%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU686^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:32:59 AM UTC 2026
% Result : Theorem 9.36s 1.76s
% Output : Refutation 9.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 13
% Syntax : Number of formulae : 249 ( 69 unt; 0 typ; 5 def)
% Number of atoms : 3458 ( 774 equ; 0 cnn)
% Maximal formula atoms : 10 ( 13 avg)
% Number of connectives : 5086 ( 178 ~; 572 |; 99 &;3878 @)
% ( 5 <=>; 203 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 110 ( 105 usr; 18 con; 0-4 aty)
% ( 109 !!; 42 ??; 0 @@+; 0 @@-)
% Number of variables : 891 ( 108 sgn 388 !; 12 ?; 891 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
breln: $i > $i > $i > $o ).
thf(func_def_11,type,
func: $i > $i > $i > $o ).
thf(func_def_12,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_13,type,
app: $o ).
thf(func_def_14,type,
ex1E2: $o ).
thf(func_def_15,type,
funcGraphProp1: $o ).
thf(func_def_16,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_21,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vNOT: $o > $o ).
thf(func_def_34,type,
sK5: $i > $i ).
thf(func_def_35,type,
sK6: $i > $i > $i > $i ).
thf(func_def_36,type,
sK7: $i > $i > $i > $i ).
thf(func_def_37,type,
sK8: $i > $i ).
thf(func_def_38,type,
sK9: $i > $i ).
thf(func_def_39,type,
sK10: $i > $i > $i > $i > $i ).
thf(func_def_40,type,
sK11: $i > $i > $i > $i > $i ).
thf(func_def_42,type,
sK13: $i > $i ).
thf(func_def_43,type,
sK14: $i > $i ).
thf(func_def_44,type,
sK15: $i > $i ).
thf(func_def_45,type,
sK16: $i > $i ).
thf(func_def_46,type,
sK17: $i > $i ).
thf(func_def_47,type,
sK18: $i > $i ).
thf(func_def_48,type,
sK19: $i > $i ).
thf(func_def_49,type,
sK20: $i > $i ).
thf(func_def_50,type,
sK21: $i > $i ).
thf(func_def_51,type,
sK22: $i > $i ).
thf(func_def_52,type,
sK23: $i > $i ).
thf(func_def_53,type,
sK24: $i > $i > $i > $i > $i ).
thf(func_def_54,type,
sK25: $i > $i > $i > $i > $i ).
thf(func_def_55,type,
sK26: $i > $i ).
thf(func_def_56,type,
sK27: $i > $i ).
thf(func_def_57,type,
sK28: $i > $i ).
thf(func_def_58,type,
sK29: $i > $i ).
thf(func_def_59,type,
sK30: $i > $i ).
thf(func_def_60,type,
sK31: $i > $i ).
thf(func_def_61,type,
sK32: $i > $i ).
thf(func_def_62,type,
sK33: $i > $i > $i > $i > $i ).
thf(func_def_63,type,
sK34: $i > $i > $i > $i > $i ).
thf(func_def_64,type,
sK35: $i > $i > $i > $i > $i ).
thf(func_def_65,type,
sK36: $i > $i ).
thf(func_def_66,type,
sK37: $i > $i ).
thf(func_def_67,type,
sK38: $i > $i > $i > $i > $i ).
thf(func_def_68,type,
sK39: $i > $i > $i > $i > $i ).
thf(func_def_69,type,
sK40: $i > $i ).
thf(func_def_70,type,
sK41: $i > $i > $i > $i > $i ).
thf(func_def_71,type,
sK42: $i > $i ).
thf(func_def_72,type,
sK43: $i > $i ).
thf(func_def_73,type,
sK44: $i > $i ).
thf(func_def_74,type,
sK45: $i > $i ).
thf(func_def_75,type,
sK46: $i > $i ).
thf(func_def_76,type,
sK47: $i > $i ).
thf(func_def_77,type,
sK48: $i > $i ).
thf(func_def_78,type,
sK49: $i > $i ).
thf(func_def_79,type,
sK50: $i > $i ).
thf(func_def_80,type,
sK51: $i > $i ).
thf(func_def_81,type,
sK52: $i > $i ).
thf(func_def_82,type,
sK53: $i > $i ).
thf(func_def_83,type,
sK54: $i > $i ).
thf(func_def_84,type,
sK55: $i > $i ).
thf(func_def_85,type,
sK56: $i > $i ).
thf(func_def_86,type,
sK57: $i > $i ).
thf(func_def_87,type,
sK58: $i > $i ).
thf(func_def_88,type,
sK59: $i > $i ).
thf(func_def_89,type,
sK60: $i > $i ).
thf(func_def_90,type,
sK61: $i > $i > $i > $i ).
thf(func_def_91,type,
sK62: $i > $i ).
thf(func_def_92,type,
sK63: $i > $i ).
thf(func_def_93,type,
sK64: $i > $i ).
thf(func_def_94,type,
sK65: $i > $i ).
thf(func_def_95,type,
sK66: $i > $i ).
thf(func_def_96,type,
sK67: $i > $i ).
thf(func_def_97,type,
sK68: $i > $i ).
thf(func_def_98,type,
sK69: $i > $i > $i > $i > $i ).
thf(func_def_99,type,
sK70: $i > $i > $i > $i > $i ).
thf(func_def_100,type,
sK71: $i > $i ).
thf(func_def_101,type,
sK72: $i > $i ).
thf(func_def_102,type,
sK73: $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(f2,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(f3,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(f4,axiom,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func) ).
thf(f5,axiom,
( app
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app) ).
thf(f6,axiom,
( ex1E2
= ( ! [X0: $i,X1: $i > $o] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2) ).
thf(f7,axiom,
( funcGraphProp1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(f8,conjecture,
( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(f9,negated_conjecture,
~ ( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f15,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( app
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f18,plain,
( app
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( ex1E2
= ( ! [X0: $i,X1: $i > $o] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( X1 @ X3 )
=> ( ( X1 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( ex1E2
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ex1 @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
( funcGraphProp1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f22,plain,
( funcGraphProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) ) @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
~ ( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f24,plain,
~ ( ( app = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( func @ X0 @ X1 @ X2 )
= $true ) )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( app = $true ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( func @ X0 @ X1 @ X2 )
= $true ) )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( app = $true ) ),
inference(flattening,[],[f25]) ).
thf(f27,plain,
( ( sK4
!= ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
& ( $true
= ( in @ sK4 @ sK1 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( func @ sK0 @ sK1 @ sK2 ) )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( app = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f26]) ).
thf(f28,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f29,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f30,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f31,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f32,plain,
( app
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f33,plain,
( ex1E2
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ex1 @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f34,plain,
( funcGraphProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) ) @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f35,plain,
app = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f36,plain,
ex1E2 = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f37,plain,
funcGraphProp1 = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f38,plain,
( $true
= ( func @ sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f39,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f40,plain,
( $true
= ( in @ sK4 @ sK1 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f41,plain,
( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f42,plain,
( sK4
!= ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f45,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f29,f28]) ).
thf(f46,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y6 )
& ( ( setadjoin @ Y7 @ emptyset )
= Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f31,f30,f45]) ).
thf(f47,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y2
@ Y1
@ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f32,f35,f46]) ).
thf(f48,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i > $o] :
( ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y4 )
& ( ( setadjoin @ Y5 @ emptyset )
= Y4 ) ) )
@ ( dsetconstr @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f33,f36,f45]) ).
thf(f49,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y2
@ Y1
@ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) ) @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f34,f37,f46]) ).
thf(f50,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y6 )
& ( ( setadjoin @ Y7 @ emptyset )
= Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
@ sK0
@ sK1
@ sK2 ) ),
inference(definition_unfolding,[],[f38,f46]) ).
thf(f51,plain,
( $true
= ( ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( $true
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f54,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) ) )
@ ( sK5 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ( in @ ( sK5 @ X1 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
& ( ( setadjoin @ ( sK5 @ X1 ) @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ( setadjoin @ ( sK5 @ X1 ) @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f58]) ).
thf(f61,plain,
! [X1: $i] :
( ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) )
= ( setadjoin @ ( sK5 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(equality_proxy_clausification,[],[f59]) ).
thf(f62,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y2
@ Y1
@ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) ) @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f63,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( kpair @ Y2 @ ( ap @ Y1 @ Y0 @ X1 @ Y2 ) ) @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( kpair @ Y2 @ ( ap @ Y1 @ Y0 @ X1 @ Y2 ) ) @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y0 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( kpair @ Y1 @ ( ap @ Y0 @ X2 @ X1 @ Y1 ) ) @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y0 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( kpair @ Y1 @ ( ap @ Y0 @ X2 @ X1 @ Y1 ) ) @ X1 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( subset @ X1 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X3 @ X2 @ X1 @ Y0 ) ) @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( subset @ X1 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X3 @ X2 @ X1 @ Y0 ) ) @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X3 @ X2 @ X1 @ Y0 ) ) @ X1 ) ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) )
@ ( sK6 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X3 @ X2 @ X1 @ Y0 ) ) @ X1 ) ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) )
@ ( sK6 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X3 @ X2 @ X1 @ Y0 ) ) @ X1 ) )
@ X4 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( in @ ( sK6 @ X3 @ X1 @ X2 ) @ X3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) ) ) ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in @ ( kpair @ X4 @ ( ap @ X3 @ X2 @ X1 @ X4 ) ) @ X1 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) ) ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in @ ( kpair @ X4 @ ( ap @ X3 @ X2 @ X1 @ X4 ) ) @ X1 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK6 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in @ ( kpair @ X4 @ ( ap @ X3 @ X2 @ X1 @ X4 ) ) @ X1 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f72]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ ( ap @ X3 @ X2 @ X1 @ X4 ) ) @ X1 ) )
| ( $true
= ( in @ ( sK6 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( in @ X4 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) )
@ X5 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in @ ( kpair @ X4 @ ( ap @ X3 @ X2 @ X1 @ X4 ) ) @ X1 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) )
@ X5 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in @ ( kpair @ X4 @ ( ap @ X3 @ X2 @ X1 @ X4 ) ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) )
& ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in @ ( kpair @ X4 @ ( ap @ X3 @ X2 @ X1 @ X4 ) ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in @ ( kpair @ X4 @ ( ap @ X3 @ X2 @ X1 @ X4 ) ) @ X1 ) )
| ( $false
= ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) )
!= ( setadjoin @ X5 @ emptyset ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in @ ( kpair @ X4 @ ( ap @ X3 @ X2 @ X1 @ X4 ) ) @ X1 ) )
| ( $false
= ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i > $o] :
( ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y4 )
& ( ( setadjoin @ Y5 @ emptyset )
= Y4 ) ) )
@ ( dsetconstr @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f82,plain,
! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ Y0 @ X1 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( ( X1 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ Y0 @ X1 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( ( X1 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2 @ X1 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2 @ X1 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2 @ X1 ) ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2 @ X1 ) ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
& ( ( setadjoin @ X3 @ emptyset )
= ( dsetconstr @ X2 @ X1 ) ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ X4 )
=> ( ( X1 @ Y0 )
=> ( X4 = Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( ( setadjoin @ X3 @ emptyset )
= ( dsetconstr @ X2 @ X1 ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ X4 )
=> ( ( X1 @ Y0 )
=> ( X4 = Y0 ) ) ) ) ) ) )
| ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ X4 )
=> ( ( X1 @ Y0 )
=> ( X4 = Y0 ) ) ) ) ) ) )
| ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ X4 )
=> ( ( X1 @ Y0 )
=> ( X4 = Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ X4 )
=> ( ( X1 @ Y0 )
=> ( X4 = Y0 ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( $true
= ( ( in @ X5 @ X2 )
=> ( ( X1 @ X4 )
=> ( ( X1 @ X5 )
=> ( X4 = X5 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( $false
= ( in @ X5 @ X2 ) )
| ( $true
= ( ( X1 @ X4 )
=> ( ( X1 @ X5 )
=> ( X4 = X5 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( $false
= ( in @ X5 @ X2 ) )
| ( ( X1 @ X4 )
= $false )
| ( $true
= ( ( X1 @ X5 )
=> ( X4 = X5 ) ) ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( $false
= ( in @ X5 @ X2 ) )
| ( ( X1 @ X4 )
= $false )
| ( $false
= ( X1 @ X5 ) )
| ( $true
= ( X4 = X5 ) ) ),
inference(imp_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( $false
= ( in @ X5 @ X2 ) )
| ( ( X1 @ X4 )
= $false )
| ( $false
= ( X1 @ X5 ) )
| ( X4 = X5 ) ),
inference(equality_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y2
@ Y1
@ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f99,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( ap @ Y1 @ Y0 @ X1 @ Y2 ) @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( ap @ Y1 @ Y0 @ X1 @ Y2 ) @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y0 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( ap @ Y0 @ X2 @ X1 @ Y1 ) @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y0 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( ap @ Y0 @ X2 @ X1 @ Y1 ) @ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( subset @ X1 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( ap @ X3 @ X2 @ X1 @ Y0 ) @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( subset @ X1 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( ap @ X3 @ X2 @ X1 @ Y0 ) @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( ap @ X3 @ X2 @ X1 @ Y0 ) @ X2 ) ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) )
@ ( sK7 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( ap @ X3 @ X2 @ X1 @ Y0 ) @ X2 ) ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) )
@ ( sK7 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( ap @ X3 @ X2 @ X1 @ Y0 ) @ X2 ) )
@ X4 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( in @ ( sK7 @ X3 @ X1 @ X2 ) @ X3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) ) ) ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in @ ( ap @ X3 @ X2 @ X1 @ X4 ) @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) ) ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in @ ( ap @ X3 @ X2 @ X1 @ X4 ) @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK7 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in @ ( ap @ X3 @ X2 @ X1 @ X4 ) @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f111,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( ap @ X3 @ X2 @ X1 @ X4 ) @ X2 ) )
| ( $true
= ( in @ ( sK7 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( in @ X4 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) )
@ X5 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in @ ( ap @ X3 @ X2 @ X1 @ X4 ) @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f109]) ).
thf(f113,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) )
@ X5 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in @ ( ap @ X3 @ X2 @ X1 @ X4 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) )
& ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in @ ( ap @ X3 @ X2 @ X1 @ X4 ) @ X2 ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in @ ( ap @ X3 @ X2 @ X1 @ X4 ) @ X2 ) )
| ( $false
= ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( setadjoin @ X5 @ emptyset )
!= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in @ ( ap @ X3 @ X2 @ X1 @ X4 ) @ X2 ) )
| ( $false
= ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK7 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f115]) ).
thf(f124,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( sK5 @ X1 ) @ emptyset )
= ( setadjoin @ ( sK5 @ X0 ) @ emptyset ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(constrained_superposition,[],[f61,f61]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ ( sK5 @ X0 ) @ emptyset ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $false
= ( in @ X1 @ ( setadjoin @ ( sK5 @ X0 ) @ emptyset ) ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 )
@ X3 ) )
| ( X2 = X3 )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f97,f61]) ).
thf(f126,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ ( setadjoin @ ( sK5 @ X0 ) @ emptyset ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(constrained_superposition,[],[f60,f61]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ ( sK5 @ X0 ) @ emptyset ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $false
= ( in @ X1 @ ( setadjoin @ ( sK5 @ X0 ) @ emptyset ) ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X2 ) @ sK2 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X3 ) @ sK2 ) )
| ( X2 = X3 )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( setadjoin @ X3 @ emptyset )
!= ( setadjoin @ ( sK5 @ ( sK7 @ X0 @ X1 @ X2 ) ) @ emptyset ) )
| ( $false
= ( in @ X5 @ X4 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X4 @ sK1 ) ) )
| ( $true
= ( in @ ( ap @ X4 @ sK1 @ sK2 @ X5 ) @ sK1 ) )
| ( $false
= ( in @ X3 @ ( setadjoin @ ( sK5 @ ( sK7 @ X0 @ X1 @ X2 ) ) @ emptyset ) ) )
| ( $false
= ( in @ ( sK7 @ X0 @ X1 @ X2 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : sK2 )
!= ( ^ [Y0: $i] : X1 ) )
| ( ( ^ [Y0: $i] : X2 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X4 ) ) ),
inference(constrained_superposition,[],[f116,f61]) ).
thf(f142,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ ( setadjoin @ ( sK5 @ X0 ) @ emptyset ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X2 @ sK0 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X2 ) )
| ( $false
= ( in @ X2 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(constrained_superposition,[],[f126,f124]) ).
thf(f143,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ ( setadjoin @ ( sK5 @ X0 ) @ emptyset ) ) )
| ( $false
= ( in @ X2 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X2 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(duplicate_literal_removal,[],[f142]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( setadjoin @ ( sK5 @ ( sK6 @ X0 @ X1 @ X2 ) ) @ emptyset )
!= ( setadjoin @ X4 @ emptyset ) )
| ( $false
= ( in @ X5 @ X3 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X3 @ sK1 ) ) )
| ( $true
= ( in @ ( kpair @ X5 @ ( ap @ X3 @ sK1 @ sK2 @ X5 ) ) @ sK2 ) )
| ( $false
= ( in @ X4 @ ( setadjoin @ ( sK5 @ ( sK6 @ X0 @ X1 @ X2 ) ) @ emptyset ) ) )
| ( $false
= ( in @ ( sK6 @ X0 @ X1 @ X2 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : sK2 )
!= ( ^ [Y0: $i] : X1 ) )
| ( ( ^ [Y0: $i] : X2 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X3 ) ) ),
inference(constrained_superposition,[],[f80,f61]) ).
thf(f152,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK5 @ X1 ) @ ( setadjoin @ ( sK5 @ X1 ) @ emptyset ) ) )
| ( $false
= ( in @ ( kpair @ X1 @ X2 ) @ sK2 ) )
| ( $false
= ( in @ ( kpair @ X1 @ X0 ) @ sK2 ) )
| ( X0 = X2 )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(equality_resolution,[],[f127]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] : sK2 )
!= ( ^ [Y0: $i] : X3 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( $true
= ( in @ ( ap @ X1 @ sK1 @ sK2 @ X0 ) @ sK1 ) )
| ( $false
= ( in @ ( sK5 @ ( sK7 @ X2 @ X3 @ X4 ) ) @ ( setadjoin @ ( sK5 @ ( sK7 @ X2 @ X3 @ X4 ) ) @ emptyset ) ) )
| ( $false
= ( in @ ( sK7 @ X2 @ X3 @ X4 ) @ sK0 ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( ( ^ [Y0: $i] : sK1 )
!= ( ^ [Y0: $i] : X4 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(equality_resolution,[],[f140]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] : sK2 )
!= ( ^ [Y0: $i] : X3 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( $true
= ( in @ ( kpair @ X0 @ ( ap @ X1 @ sK1 @ sK2 @ X0 ) ) @ sK2 ) )
| ( $false
= ( in @ ( sK5 @ ( sK6 @ X2 @ X3 @ X4 ) ) @ ( setadjoin @ ( sK5 @ ( sK6 @ X2 @ X3 @ X4 ) ) @ emptyset ) ) )
| ( $false
= ( in @ ( sK6 @ X2 @ X3 @ X4 ) @ sK0 ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( ( ^ [Y0: $i] : sK1 )
!= ( ^ [Y0: $i] : X4 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(equality_resolution,[],[f145]) ).
thf(f359,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X0 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sK2 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X2 ) @ sK2 ) )
| ( X1 = X2 )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f126,f152]) ).
thf(f368,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X0 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sK2 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X2 ) @ sK2 ) )
| ( X1 = X2 )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X2 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f359]) ).
thf(f369,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ X0 @ X2 ) @ sK2 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sK2 ) )
| ( X1 = X2 )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f368]) ).
thf(f428,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK6 @ X1 @ sK2 @ X2 ) @ X1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X3 ) @ sK2 ) )
| ( ( ap @ X1 @ X2 @ sK2 @ X0 )
= X3 )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ ( ap @ X1 @ X2 @ sK2 @ X0 ) @ sK1 ) )
| ( $false
= ( in @ X3 @ sK1 ) ) ),
inference(constrained_superposition,[],[f75,f369]) ).
thf(f429,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( sK4 = X0 )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( in @ sK4 @ sK1 )
= $false )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f41,f369]) ).
thf(f434,plain,
! [X0: $i] :
( ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( sK4 = X0 )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( in @ sK4 @ sK1 )
= $false )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f429]) ).
thf(f435,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( ap @ X1 @ X2 @ sK2 @ X0 ) @ sK1 ) )
| ( $true
= ( in @ ( sK6 @ X1 @ sK2 @ X2 ) @ X1 ) )
| ( ( ap @ X1 @ X2 @ sK2 @ X0 )
= X3 )
| ( $false
= ( in @ ( kpair @ X0 @ X3 ) @ sK2 ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( in @ X3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f428]) ).
thf(f444,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( sK4 = X0 )
| ( ( in @ sK4 @ sK1 )
= $false )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f434,f39]) ).
thf(f445,plain,
! [X0: $i] :
( ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( sK4 = X0 )
| ( ( in @ sK4 @ sK1 )
= $false )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f444]) ).
thf(f452,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( sK4 = X0 )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f445,f40]) ).
thf(f453,plain,
! [X0: $i] :
( ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( sK4 = X0 )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f452]) ).
thf(f462,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK6 @ X0 @ sK2 @ X1 ) @ X0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( sK4
= ( ap @ X0 @ X1 @ sK2 @ sK3 ) )
| ( $false
= ( in @ ( ap @ X0 @ X1 @ sK2 @ sK3 ) @ sK1 ) ) ),
inference(constrained_superposition,[],[f75,f453]) ).
thf(f463,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( ap @ X0 @ X1 @ sK2 @ sK3 ) @ sK1 ) )
| ( $true
= ( in @ ( sK6 @ X0 @ sK2 @ X1 ) @ X0 ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( sK4
= ( ap @ X0 @ X1 @ sK2 @ sK3 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f462]) ).
thf(f467,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X3 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( $true
= ( in @ ( ap @ X0 @ sK1 @ sK2 @ X1 ) @ sK1 ) )
| ( $false
= ( in @ ( sK5 @ ( sK7 @ X2 @ sK2 @ X3 ) ) @ ( setadjoin @ ( sK5 @ ( sK7 @ X2 @ sK2 @ X3 ) ) @ emptyset ) ) )
| ( $false
= ( in @ ( sK7 @ X2 @ sK2 @ X3 ) @ sK0 ) )
| ( ( in @ X1 @ X0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(equality_resolution,[],[f159]) ).
thf(f470,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X3 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( $true
= ( in @ ( kpair @ X1 @ ( ap @ X0 @ sK1 @ sK2 @ X1 ) ) @ sK2 ) )
| ( $false
= ( in @ ( sK5 @ ( sK6 @ X2 @ sK2 @ X3 ) ) @ ( setadjoin @ ( sK5 @ ( sK6 @ X2 @ sK2 @ X3 ) ) @ emptyset ) ) )
| ( $false
= ( in @ ( sK6 @ X2 @ sK2 @ X3 ) @ sK0 ) )
| ( ( in @ X1 @ X0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(equality_resolution,[],[f166]) ).
thf(f600,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $true
= ( in @ ( sK6 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( sK4
= ( ap @ X0 @ sK1 @ sK2 @ sK3 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f111,f463]) ).
thf(f601,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $true
= ( in @ ( sK6 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( sK4
= ( ap @ X0 @ sK1 @ sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f600]) ).
thf(f602,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $true
= ( in @ ( sK6 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( sK4
= ( ap @ X0 @ sK1 @ sK2 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f601]) ).
thf(f691,definition,
( spl12_1
<=> ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f692,plain,
( ( $true
!= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| spl12_1 ),
inference(avatar_component_clause,[],[f691]) ).
thf(f693,plain,
( ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f691]) ).
thf(f959,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK5 @ X0 ) @ ( setadjoin @ ( sK5 @ X1 ) @ emptyset ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : ( sK6 @ sK0 @ sK2 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : ( sK6 @ sK0 @ sK2 @ sK1 ) ) ) )
| ~ spl12_1 ),
inference(constrained_superposition,[],[f143,f693]) ).
thf(f974,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : ( sK6 @ sK0 @ sK2 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : ( sK6 @ sK0 @ sK2 @ sK1 ) ) )
| ( $true
= ( in @ ( sK5 @ X0 ) @ ( setadjoin @ ( sK5 @ X1 ) @ emptyset ) ) ) )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f959]) ).
thf(f1083,definition,
( spl12_9
<=> ( $false
= ( in @ ( sK7 @ sK0 @ sK2 @ sK1 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
thf(f1084,plain,
( ( $false
!= ( in @ ( sK7 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| spl12_9 ),
inference(avatar_component_clause,[],[f1083]) ).
thf(f1085,plain,
( ( $false
= ( in @ ( sK7 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f1083]) ).
thf(f1119,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X1
@ ( sK17 @ X1 ) )
!= ( ^ [Y0: $i] : ( sK6 @ sK0 @ sK2 @ sK1 )
@ ( sK17 @ X1 ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : ( sK6 @ sK0 @ sK2 @ sK1 ) ) )
| ( $true
= ( in @ ( sK5 @ X0 ) @ ( setadjoin @ ( sK5 @ X1 ) @ emptyset ) ) ) )
| ~ spl12_1 ),
inference(negative_extensionality,[],[f974]) ).
thf(f1121,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : ( sK6 @ sK0 @ sK2 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( ( sK6 @ sK0 @ sK2 @ sK1 )
!= X1 )
| ( $true
= ( in @ ( sK5 @ X0 ) @ ( setadjoin @ ( sK5 @ X1 ) @ emptyset ) ) ) )
| ~ spl12_1 ),
inference(beta-eta_normalization,[],[f1119]) ).
thf(f1122,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X0
@ ( sK18 @ X0 ) )
!= ( ^ [Y0: $i] : ( sK6 @ sK0 @ sK2 @ sK1 )
@ ( sK18 @ X0 ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( ( sK6 @ sK0 @ sK2 @ sK1 )
!= X1 )
| ( $true
= ( in @ ( sK5 @ X0 ) @ ( setadjoin @ ( sK5 @ X1 ) @ emptyset ) ) ) )
| ~ spl12_1 ),
inference(negative_extensionality,[],[f1121]) ).
thf(f1124,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK6 @ sK0 @ sK2 @ sK1 )
!= X1 )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( ( sK6 @ sK0 @ sK2 @ sK1 )
!= X0 )
| ( $true
= ( in @ ( sK5 @ X0 ) @ ( setadjoin @ ( sK5 @ X1 ) @ emptyset ) ) ) )
| ~ spl12_1 ),
inference(beta-eta_normalization,[],[f1122]) ).
thf(f1125,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( sK6 @ sK0 @ sK2 @ sK1 )
!= X0 )
| ( $true
= ( in @ ( sK5 @ X0 ) @ ( setadjoin @ ( sK5 @ ( sK6 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) ) )
| ~ spl12_1 ),
inference(equality_resolution,[],[f1124]) ).
thf(f1126,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( sK6 @ sK0 @ sK2 @ sK1 )
!= X0 )
| ( $true
= ( in @ ( sK5 @ X0 ) @ ( setadjoin @ ( sK5 @ ( sK6 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) ) )
| ~ spl12_1 ),
inference(forward_demodulation,[],[f1125,f693]) ).
thf(f1127,plain,
( ! [X0: $i] :
( ( ( sK6 @ sK0 @ sK2 @ sK1 )
!= X0 )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
= ( in @ ( sK5 @ X0 ) @ ( setadjoin @ ( sK5 @ ( sK6 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) ) )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f1126]) ).
thf(f1128,plain,
( ( $false
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $true
= ( in @ ( sK5 @ ( sK6 @ sK0 @ sK2 @ sK1 ) ) @ ( setadjoin @ ( sK5 @ ( sK6 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) )
| ~ spl12_1 ),
inference(equality_resolution,[],[f1127]) ).
thf(f1129,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK5 @ ( sK6 @ sK0 @ sK2 @ sK1 ) ) @ ( setadjoin @ ( sK5 @ ( sK6 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) )
| ~ spl12_1 ),
inference(forward_demodulation,[],[f1128,f693]) ).
thf(f1130,plain,
( ( $true
= ( in @ ( sK5 @ ( sK6 @ sK0 @ sK2 @ sK1 ) ) @ ( setadjoin @ ( sK5 @ ( sK6 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f1129]) ).
thf(f1175,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK5 @ ( sK7 @ X2 @ sK2 @ sK1 ) ) @ ( setadjoin @ ( sK5 @ ( sK7 @ X2 @ sK2 @ sK1 ) ) @ emptyset ) ) )
| ( $true
= ( in @ ( ap @ X0 @ sK1 @ sK2 @ X1 ) @ sK1 ) )
| ( $false
= ( in @ ( sK7 @ X2 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( in @ X1 @ X0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(equality_resolution,[],[f467]) ).
thf(f1193,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK5 @ ( sK6 @ X2 @ sK2 @ sK1 ) ) @ ( setadjoin @ ( sK5 @ ( sK6 @ X2 @ sK2 @ sK1 ) ) @ emptyset ) ) )
| ( $true
= ( in @ ( kpair @ X0 @ ( ap @ X1 @ sK1 @ sK2 @ X0 ) ) @ sK2 ) )
| ( $false
= ( in @ ( sK6 @ X2 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(equality_resolution,[],[f470]) ).
thf(f1369,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( sK4
= ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) )
| ~ spl12_9 ),
inference(constrained_superposition,[],[f1085,f602]) ).
thf(f1515,definition,
( spl12_14
<=> ( $false
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
thf(f1516,plain,
( ( $false
!= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| spl12_14 ),
inference(avatar_component_clause,[],[f1515]) ).
thf(f1517,plain,
( ( $false
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f1515]) ).
thf(f2360,plain,
( ( $true = $false )
| ~ spl12_1
| ~ spl12_14 ),
inference(constrained_superposition,[],[f1517,f693]) ).
thf(f2366,plain,
( $false
| ~ spl12_1
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f2360]) ).
thf(f2367,plain,
( ~ spl12_1
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f2366]) ).
thf(f2443,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : ( sK7 @ X0 @ sK2 @ sK1 ) )
!= ( ^ [Y0: $i] : ( sK7 @ X0 @ sK2 @ sK1 ) ) )
| ( $true
= ( in @ ( ap @ X1 @ sK1 @ sK2 @ X2 ) @ sK1 ) )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ X2 @ X1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(constrained_superposition,[],[f126,f1175]) ).
thf(f2450,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : ( sK7 @ X0 @ sK2 @ sK1 ) )
!= ( ^ [Y0: $i] : ( sK7 @ X0 @ sK2 @ sK1 ) ) )
| ( $true
= ( in @ ( ap @ X1 @ sK1 @ sK2 @ X2 ) @ sK1 ) )
| ( $false
= ( in @ X2 @ X1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(duplicate_literal_removal,[],[f2443]) ).
thf(f2451,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( ap @ X1 @ sK1 @ sK2 @ X2 ) @ sK1 ) )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ X2 @ X1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(trivial_inequality_removal,[],[f2450]) ).
thf(f2961,plain,
! [X0: $i] :
( ( sK4 != X0 )
| ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f42,f435]) ).
thf(f2978,plain,
! [X0: $i] :
( ( sK4 != X0 )
| ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f2961]) ).
thf(f2998,plain,
! [X0: $i] :
( ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(forward_subsumption_resolution,[],[f2978,f453]) ).
thf(f3256,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( kpair @ X0 @ ( ap @ X1 @ sK1 @ sK2 @ X0 ) ) @ sK2 ) )
| ( $false
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_1 ),
inference(constrained_superposition,[],[f1130,f1193]) ).
thf(f3271,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X0 @ ( ap @ X1 @ sK1 @ sK2 @ X0 ) ) @ sK2 ) )
| ( $false
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f3256]) ).
thf(f3319,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK0 ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( $true
= ( in @ ( kpair @ X0 @ ( ap @ X1 @ sK1 @ sK2 @ X0 ) ) @ sK2 ) ) )
| ~ spl12_1
| spl12_14 ),
inference(forward_subsumption_resolution,[],[f3271,f1516]) ).
thf(f3322,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $true
= ( in @ ( kpair @ X0 @ ( ap @ sK0 @ sK1 @ sK2 @ X0 ) ) @ sK2 ) ) )
| ~ spl12_1
| spl12_14 ),
inference(equality_resolution,[],[f3319]) ).
thf(f3324,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
= ( in @ ( kpair @ X0 @ ( ap @ sK0 @ sK1 @ sK2 @ X0 ) ) @ sK2 ) ) )
| ~ spl12_1
| spl12_14 ),
inference(forward_demodulation,[],[f3322,f53]) ).
thf(f3325,plain,
( ! [X0: $i] :
( ( $true
= ( in @ ( kpair @ X0 @ ( ap @ sK0 @ sK1 @ sK2 @ X0 ) ) @ sK2 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) )
| ~ spl12_1
| spl12_14 ),
inference(trivial_inequality_removal,[],[f3324]) ).
thf(f3338,plain,
( ( $true = $false )
| ( sK4
= ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) )
| ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl12_1
| spl12_14 ),
inference(constrained_superposition,[],[f453,f3325]) ).
thf(f3357,plain,
( ( sK4
= ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) )
| ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl12_1
| spl12_14 ),
inference(trivial_inequality_removal,[],[f3338]) ).
thf(f3373,plain,
( ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl12_1
| spl12_14 ),
inference(forward_subsumption_resolution,[],[f3357,f42]) ).
thf(f3375,plain,
( ( $true = $false )
| ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ~ spl12_1
| spl12_14 ),
inference(forward_demodulation,[],[f3373,f39]) ).
thf(f3376,plain,
( ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ~ spl12_1
| spl12_14 ),
inference(trivial_inequality_removal,[],[f3375]) ).
thf(f3693,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK7 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl12_1
| spl12_14 ),
inference(constrained_superposition,[],[f111,f3376]) ).
thf(f3694,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_1
| spl12_14 ),
inference(constrained_superposition,[],[f2451,f3376]) ).
thf(f3695,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_1
| spl12_14 ),
inference(trivial_inequality_removal,[],[f3694]) ).
thf(f3696,plain,
( ( $true
= ( in @ ( sK7 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl12_1
| spl12_14 ),
inference(trivial_inequality_removal,[],[f3693]) ).
thf(f3703,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_1
| spl12_14 ),
inference(forward_demodulation,[],[f3695,f39]) ).
thf(f3704,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_1
| spl12_14 ),
inference(trivial_inequality_removal,[],[f3703]) ).
thf(f3705,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl12_1
| ~ spl12_9
| spl12_14 ),
inference(forward_demodulation,[],[f3696,f1085]) ).
thf(f3706,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl12_1
| ~ spl12_9
| spl12_14 ),
inference(trivial_inequality_removal,[],[f3705]) ).
thf(f3711,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_1
| spl12_14 ),
inference(forward_demodulation,[],[f3704,f53]) ).
thf(f3712,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) ) )
| ~ spl12_1
| spl12_14 ),
inference(trivial_inequality_removal,[],[f3711]) ).
thf(f3713,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ~ spl12_1
| ~ spl12_9
| spl12_14 ),
inference(forward_demodulation,[],[f3706,f39]) ).
thf(f3714,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ~ spl12_1
| ~ spl12_9
| spl12_14 ),
inference(trivial_inequality_removal,[],[f3713]) ).
thf(f3719,plain,
( ( $true = $false )
| ~ spl12_1
| ~ spl12_9
| spl12_14 ),
inference(constrained_superposition,[],[f3714,f53]) ).
thf(f3725,plain,
( $false
| ~ spl12_1
| ~ spl12_9
| spl12_14 ),
inference(trivial_inequality_removal,[],[f3719]) ).
thf(f3726,plain,
( ~ spl12_1
| ~ spl12_9
| spl12_14 ),
inference(avatar_contradiction_clause,[],[f3725]) ).
thf(f4883,plain,
( ( $false
= ( in @ ( sK7 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl12_1
| spl12_14 ),
inference(equality_resolution,[],[f3712]) ).
thf(f4885,plain,
( $false
| ~ spl12_1
| spl12_9
| spl12_14 ),
inference(forward_subsumption_resolution,[],[f4883,f1084]) ).
thf(f4886,plain,
( ~ spl12_1
| spl12_9
| spl12_14 ),
inference(avatar_contradiction_clause,[],[f4885]) ).
thf(f4924,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f2998,f39]) ).
thf(f4925,plain,
! [X0: $i] :
( ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f4924]) ).
thf(f5203,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f4925,f53]) ).
thf(f5204,plain,
! [X0: $i] :
( ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f5203]) ).
thf(f5458,definition,
( spl12_48
<=> ! [X0: $i] :
( ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_48])],[avatar_definition]) ).
thf(f5459,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( kpair @ sK3 @ X0 ) @ sK2 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl12_48 ),
inference(avatar_component_clause,[],[f5458]) ).
thf(f5465,definition,
( spl12_50
<=> ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_50])],[avatar_definition]) ).
thf(f5467,plain,
( ( $false
= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
| ~ spl12_50 ),
inference(avatar_component_clause,[],[f5465]) ).
thf(f5525,plain,
( spl12_48
| spl12_1
| spl12_50 ),
inference(avatar_split_clause,[],[f5204,f5465,f691,f5458]) ).
thf(f5676,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_50 ),
inference(constrained_superposition,[],[f2451,f5467]) ).
thf(f5677,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_50 ),
inference(trivial_inequality_removal,[],[f5676]) ).
thf(f5685,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_50 ),
inference(forward_demodulation,[],[f5677,f39]) ).
thf(f5686,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_50 ),
inference(trivial_inequality_removal,[],[f5685]) ).
thf(f5695,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl12_50 ),
inference(forward_demodulation,[],[f5686,f53]) ).
thf(f5696,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) )
| ( $false
= ( in @ ( sK7 @ X0 @ sK2 @ sK1 ) @ sK0 ) ) )
| ~ spl12_50 ),
inference(trivial_inequality_removal,[],[f5695]) ).
thf(f5974,plain,
( ( $false
= ( in @ ( sK7 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl12_50 ),
inference(equality_resolution,[],[f5696]) ).
thf(f5976,plain,
( $false
| spl12_9
| ~ spl12_50 ),
inference(forward_subsumption_resolution,[],[f5974,f1084]) ).
thf(f5977,plain,
( spl12_9
| ~ spl12_50 ),
inference(avatar_contradiction_clause,[],[f5976]) ).
thf(f5984,plain,
( ( $true = $false )
| ( ( in @ sK4 @ sK1 )
= $false )
| ~ spl12_48 ),
inference(constrained_superposition,[],[f41,f5459]) ).
thf(f5985,plain,
( ( ( in @ sK4 @ sK1 )
= $false )
| ~ spl12_48 ),
inference(trivial_inequality_removal,[],[f5984]) ).
thf(f5992,plain,
( ( $true = $false )
| ~ spl12_48 ),
inference(constrained_superposition,[],[f5985,f40]) ).
thf(f5998,plain,
( $false
| ~ spl12_48 ),
inference(trivial_inequality_removal,[],[f5992]) ).
thf(f5999,plain,
~ spl12_48,
inference(avatar_contradiction_clause,[],[f5998]) ).
thf(f6000,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $true
= ( in @ ( sK6 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( sK4
= ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) )
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f1369]) ).
thf(f6028,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( sK4
= ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) )
| spl12_1
| ~ spl12_9 ),
inference(forward_subsumption_resolution,[],[f6000,f692]) ).
thf(f6062,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| spl12_1
| ~ spl12_9 ),
inference(forward_subsumption_resolution,[],[f6028,f42]) ).
thf(f6090,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| spl12_1
| ~ spl12_9 ),
inference(forward_demodulation,[],[f6062,f39]) ).
thf(f6091,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| spl12_1
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f6090]) ).
thf(f6159,plain,
( ( $true = $false )
| spl12_1
| ~ spl12_9 ),
inference(constrained_superposition,[],[f6091,f53]) ).
thf(f6165,plain,
( $false
| spl12_1
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f6159]) ).
thf(f6166,plain,
( spl12_1
| ~ spl12_9 ),
inference(avatar_contradiction_clause,[],[f6165]) ).
cnf(s25,plain,
( ~ spl12_1
| ~ spl12_14 ),
inference(sat_conversion,[],[f2367]) ).
cnf(s27,plain,
( ~ spl12_1
| ~ spl12_9
| spl12_14 ),
inference(sat_conversion,[],[f3726]) ).
cnf(s71,plain,
( ~ spl12_1
| spl12_9
| spl12_14 ),
inference(sat_conversion,[],[f4886]) ).
cnf(s159,plain,
( spl12_1
| spl12_48
| spl12_50 ),
inference(sat_conversion,[],[f5525]) ).
cnf(s322,plain,
( spl12_9
| ~ spl12_50 ),
inference(sat_conversion,[],[f5977]) ).
cnf(s324,plain,
~ spl12_48,
inference(sat_conversion,[],[f5999]) ).
cnf(s342,plain,
( spl12_1
| ~ spl12_9 ),
inference(sat_conversion,[],[f6166]) ).
cnf(s345,plain,
( spl12_1
| spl12_50 ),
inference(rat,[],[s159,s324]) ).
cnf(s347,plain,
spl12_1,
inference(rat,[],[s322,s345,s342]) ).
cnf(s348,plain,
~ spl12_14,
inference(rat,[],[s25,s347]) ).
cnf(s351,plain,
spl12_9,
inference(rat,[],[s71,s347,s348]) ).
cnf(s359,plain,
$false,
inference(rat,[],[s27,s347,s348,s351]) ).
thf(f6167,plain,
$false,
inference(avatar_sat_refutation,[],[s359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU686^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.18 % Computer : n008.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 14:09:39 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.22 Running first-order model finding
% 0.12/0.22 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
% 6.36/1.38 % (3215551)Will run a generic schedule for satisfiability detection.
% 6.36/1.38 % (3215558)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1177037447:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.36/1.38 % (3215557)% WARNING: option uhcvi not known.
% 6.36/1.38 % (3215557)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3075664303:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.36/1.38 % (3215556)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1161826111_2999 on theBenchmark for (2999ds/0Mi)
% 6.36/1.38 % (3215560)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2856339392:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.36/1.38 % (3215557)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.36/1.38 % (3215560)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.36/1.38 % (3215557)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.36/1.38 % Exception at run slice level
% 6.36/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.38 % (3215561)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2758743042:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.36/1.38 % (3215559)dis+10_1_sil=32000:sp=arity:random_seed=983367223:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.36/1.38 % (3215562)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3337427568:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.36/1.38 % (3215567)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2033708239:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.36/1.38 % Exception at run slice level
% 6.36/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.38 % (3215572)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2008196668:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.36/1.38 % (3215561)Instruction limit reached!
% 6.36/1.38 % (3215561)------------------------------
% 6.36/1.38 % (3215561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.38 % (3215561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.38 % (3215561)CaDiCaL version: 2.1.3
% 6.36/1.38 % (3215561)Termination reason: Instruction limit
% 6.36/1.38 % (3215561)Termination phase: Saturation
% 6.36/1.38 % (3215561)Time elapsed: 0.065 s
% 6.36/1.38 % (3215561)Peak memory usage: 12 MB
% 6.36/1.38 % (3215561)Instructions burned: 131 (million)
% 6.36/1.38 % (3215574)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2624444959:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.36/1.38 % (3215574)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.36/1.38 % (3215559)Instruction limit reached!
% 6.36/1.38 % (3215559)------------------------------
% 6.36/1.38 % (3215559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.38 % (3215559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.38 % (3215559)CaDiCaL version: 2.1.3
% 6.36/1.38 % (3215559)Termination reason: Instruction limit
% 6.36/1.38 % (3215559)Termination phase: Saturation
% 6.36/1.38 % (3215559)Time elapsed: 0.087 s
% 6.36/1.38 % (3215559)Peak memory usage: 12 MB
% 6.36/1.38 % (3215559)Instructions burned: 103 (million)
% 6.36/1.38 % (3215574)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.36/1.38 % (3215560)Instruction limit reached!
% 6.36/1.38 % (3215560)------------------------------
% 6.36/1.38 % (3215560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.38 % (3215560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.38 % (3215560)CaDiCaL version: 2.1.3
% 6.36/1.38 % (3215560)Termination reason: Instruction limit
% 6.36/1.38 % (3215560)Termination phase: Saturation
% 6.36/1.38 % (3215560)Time elapsed: 0.107 s
% 6.36/1.38 % (3215560)Peak memory usage: 12 MB
% 6.36/1.38 % (3215560)Instructions burned: 116 (million)
% 6.36/1.38 % (3215572)Instruction limit reached!
% 6.36/1.38 % (3215572)------------------------------
% 6.36/1.38 % (3215572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.36/1.76 % (3215572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.36/1.76 % (3215572)CaDiCaL version: 2.1.3
% 9.36/1.76 % (3215572)Termination reason: Instruction limit
% 9.36/1.76 % (3215572)Termination phase: Saturation
% 9.36/1.76 % (3215572)Time elapsed: 0.066 s
% 9.36/1.76 % (3215572)Peak memory usage: 13 MB
% 9.36/1.76 % (3215572)Instructions burned: 133 (million)
% 9.36/1.76 % (3215576)ott-21_1_sil=16000:fs=off:random_seed=2396340479:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 9.36/1.76 % (3215578)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=520868748:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 9.36/1.76 % Exception at run slice level
% 9.36/1.76 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.36/1.76 % (3215577)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2660466637:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 9.36/1.76 % (3215562)Instruction limit reached!
% 9.36/1.76 % (3215562)------------------------------
% 9.36/1.76 % (3215562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.36/1.76 % (3215562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.36/1.76 % (3215562)CaDiCaL version: 2.1.3
% 9.36/1.76 % (3215562)Termination reason: Instruction limit
% 9.36/1.76 % (3215562)Termination phase: Saturation
% 9.36/1.76 % (3215562)Time elapsed: 0.128 s
% 9.36/1.76 % (3215562)Peak memory usage: 12 MB
% 9.36/1.76 % (3215562)Instructions burned: 159 (million)
% 9.36/1.76 % (3215583)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1923980989:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 9.36/1.76 % Exception at run slice level
% 9.36/1.76 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.36/1.76 % (3215581)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=639967842:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 9.36/1.76 % (3215585)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2868661350:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 9.36/1.76 % (3215585)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.36/1.76 % (3215576)Instruction limit reached!
% 9.36/1.76 % (3215576)------------------------------
% 9.36/1.76 % (3215576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.36/1.76 % (3215576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.36/1.76 % (3215576)CaDiCaL version: 2.1.3
% 9.36/1.76 % (3215576)Termination reason: Instruction limit
% 9.36/1.76 % (3215576)Termination phase: Saturation
% 9.36/1.76 % (3215576)Time elapsed: 0.148 s
% 9.36/1.76 % (3215576)Peak memory usage: 13 MB
% 9.36/1.76 % (3215576)Instructions burned: 180 (million)
% 9.36/1.76 % (3215588)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=569458974:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 9.36/1.76 % (3215588)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.36/1.76 % (3215574)Instruction limit reached!
% 9.36/1.76 % (3215574)------------------------------
% 9.36/1.76 % (3215574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.36/1.76 % (3215574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.36/1.76 % (3215574)CaDiCaL version: 2.1.3
% 9.36/1.76 % (3215574)Termination reason: Instruction limit
% 9.36/1.76 % (3215574)Termination phase: Saturation
% 9.36/1.76 % (3215574)Time elapsed: 0.416 s
% 9.36/1.76 % (3215574)Peak memory usage: 14 MB
% 9.36/1.76 % (3215574)Instructions burned: 686 (million)
% 9.36/1.76 % (3215591)fmb+10_1_sil=64000:random_seed=3905837074:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 9.36/1.76 % (3215591)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 9.36/1.76 % Exception at run slice level
% 9.36/1.76 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.36/1.76 % (3215593)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=105931760:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 9.36/1.76 % Exception at run slice level
% 9.36/1.76 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.36/1.76 % (3215577)Instruction limit reached!
% 9.36/1.76 % (3215577)------------------------------
% 9.36/1.76 % (3215577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.36/1.76 % (3215577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.36/1.76 % (3215577)CaDiCaL version: 2.1.3
% 9.36/1.76 % (3215577)Termination reason: Instruction limit
% 9.36/1.76 % (3215577)Termination phase: Saturation
% 9.36/1.76 % (3215577)Time elapsed: 0.431 s
% 9.36/1.76 % (3215577)Peak memory usage: 12 MB
% 9.36/1.76 % (3215577)Instructions burned: 478 (million)
% 9.36/1.76 % (3215595)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=4278086606:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 9.36/1.76 % Exception at run slice level
% 9.36/1.76 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.36/1.76 % (3215596)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3433149145:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 9.36/1.76 % (3215596)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.36/1.76 % (3215598)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3438407212:i=1472:ins=7:fdi=8:gsp=on_2993 on theBenchmark for (2993ds/1472Mi)
% 9.36/1.76 % (3215598)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 9.36/1.76 % (3215598)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 9.36/1.76 % (3215585)Instruction limit reached!
% 9.36/1.76 % (3215585)------------------------------
% 9.36/1.76 % (3215585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.36/1.76 % (3215585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.36/1.76 % (3215585)CaDiCaL version: 2.1.3
% 9.36/1.76 % (3215585)Termination reason: Instruction limit
% 9.36/1.76 % (3215585)Termination phase: Saturation
% 9.36/1.76 % (3215585)Time elapsed: 0.490 s
% 9.36/1.76 % (3215585)Peak memory usage: 14 MB
% 9.36/1.76 % (3215585)Instructions burned: 693 (million)
% 9.36/1.76 % (3215601)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=44590289:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 9.36/1.76 % Exception at run slice level
% 9.36/1.76 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.36/1.76 % (3215603)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2766858648:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 9.36/1.76 % Exception at run slice level
% 9.36/1.76 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.36/1.76 % (3215605)ott-2_1_sil=16000:newcnf=on:random_seed=1548722140:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 9.36/1.76 % (3215605)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.36/1.76 % (3215581)Instruction limit reached!
% 9.36/1.76 % (3215581)------------------------------
% 9.36/1.76 % (3215581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.36/1.76 % (3215581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.36/1.76 % (3215581)CaDiCaL version: 2.1.3
% 9.36/1.76 % (3215581)Termination reason: Instruction limit
% 9.36/1.76 % (3215581)Termination phase: Saturation
% 9.36/1.76 % (3215581)Time elapsed: 0.868 s
% 9.36/1.76 % (3215581)Peak memory usage: 14 MB
% 9.36/1.76 % (3215581)Instructions burned: 1179 (million)
% 9.36/1.76 % (3215588)Instruction limit reached!
% 9.36/1.76 % (3215588)------------------------------
% 9.36/1.76 % (3215588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.36/1.76 % (3215588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.36/1.76 % (3215588)CaDiCaL version: 2.1.3
% 9.36/1.76 % (3215588)Termination reason: Instruction limit
% 9.36/1.76 % (3215588)Termination phase: Saturation
% 9.36/1.76 % (3215588)Time elapsed: 0.749 s
% 9.36/1.76 % (3215588)Peak memory usage: 14 MB
% 9.36/1.76 % (3215588)Instructions burned: 879 (million)
% 9.36/1.76 % (3215607)ott+10_1_sil=32000:tgt=ground:random_seed=2649604651:i=5114:av=off_2989 on theBenchmark for (2989ds/5114Mi)
% 9.36/1.76 % (3215608)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1538879583:i=54282_2988 on theBenchmark for (2988ds/54282Mi)
% 9.36/1.76 % Exception at run slice level
% 9.36/1.76 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.36/1.76 % (3215611)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=4218388559:i=3512:aac=none_2988 on theBenchmark for (2988ds/3512Mi)
% 9.36/1.76 % (3215611)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 9.36/1.76 % (3215605)Instruction limit reached!
% 9.36/1.76 % (3215605)------------------------------
% 9.36/1.76 % (3215605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.36/1.76 % (3215605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.36/1.76 % (3215605)CaDiCaL version: 2.1.3
% 9.36/1.76 % (3215605)Termination reason: Instruction limit
% 9.36/1.76 % (3215605)Termination phase: Saturation
% 9.36/1.76 % (3215605)Time elapsed: 0.499 s
% 9.36/1.76 % (3215605)Peak memory usage: 14 MB
% 9.36/1.76 % (3215605)Instructions burned: 869 (million)
% 9.36/1.76 % (3215613)dis+21_1_sil=32000:sas=cadical:random_seed=2030578325:i=3773:amm=off_2986 on theBenchmark for (2986ds/3773Mi)
% 9.36/1.76 % (3215557) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3215551-3215557"...
% 9.36/1.76 % (3215557)...printing done.
% 9.36/1.76 % (3215557)Refutation found. Thanks to Tanya!
% 9.36/1.76 % SZS status Theorem for theBenchmark
% 9.36/1.76 % SZS output start Proof for theBenchmark
% See solution above
% 9.36/1.77 % (3215557)------------------------------
% 9.36/1.77 % (3215557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.36/1.77 % (3215557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.36/1.77 % (3215557)CaDiCaL version: 2.1.3
% 9.36/1.77 % (3215557)Termination reason: Refutation
% 9.36/1.77 % (3215557)Time elapsed: 1.500 s
% 9.36/1.77 % (3215557)Peak memory usage: 15 MB
% 9.36/1.77 % (3215557)Instructions burned: 3157 (million)
% 9.36/1.77 % (3215551)Success in time 1.537 s
% 9.36/1.77 % Vampire exiting
%------------------------------------------------------------------------------