
sF8 = $true,
inference(definition_folding,[],[f40,f52]) ).
thf(f54,definition,
( sF9
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ ( binunion @ Y3 @ Y0 ) )
=> ( ( ( in @ Y1 @ Y3 )
=> Y2 )
=> ( ( ( in @ Y1 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f55,plain,
sF9 = $true,
inference(definition_folding,[],[f41,f54]) ).
thf(f57,plain,
( ( $false = sF3 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f42]) ).
thf(f58,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) )
@ X1 )
= $true )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) ) )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( $false = sF3 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( $false = sF3 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X2 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF3 )
| ( ( ^ [Y0: $i] :
( ( subset @ X2 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( subset @ X2 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF3 )
| ( $false
= ( subset @ X2 @ X1 ) )
| ( ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF3 )
| ( ( in @ X3 @ X1 )
= $true )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f76,plain,
( ( $false
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sF4 ) )
| ( sF5 = $true ) ),
inference(iff_proxy_clausification,[],[f45]) ).
thf(f79,plain,
( ( sF5 = $true )
| ( $false
= ( subset @ sF4 @ ( cartprod @ sK0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f81,plain,
( ( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sK2 )
= $true )
| ( $false = sF6 ) ),
inference(iff_proxy_clausification,[],[f47]) ).
thf(f82,plain,
( ( $false = sF6 )
| ( ( subset @ sK2 @ ( cartprod @ sK0 @ sK0 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f85,plain,
( ( $false = sF9 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ ( binunion @ Y3 @ Y0 ) )
=> ( ( ( in @ Y1 @ Y3 )
=> Y2 )
=> ( ( ( in @ Y1 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f54]) ).
thf(f86,plain,
! [X1: $i] :
( ( $false = sF9 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ ( binunion @ Y3 @ Y0 ) )
=> ( ( ( in @ Y1 @ Y3 )
=> Y2 )
=> ( ( ( in @ Y1 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ X1 ) )
=> ( ( ( in @ Y0 @ Y2 )
=> Y1 )
=> ( ( ( in @ Y0 @ X1 )
=> Y1 )
=> Y1 ) ) ) ) ) ) )
| ( $false = sF9 ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ X1 ) )
=> ( ( ( in @ Y0 @ Y2 )
=> Y1 )
=> ( ( ( in @ Y0 @ X1 )
=> Y1 )
=> Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $false = sF9 ) ),
inference(pi_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X1: $i] :
( ( $false = sF9 )
| ( ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X2 @ ( binunion @ Y1 @ X1 ) )
=> ( ( ( in @ X2 @ Y1 )
=> Y0 )
=> ( ( ( in @ X2 @ X1 )
=> Y0 )
=> Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false = sF9 )
| ( ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X2 @ ( binunion @ Y1 @ X1 ) )
=> ( ( ( in @ X2 @ Y1 )
=> Y0 )
=> ( ( ( in @ X2 @ X1 )
=> Y0 )
=> Y0 ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false = sF9 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( binunion @ Y0 @ X1 ) )
=> ( ( ( in @ X2 @ Y0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( $false = sF9 )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ ( binunion @ Y0 @ X1 ) )
=> ( ( ( in @ X2 @ Y0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( ( ( in @ X2 @ ( binunion @ X4 @ X1 ) )
=> ( ( ( in @ X2 @ X4 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
= $true )
| ( $false = sF9 ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( $false
= ( in @ X2 @ ( binunion @ X4 @ X1 ) ) )
| ( ( ( ( in @ X2 @ X4 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) )
= $true )
| ( $false = sF9 ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( $false = sF9 )
| ( $false
= ( in @ X2 @ ( binunion @ X4 @ X1 ) ) )
| ( ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 )
= $true )
| ( $false
= ( ( in @ X2 @ X4 )
=> X3 ) ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( $false
= ( in @ X2 @ ( binunion @ X4 @ X1 ) ) )
| ( $false
= ( ( in @ X2 @ X4 )
=> X3 ) )
| ( $false = sF9 )
| ( $false
= ( ( in @ X2 @ X1 )
=> X3 ) )
| ( $true = X3 ) ),
inference(imp_proxy_clausification,[],[f95]) ).
thf(f98,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( ( in @ X2 @ X4 )
= $true )
| ( $false
= ( ( in @ X2 @ X1 )
=> X3 ) )
| ( $true = X3 )
| ( $false
= ( in @ X2 @ ( binunion @ X4 @ X1 ) ) )
| ( $false = sF9 ) ),
inference(imp_proxy_clausification,[],[f96]) ).
thf(f100,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( $false = sF9 )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true = X3 )
| ( ( in @ X2 @ X4 )
= $true )
| ( $false
= ( in @ X2 @ ( binunion @ X4 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f98]) ).
thf(f121,plain,
( ( $true
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sK1 ) )
| ( $false = sF7 ) ),
inference(iff_proxy_clausification,[],[f49]) ).
thf(f122,plain,
( ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $true )
| ( $false = sF7 ) ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f124,plain,
( ( $false = sF8 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f52]) ).
thf(f135,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( $false = sF8 ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f136,plain,
! [X1: $i] :
( ( $false = sF8 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) )
@ X2 ) )
| ( $false = sF8 ) ),
inference(pi_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( subset @ X2 @ X1 ) )
= $true )
| ( $false = sF8 ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( ( subset @ X2 @ X1 )
= $true )
| ( $false = sF8 ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK19 @ X1 @ X2 ) ) )
| ( ( subset @ X2 @ X1 )
= $true )
| ( $false = sF8 ) ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK19 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK19 @ X1 @ X2 ) @ X1 ) ) )
| ( ( subset @ X2 @ X1 )
= $true )
| ( $false = sF8 ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
| ( $false
= ( in @ ( sK19 @ X1 @ X2 ) @ X1 ) )
| ( $false = sF8 ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
| ( $false = sF8 )
| ( ( in @ ( sK19 @ X1 @ X2 ) @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f145,definition,
( spl20_1
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
thf(f147,plain,
( ( $false = sF3 )
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f149,definition,
( spl20_2
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
| ( $false
= ( subset @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
thf(f150,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X1 )
= $true ) )
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f149]) ).
thf(f151,plain,
( spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f65,f149,f145]) ).
thf(f153,definition,
( spl20_3
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
thf(f155,plain,
( ( sF3 = $true )
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f153]) ).
thf(f181,definition,
( spl20_9
<=> ( sF5 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
thf(f185,definition,
( spl20_10
<=> ( $false
= ( subset @ sF4 @ ( cartprod @ sK0 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_10])],[avatar_definition]) ).
thf(f187,plain,
( ( $false
= ( subset @ sF4 @ ( cartprod @ sK0 @ sK0 ) ) )
| ~ spl20_10 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f188,plain,
( spl20_9
| spl20_10 ),
inference(avatar_split_clause,[],[f79,f185,f181]) ).
thf(f190,definition,
( spl20_11
<=> ( ( subset @ sK2 @ ( cartprod @ sK0 @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_11])],[avatar_definition]) ).
thf(f192,plain,
( ( ( subset @ sK2 @ ( cartprod @ sK0 @ sK0 ) )
= $true )
| ~ spl20_11 ),
inference(avatar_component_clause,[],[f190]) ).
thf(f194,definition,
( spl20_12
<=> ( $false = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl20_12])],[avatar_definition]) ).
thf(f196,plain,
( ( $false = sF6 )
| ~ spl20_12 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f197,plain,
( spl20_11
| spl20_12 ),
inference(avatar_split_clause,[],[f82,f194,f190]) ).
thf(f199,definition,
( spl20_13
<=> ( sF6 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_13])],[avatar_definition]) ).
thf(f201,plain,
( ( sF6 = $true )
| ~ spl20_13 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f207,plain,
~ spl20_9,
inference(avatar_split_clause,[],[f46,f181]) ).
thf(f208,plain,
spl20_13,
inference(avatar_split_clause,[],[f48,f199]) ).
thf(f210,definition,
( spl20_15
<=> ! [X2: $i,X1: $i,X4: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $false
= ( in @ X2 @ ( binunion @ X4 @ X1 ) ) )
| ( ( in @ X2 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl20_15])],[avatar_definition]) ).
thf(f211,plain,
( ! [X2: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X2 @ ( binunion @ X4 @ X1 ) ) )
| ( ( in @ X2 @ X4 )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ~ spl20_15 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f213,definition,
( spl20_16
<=> ! [X3: $o] : ( $true = X3 ) ),
introduced(definition,[new_symbols(definition,[spl20_16])],[avatar_definition]) ).
thf(f214,plain,
( ! [X3: $o] : ( $true = X3 )
| ~ spl20_16 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f216,definition,
( spl20_17
<=> ( $false = sF9 ) ),
introduced(definition,[new_symbols(definition,[spl20_17])],[avatar_definition]) ).
thf(f218,plain,
( ( $false = sF9 )
| ~ spl20_17 ),
inference(avatar_component_clause,[],[f216]) ).
thf(f219,plain,
( spl20_15
| spl20_16
| spl20_17 ),
inference(avatar_split_clause,[],[f100,f216,f213,f210]) ).
thf(f236,definition,
( spl20_22
<=> ( sF9 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_22])],[avatar_definition]) ).
thf(f238,plain,
( ( sF9 = $true )
| ~ spl20_22 ),
inference(avatar_component_clause,[],[f236]) ).
thf(f263,plain,
spl20_22,
inference(avatar_split_clause,[],[f55,f236]) ).
thf(f265,definition,
( spl20_28
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl20_28])],[avatar_definition]) ).
thf(f267,plain,
( ( $false = sF7 )
| ~ spl20_28 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f269,definition,
( spl20_29
<=> ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_29])],[avatar_definition]) ).
thf(f271,plain,
( ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $true )
| ~ spl20_29 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f272,plain,
( spl20_28
| spl20_29 ),
inference(avatar_split_clause,[],[f122,f269,f265]) ).
thf(f278,definition,
( spl20_31
<=> ( sF7 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_31])],[avatar_definition]) ).
thf(f280,plain,
( ( sF7 = $true )
| ~ spl20_31 ),
inference(avatar_component_clause,[],[f278]) ).
thf(f286,definition,
( spl20_33
<=> ( sF8 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_33])],[avatar_definition]) ).
thf(f288,plain,
( ( sF8 = $true )
| ~ spl20_33 ),
inference(avatar_component_clause,[],[f286]) ).
thf(f296,definition,
( spl20_35
<=> ( $false = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl20_35])],[avatar_definition]) ).
thf(f298,plain,
( ( $false = sF8 )
| ~ spl20_35 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f300,definition,
( spl20_36
<=> ! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
| ( ( in @ ( sK19 @ X1 @ X2 ) @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl20_36])],[avatar_definition]) ).
thf(f301,plain,
( ! [X2: $i,X1: $i] :
( ( ( in @ ( sK19 @ X1 @ X2 ) @ X2 )
= $true )
| ( ( subset @ X2 @ X1 )
= $true ) )
| ~ spl20_36 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f302,plain,
( spl20_35
| spl20_36 ),
inference(avatar_split_clause,[],[f143,f300,f296]) ).
thf(f304,definition,
( spl20_37
<=> ! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
| ( $false
= ( in @ ( sK19 @ X1 @ X2 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_37])],[avatar_definition]) ).
thf(f305,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK19 @ X1 @ X2 ) @ X1 ) )
| ( ( subset @ X2 @ X1 )
= $true ) )
| ~ spl20_37 ),
inference(avatar_component_clause,[],[f304]) ).
thf(f306,plain,
( spl20_37
| spl20_35 ),
inference(avatar_split_clause,[],[f142,f296,f304]) ).
thf(f307,plain,
spl20_3,
inference(avatar_split_clause,[],[f43,f153]) ).
thf(f308,plain,
spl20_31,
inference(avatar_split_clause,[],[f50,f278]) ).
thf(f309,plain,
spl20_33,
inference(avatar_split_clause,[],[f53,f286]) ).
thf(f311,plain,
( ( $false = $true )
| ~ spl20_28
| ~ spl20_31 ),
inference(forward_demodulation,[],[f280,f267]) ).
thf(f312,plain,
( $false
| ~ spl20_28
| ~ spl20_31 ),
inference(trivial_inequality_removal,[],[f311]) ).
thf(f313,plain,
( ~ spl20_28
| ~ spl20_31 ),
inference(avatar_contradiction_clause,[],[f312]) ).
thf(f316,plain,
( ( $false = $true )
| ~ spl20_33
| ~ spl20_35 ),
inference(forward_demodulation,[],[f298,f288]) ).
thf(f317,plain,
( $false
| ~ spl20_33
| ~ spl20_35 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f318,plain,
( ~ spl20_33
| ~ spl20_35 ),
inference(avatar_contradiction_clause,[],[f317]) ).
thf(f320,plain,
( ( $false = $true )
| ~ spl20_17
| ~ spl20_22 ),
inference(forward_demodulation,[],[f218,f238]) ).
thf(f321,plain,
( $false
| ~ spl20_17
| ~ spl20_22 ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f322,plain,
( ~ spl20_17
| ~ spl20_22 ),
inference(avatar_contradiction_clause,[],[f321]) ).
thf(f349,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( in @ X0 @ ( cartprod @ sK0 @ sK0 ) )
= $true )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl20_2
| ~ spl20_29 ),
inference(constrained_superposition,[],[f150,f271]) ).
thf(f352,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( in @ X0 @ ( cartprod @ sK0 @ sK0 ) )
= $true )
| ( $false
= ( in @ X0 @ sK2 ) ) )
| ~ spl20_2
| ~ spl20_11 ),
inference(constrained_superposition,[],[f192,f150]) ).
thf(f358,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ ( cartprod @ sK0 @ sK0 ) )
= $true )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl20_2
| ~ spl20_29 ),
inference(trivial_inequality_removal,[],[f349]) ).
thf(f359,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ ( cartprod @ sK0 @ sK0 ) )
= $true )
| ( $false
= ( in @ X0 @ sK2 ) ) )
| ~ spl20_2
| ~ spl20_11 ),
inference(trivial_inequality_removal,[],[f352]) ).
thf(f363,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK19 @ ( cartprod @ sK0 @ sK0 ) @ X0 ) @ sK1 ) )
| ( ( subset @ X0 @ ( cartprod @ sK0 @ sK0 ) )
= $true )
| ( $false = $true ) )
| ~ spl20_2
| ~ spl20_29
| ~ spl20_37 ),
inference(constrained_superposition,[],[f305,f358]) ).
thf(f364,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK19 @ ( cartprod @ sK0 @ sK0 ) @ X0 ) @ sK1 ) )
| ( ( subset @ X0 @ ( cartprod @ sK0 @ sK0 ) )
= $true ) )
| ~ spl20_2
| ~ spl20_29
| ~ spl20_37 ),
inference(trivial_inequality_removal,[],[f363]) ).
thf(f367,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( in @ ( sK19 @ ( cartprod @ sK0 @ sK0 ) @ X0 ) @ sK2 ) )
| ( ( subset @ X0 @ ( cartprod @ sK0 @ sK0 ) )
= $true ) )
| ~ spl20_2
| ~ spl20_11
| ~ spl20_37 ),
inference(constrained_superposition,[],[f305,f359]) ).
thf(f368,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK19 @ ( cartprod @ sK0 @ sK0 ) @ X0 ) @ sK2 ) )
| ( ( subset @ X0 @ ( cartprod @ sK0 @ sK0 ) )
= $true ) )
| ~ spl20_2
| ~ spl20_11
| ~ spl20_37 ),
inference(trivial_inequality_removal,[],[f367]) ).
thf(f468,plain,
( ( $false = $true )
| ~ spl20_10
| ~ spl20_16 ),
inference(constrained_superposition,[],[f187,f214]) ).
thf(f489,plain,
( $false
| ~ spl20_10
| ~ spl20_16 ),
inference(trivial_inequality_removal,[],[f468]) ).
thf(f490,plain,
( ~ spl20_10
| ~ spl20_16 ),
inference(avatar_contradiction_clause,[],[f489]) ).
thf(f491,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sF4 ) )
| ( ( in @ X0 @ sK1 )
= $true )
| ( ( in @ X0 @ sK2 )
= $true ) )
| ~ spl20_15 ),
inference(constrained_superposition,[],[f211,f44]) ).
thf(f500,plain,
( ! [X0: $i] :
( ( ( in @ ( sK19 @ X0 @ sF4 ) @ sK1 )
= $true )
| ( $true
= ( in @ ( sK19 @ X0 @ sF4 ) @ sK2 ) )
| ( $false = $true )
| ( ( subset @ sF4 @ X0 )
= $true ) )
| ~ spl20_15
| ~ spl20_36 ),
inference(constrained_superposition,[],[f301,f491]) ).
thf(f501,plain,
( ! [X0: $i] :
( ( $true
= ( in @ ( sK19 @ X0 @ sF4 ) @ sK2 ) )
| ( ( in @ ( sK19 @ X0 @ sF4 ) @ sK1 )
= $true )
| ( ( subset @ sF4 @ X0 )
= $true ) )
| ~ spl20_15
| ~ spl20_36 ),
inference(trivial_inequality_removal,[],[f500]) ).
thf(f505,plain,
( ( $true
= ( subset @ sF4 @ ( cartprod @ sK0 @ sK0 ) ) )
| ( $true
= ( subset @ sF4 @ ( cartprod @ sK0 @ sK0 ) ) )
| ( ( in @ ( sK19 @ ( cartprod @ sK0 @ sK0 ) @ sF4 ) @ sK1 )
= $true )
| ( $false = $true )
| ~ spl20_2
| ~ spl20_11
| ~ spl20_15
| ~ spl20_36
| ~ spl20_37 ),
inference(constrained_superposition,[],[f501,f368]) ).
thf(f510,plain,
( ( ( in @ ( sK19 @ ( cartprod @ sK0 @ sK0 ) @ sF4 ) @ sK1 )
= $true )
| ( $true
= ( subset @ sF4 @ ( cartprod @ sK0 @ sK0 ) ) )
| ( $false = $true )
| ~ spl20_2
| ~ spl20_11
| ~ spl20_15
| ~ spl20_36
| ~ spl20_37 ),
inference(duplicate_literal_removal,[],[f505]) ).
thf(f511,plain,
( ( $true
= ( subset @ sF4 @ ( cartprod @ sK0 @ sK0 ) ) )
| ( ( in @ ( sK19 @ ( cartprod @ sK0 @ sK0 ) @ sF4 ) @ sK1 )
= $true )
| ~ spl20_2
| ~ spl20_11
| ~ spl20_15
| ~ spl20_36
| ~ spl20_37 ),
inference(trivial_inequality_removal,[],[f510]) ).
thf(f516,plain,
( ( $false = $true )
| ( ( in @ ( sK19 @ ( cartprod @ sK0 @ sK0 ) @ sF4 ) @ sK1 )
= $true )
| ~ spl20_2
| ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_36
| ~ spl20_37 ),
inference(forward_demodulation,[],[f511,f187]) ).
thf(f517,plain,
( ( ( in @ ( sK19 @ ( cartprod @ sK0 @ sK0 ) @ sF4 ) @ sK1 )
= $true )
| ~ spl20_2
| ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_36
| ~ spl20_37 ),
inference(trivial_inequality_removal,[],[f516]) ).
thf(f520,plain,
( ( $false = $true )
| ( $true
= ( subset @ sF4 @ ( cartprod @ sK0 @ sK0 ) ) )
| ~ spl20_2
| ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_29
| ~ spl20_36
| ~ spl20_37 ),
inference(constrained_superposition,[],[f517,f364]) ).
thf(f523,plain,
( ( $true
= ( subset @ sF4 @ ( cartprod @ sK0 @ sK0 ) ) )
| ~ spl20_2
| ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_29
| ~ spl20_36
| ~ spl20_37 ),
inference(trivial_inequality_removal,[],[f520]) ).
thf(f527,plain,
( ( $false = $true )
| ~ spl20_2
| ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_29
| ~ spl20_36
| ~ spl20_37 ),
inference(forward_demodulation,[],[f523,f187]) ).
thf(f528,plain,
( $false
| ~ spl20_2
| ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_29
| ~ spl20_36
| ~ spl20_37 ),
inference(trivial_inequality_removal,[],[f527]) ).
thf(f529,plain,
( ~ spl20_2
| ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_29
| ~ spl20_36
| ~ spl20_37 ),
inference(avatar_contradiction_clause,[],[f528]) ).
thf(f530,plain,
( ( $false = $true )
| ~ spl20_12
| ~ spl20_13 ),
inference(forward_demodulation,[],[f196,f201]) ).
thf(f531,plain,
( $false
| ~ spl20_12
| ~ spl20_13 ),
inference(trivial_inequality_removal,[],[f530]) ).
thf(f532,plain,
( ~ spl20_12
| ~ spl20_13 ),
inference(avatar_contradiction_clause,[],[f531]) ).
thf(f533,plain,
( ( $false = $true )
| ~ spl20_1
| ~ spl20_3 ),
inference(forward_demodulation,[],[f147,f155]) ).
thf(f534,plain,
( $false
| ~ spl20_1
| ~ spl20_3 ),
inference(trivial_inequality_removal,[],[f533]) ).
thf(f535,plain,
( ~ spl20_1
| ~ spl20_3 ),
inference(avatar_contradiction_clause,[],[f534]) ).
cnf(s1,plain,
( spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f151]) ).
cnf(s6,plain,
( spl20_9
| spl20_10 ),
inference(sat_conversion,[],[f188]) ).
cnf(s7,plain,
( spl20_11
| spl20_12 ),
inference(sat_conversion,[],[f197]) ).
cnf(s9,plain,
~ spl20_9,
inference(sat_conversion,[],[f207]) ).
cnf(s10,plain,
spl20_13,
inference(sat_conversion,[],[f208]) ).
cnf(s11,plain,
( spl20_15
| spl20_16
| spl20_17 ),
inference(sat_conversion,[],[f219]) ).
cnf(s19,plain,
spl20_22,
inference(sat_conversion,[],[f263]) ).
cnf(s20,plain,
( spl20_28
| spl20_29 ),
inference(sat_conversion,[],[f272]) ).
cnf(s24,plain,
( spl20_35
| spl20_36 ),
inference(sat_conversion,[],[f302]) ).
cnf(s25,plain,
( spl20_35
| spl20_37 ),
inference(sat_conversion,[],[f306]) ).
cnf(s26,plain,
spl20_3,
inference(sat_conversion,[],[f307]) ).
cnf(s27,plain,
spl20_31,
inference(sat_conversion,[],[f308]) ).
cnf(s28,plain,
spl20_33,
inference(sat_conversion,[],[f309]) ).
cnf(s29,plain,
( ~ spl20_28
| ~ spl20_31 ),
inference(sat_conversion,[],[f313]) ).
cnf(s31,plain,
( ~ spl20_33
| ~ spl20_35 ),
inference(sat_conversion,[],[f318]) ).
cnf(s32,plain,
( ~ spl20_17
| ~ spl20_22 ),
inference(sat_conversion,[],[f322]) ).
cnf(s36,plain,
( ~ spl20_10
| ~ spl20_16 ),
inference(sat_conversion,[],[f490]) ).
cnf(s38,plain,
( ~ spl20_2
| ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_29
| ~ spl20_36
| ~ spl20_37 ),
inference(sat_conversion,[],[f529]) ).
cnf(s39,plain,
( ~ spl20_12
| ~ spl20_13 ),
inference(sat_conversion,[],[f532]) ).
cnf(s40,plain,
( ~ spl20_1
| ~ spl20_3 ),
inference(sat_conversion,[],[f535]) ).
cnf(s41,plain,
~ spl20_35,
inference(rat,[],[s31,s28]) ).
cnf(s42,plain,
~ spl20_28,
inference(rat,[],[s29,s27]) ).
cnf(s43,plain,
~ spl20_1,
inference(rat,[],[s40,s26]) ).
cnf(s44,plain,
spl20_37,
inference(rat,[],[s25,s41]) ).
cnf(s45,plain,
spl20_36,
inference(rat,[],[s24,s41]) ).
cnf(s46,plain,
spl20_29,
inference(rat,[],[s20,s42]) ).
cnf(s48,plain,
~ spl20_17,
inference(rat,[],[s32,s19]) ).
cnf(s49,plain,
( spl20_15
| spl20_16 ),
inference(rat,[],[s11,s48]) ).
cnf(s50,plain,
~ spl20_12,
inference(rat,[],[s39,s10]) ).
cnf(s51,plain,
spl20_11,
inference(rat,[],[s7,s50]) ).
cnf(s52,plain,
spl20_10,
inference(rat,[],[s6,s9]) ).
cnf(s53,plain,
~ spl20_16,
inference(rat,[],[s36,s52]) ).
cnf(s54,plain,
spl20_15,
inference(rat,[],[s49,s53]) ).
cnf(s55,plain,
~ spl20_2,
inference(rat,[],[s38,s44,s45,s46,s52,s51,s54]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s1,s55,s43]) ).
thf(f537,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU782^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n009.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 14:28:30 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 Running higher-order theorem proving
% 0.25/0.30 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
% 0.25/0.35 % (4078020)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.35 % (4078031)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.35 % (4078031)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
% 0.25/0.35 % (4078031)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=2809957388:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.35 % (4078030)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2063508899:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.35 % (4078031) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4078020-4078031"...
% 0.25/0.35 % (4078025)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=707881488:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.35 % (4078029)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3929562731:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.35 % (4078027)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3074908239:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.35 % (4078026)lrs+10_16_si=on:nwc=1.5:random_seed=4151516793:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.35 % (4078028)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=249158883: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)
% 0.25/0.35 % (4078027)Instruction limit reached!
% 0.25/0.35 % (4078027)------------------------------
% 0.25/0.35 % (4078027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (4078027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (4078027)CaDiCaL version: 2.1.3
% 0.25/0.35 % (4078027)Termination reason: Instruction limit
% 0.25/0.35 % (4078027)Termination phase: Saturation
% 0.25/0.35 % (4078027)Time elapsed: 0.003 s
% 0.25/0.35 % (4078027)Peak memory usage: 11 MB
% 0.25/0.35 % (4078027)Instructions burned: 3 (million)
% 0.25/0.35 % (4078031)...printing done.
% 0.25/0.35 % (4078031)Refutation found. Thanks to Tanya!
% 0.25/0.35 % SZS status Theorem for theBenchmark
% 0.25/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.35 % (4078031)------------------------------
% 0.25/0.35 % (4078031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (4078031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (4078031)CaDiCaL version: 2.1.3
% 0.25/0.35 % (4078031)Termination reason: Refutation
% 0.25/0.35 % (4078031)Time elapsed: 0.016 s
% 0.25/0.35 % (4078031)Peak memory usage: 13 MB
% 0.25/0.35 % (4078031)Instructions burned: 30 (million)
% 0.25/0.35 % (4078020)Success in time 0.039 s
% 0.25/0.35 % Vampire exiting
%------------------------------------------------------------------------------