%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU674^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:32:56 AM UTC 2026
% Result : Theorem 17.66s 2.92s
% Output : Refutation 17.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 10
% Syntax : Number of formulae : 122 ( 51 unt; 0 typ; 3 def)
% Number of atoms : 1279 ( 260 equ; 0 cnn)
% Maximal formula atoms : 7 ( 10 avg)
% Number of connectives : 2133 ( 63 ~; 146 |; 51 &;1741 @)
% ( 3 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 129 ( 124 usr; 13 con; 0-4 aty)
% ( 42 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 458 ( 41 sgn 138 !; 6 ?; 458 :)
% 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,
setunion: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
kpair: $i > $i > $i ).
thf(func_def_7,type,
cartprod: $i > $i > $i ).
thf(func_def_8,type,
singleton: $i > $o ).
thf(func_def_10,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_11,type,
breln: $i > $i > $i > $o ).
thf(func_def_12,type,
func: $i > $i > $i > $o ).
thf(func_def_13,type,
apProp: $o ).
thf(func_def_14,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_15,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vNOT: $o > $o ).
thf(func_def_33,type,
sK4: $i > $i ).
thf(func_def_34,type,
sK5: $i > $i > $i > $i ).
thf(func_def_35,type,
sK6: $i > $i ).
thf(func_def_36,type,
sK7: $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 ).
thf(func_def_40,type,
sK11: $i > $i ).
thf(func_def_41,type,
sK12: $i > $i ).
thf(func_def_42,type,
sK13: $i > $i ).
thf(func_def_43,type,
sK14: $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 ).
thf(func_def_54,type,
sK25: $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 ).
thf(func_def_63,type,
sK34: $i > $i ).
thf(func_def_64,type,
sK35: $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 ).
thf(func_def_68,type,
sK39: $i > $i ).
thf(func_def_69,type,
sK40: $i > $i ).
thf(func_def_70,type,
sK41: $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 > $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 ).
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 ).
thf(func_def_99,type,
sK70: $i > $i ).
thf(func_def_100,type,
sK71: $i > $i > $i > $i ).
thf(func_def_101,type,
sK72: $i > $i ).
thf(func_def_102,type,
sK73: $i > $i ).
thf(func_def_103,type,
sK74: $i > $i ).
thf(func_def_104,type,
sK75: $i > $i > $i > $i ).
thf(func_def_105,type,
sK76: $i > $i ).
thf(func_def_106,type,
sK77: $i > $i ).
thf(func_def_107,type,
sK78: $i > $i ).
thf(func_def_108,type,
sK79: $i > $i > $i > $i ).
thf(func_def_109,type,
sK80: $i > $i ).
thf(func_def_110,type,
sK81: $i > $i > $i > $i ).
thf(func_def_111,type,
sK82: $i > $i > $i > $i ).
thf(func_def_112,type,
sK83: $i > $i > $i > $i ).
thf(func_def_113,type,
sK84: $i > $i ).
thf(func_def_114,type,
sK85: $i > $i ).
thf(func_def_115,type,
sK86: $i > $i ).
thf(func_def_116,type,
sK87: $i > $i ).
thf(func_def_117,type,
sK88: $i > $i ).
thf(func_def_118,type,
sK89: $i > $i ).
thf(func_def_119,type,
sK90: $i > $i ).
thf(func_def_120,type,
sK91: $i > $i ).
thf(func_def_121,type,
sK92: $i > $i ).
thf(func_def_122,type,
sK93: $i > $i ).
thf(func_def_123,type,
sK94: $i > $i ).
thf(f1,axiom,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(f2,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(f3,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(f4,axiom,
( 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/sandbox/benchmark/theBenchmark.p',func) ).
thf(f5,axiom,
( apProp
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
@ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(f6,axiom,
( ap
= ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap) ).
thf(f7,conjecture,
( apProp
=> ! [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/sandbox/benchmark/theBenchmark.p',app) ).
thf(f8,negated_conjecture,
~ ( apProp
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f14,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(f15,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,[],[f14]) ).
thf(f16,plain,
( apProp
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
@ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( apProp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 ) ) )
@ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( ap
= ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f19,plain,
( ap
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
~ ( apProp
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f21,plain,
~ ( ( apProp = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( func @ X0 @ X1 @ X2 )
= $true ) )
& ( apProp = $true ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f23,plain,
( ( $true
!= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( func @ sK0 @ sK1 @ sK2 ) )
& ( apProp = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f22]) ).
thf(f24,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f25,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f26,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f27,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,[],[f15]) ).
thf(f28,plain,
( apProp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 ) ) )
@ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f29,plain,
( ap
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f30,plain,
apProp = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f31,plain,
( $true
= ( func @ sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f32,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f33,plain,
( $true
!= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f36,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,[],[f25,f24]) ).
thf(f37,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,[],[f27,f26,f36]) ).
thf(f38,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
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 ) ) )
@ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f28,f30,f37]) ).
thf(f39,plain,
( $true
!= ( in
@ ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) )
@ sK0
@ sK1
@ sK2
@ sK3 )
@ sK1 ) ),
inference(definition_unfolding,[],[f33,f29]) ).
thf(f40,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,[],[f31,f37]) ).
thf(f41,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,[],[f40]) ).
thf(f42,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,[],[f41]) ).
thf(f43,plain,
( $true
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f44,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,[],[f42]) ).
thf(f45,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,[],[f44]) ).
thf(f46,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,[],[f45]) ).
thf(f47,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 ) ) ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ( in @ ( sK4 @ X1 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
& ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X1: $i] :
( ( $true
= ( in @ ( sK4 @ X1 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f48]) ).
thf(f51,plain,
! [X1: $i] :
( ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) )
= ( setadjoin @ ( sK4 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(equality_proxy_clausification,[],[f49]) ).
thf(f52,plain,
( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK2 ) ) )
@ sK1 ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f53,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
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 ) ) )
@ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f54,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
@ ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y2 @ Y3 ) @ X1 ) ) )
@ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,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
@ ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y2 @ Y3 ) @ X1 ) ) )
@ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f56,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
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ X1 ) ) )
@ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,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
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ X1 ) ) )
@ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,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
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,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
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f60,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
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f59]) ).
thf(f61,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 ) ) ) ) ) )
@ ( sK5 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f60]) ).
thf(f62,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 ) ) ) ) ) )
@ ( sK5 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) )
@ X4 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) ) ) ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) ) ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) ),
inference(imp_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) )
@ X5 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f64]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) )
@ X5 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) ),
inference(imp_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) )
& ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) )
| ( $false
= ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) )
!= ( setadjoin @ X5 @ emptyset ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) )
| ( $false
= ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f70]) ).
thf(f87,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( setadjoin @ ( sK4 @ X0 ) @ emptyset ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(constrained_superposition,[],[f51,f51]) ).
thf(f88,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X1 ) @ ( setadjoin @ ( sK4 @ X0 ) @ emptyset ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(constrained_superposition,[],[f50,f51]) ).
thf(f98,plain,
! [X0: $i,X1: $i] :
( ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) )
= ( setadjoin @ ( sK4 @ X0 ) @ emptyset ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(constrained_superposition,[],[f51,f87]) ).
thf(f101,plain,
! [X0: $i,X1: $i] :
( ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) )
= ( setadjoin @ ( sK4 @ X0 ) @ emptyset ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(duplicate_literal_removal,[],[f98]) ).
thf(f131,plain,
! [X0: $i,X1: $i] :
( ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(constrained_superposition,[],[f51,f101]) ).
thf(f132,plain,
! [X0: $i,X1: $i] :
( ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(duplicate_literal_removal,[],[f131]) ).
thf(f338,plain,
! [X0: $i] :
( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(constrained_superposition,[],[f52,f132]) ).
thf(f343,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(forward_demodulation,[],[f338,f32]) ).
thf(f344,plain,
! [X0: $i] :
( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(trivial_inequality_removal,[],[f343]) ).
thf(f628,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK3 ) )
| ( $true
= ( in @ ( sK5 @ X2 @ sK2 @ sK1 ) @ X2 ) )
| ( $false
= ( in @ X1 @ X2 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X2 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(constrained_superposition,[],[f344,f66]) ).
thf(f667,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK3 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
= ( in @ ( sK5 @ X2 @ sK2 @ sK1 ) @ X2 ) )
| ( $false
= ( in @ X1 @ X2 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X2 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X1 ) ) ),
inference(trivial_inequality_removal,[],[f628]) ).
thf(f739,plain,
! [X0: $i,X1: $i] :
( ( ( in @ sK3 @ sK0 )
= $false )
| ( $true
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( ( in @ X1 @ X0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(equality_resolution,[],[f667]) ).
thf(f741,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( ( in @ X1 @ X0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK3 ) ) ),
inference(forward_demodulation,[],[f739,f32]) ).
thf(f742,plain,
! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK3 ) )
| ( ( in @ X1 @ X0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $true
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f741]) ).
thf(f744,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( in @ sK3 @ X0 ) ) ),
inference(equality_resolution,[],[f742]) ).
thf(f989,definition,
( spl15_2
<=> ( $false
= ( in @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
thf(f990,plain,
( ( $false
!= ( in @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| spl15_2 ),
inference(avatar_component_clause,[],[f989]) ).
thf(f991,plain,
( ( $false
= ( in @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f989]) ).
thf(f997,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl15_2 ),
inference(constrained_superposition,[],[f744,f991]) ).
thf(f998,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl15_2 ),
inference(trivial_inequality_removal,[],[f997]) ).
thf(f1003,plain,
( ( $true = $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl15_2 ),
inference(forward_demodulation,[],[f998,f43]) ).
thf(f1004,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl15_2 ),
inference(trivial_inequality_removal,[],[f1003]) ).
thf(f1011,plain,
( ( $true = $false )
| ~ spl15_2 ),
inference(constrained_superposition,[],[f1004,f32]) ).
thf(f1017,plain,
( $false
| ~ spl15_2 ),
inference(trivial_inequality_removal,[],[f1011]) ).
thf(f1018,plain,
~ spl15_2,
inference(avatar_contradiction_clause,[],[f1017]) ).
thf(f1020,plain,
( ( ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ Y0 ) @ sK2 ) ) )
| spl15_2 ),
inference(unit_resulting_resolution,[],[f51,f990]) ).
thf(f1201,plain,
( ! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) ) )
| spl15_2 ),
inference(constrained_superposition,[],[f71,f1020]) ).
thf(f1211,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) ) )
| spl15_2 ),
inference(forward_demodulation,[],[f1201,f43]) ).
thf(f1212,plain,
( ! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) ) )
| spl15_2 ),
inference(trivial_inequality_removal,[],[f1211]) ).
thf(f3749,definition,
( spl15_5
<=> ! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
@ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
thf(f3750,plain,
( ! [X1: $i] :
( ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( in @ X1 @ sK0 ) ) )
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f3749]) ).
thf(f3752,definition,
( spl15_6
<=> ! [X0: $i] :
( ( ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
thf(f3753,plain,
( ! [X0: $i] :
( ( ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) ) )
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f3752]) ).
thf(f3754,plain,
( spl15_5
| spl15_6
| spl15_2 ),
inference(avatar_split_clause,[],[f1212,f989,f3752,f3749]) ).
thf(f3770,plain,
( ( $true != $true )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl15_5 ),
inference(constrained_superposition,[],[f52,f3750]) ).
thf(f3791,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl15_5 ),
inference(trivial_inequality_removal,[],[f3770]) ).
thf(f3824,plain,
( ( $false
= ( in @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ ( setadjoin @ ( sK4 @ ( sK5 @ sK0 @ sK2 @ sK1 ) ) @ emptyset ) ) )
| ~ spl15_6 ),
inference(equality_resolution,[],[f3753]) ).
thf(f3850,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : ( sK5 @ sK0 @ sK2 @ sK1 ) )
!= ( ^ [Y0: $i] : ( sK5 @ sK0 @ sK2 @ sK1 ) ) )
| ~ spl15_6 ),
inference(constrained_superposition,[],[f3824,f88]) ).
thf(f3871,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : ( sK5 @ sK0 @ sK2 @ sK1 ) )
!= ( ^ [Y0: $i] : ( sK5 @ sK0 @ sK2 @ sK1 ) ) )
| ~ spl15_6 ),
inference(duplicate_literal_removal,[],[f3850]) ).
thf(f3872,plain,
( ( $false
= ( in @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl15_6 ),
inference(trivial_inequality_removal,[],[f3871]) ).
thf(f3884,plain,
( $false
| spl15_2
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f3872,f990]) ).
thf(f3885,plain,
( spl15_2
| ~ spl15_6 ),
inference(avatar_contradiction_clause,[],[f3884]) ).
thf(f3924,plain,
( ( $true = $false )
| ~ spl15_5 ),
inference(constrained_superposition,[],[f3791,f32]) ).
thf(f3930,plain,
( $false
| ~ spl15_5 ),
inference(trivial_inequality_removal,[],[f3924]) ).
thf(f3931,plain,
~ spl15_5,
inference(avatar_contradiction_clause,[],[f3930]) ).
cnf(s3,plain,
~ spl15_2,
inference(sat_conversion,[],[f1018]) ).
cnf(s5,plain,
( spl15_2
| spl15_5
| spl15_6 ),
inference(sat_conversion,[],[f3754]) ).
cnf(s10,plain,
( spl15_2
| ~ spl15_6 ),
inference(sat_conversion,[],[f3885]) ).
cnf(s12,plain,
~ spl15_5,
inference(sat_conversion,[],[f3931]) ).
cnf(s13,plain,
( spl15_2
| spl15_6 ),
inference(rat,[],[s5,s12]) ).
cnf(s14,plain,
~ spl15_6,
inference(rat,[],[s10,s3]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s13,s14,s3]) ).
thf(f3932,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU674^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:09:52 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.78/0.95 % (1344224)Will run a generic schedule for satisfiability detection.
% 3.78/0.95 % (1344229)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1682465965_2999 on theBenchmark for (2999ds/0Mi)
% 3.78/0.95 % Exception at run slice level
% 3.78/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.78/0.95 % (1344230)% WARNING: option uhcvi not known.
% 3.78/0.95 % (1344232)dis+10_1_sil=32000:sp=arity:random_seed=2708557090:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.78/0.95 % (1344230)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3945045635:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.78/0.95 % (1344233)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4073648224:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.78/0.95 % (1344230)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.78/0.95 % (1344233)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.78/0.95 % (1344230)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.78/0.95 % (1344234)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4168996900:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.78/0.95 % (1344231)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=466271257:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.78/0.95 % (1344235)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2998803726:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.78/0.95 % (1344237)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2480123125:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.78/0.95 % Exception at run slice level
% 3.78/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.78/0.95 % (1344234)Instruction limit reached!
% 3.78/0.95 % (1344234)------------------------------
% 3.78/0.95 % (1344234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.78/0.95 % (1344234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/0.95 % (1344234)CaDiCaL version: 2.1.3
% 3.78/0.95 % (1344234)Termination reason: Instruction limit
% 3.78/0.95 % (1344234)Termination phase: Saturation
% 3.78/0.95 % (1344234)Time elapsed: 0.034 s
% 3.78/0.95 % (1344234)Peak memory usage: 12 MB
% 3.78/0.95 % (1344234)Instructions burned: 135 (million)
% 3.78/0.95 % (1344246)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=1500478323:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.78/0.95 % (1344246)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.78/0.95 % (1344246)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.78/0.95 % (1344233)Instruction limit reached!
% 3.78/0.95 % (1344233)------------------------------
% 3.78/0.95 % (1344233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.78/0.95 % (1344233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/0.95 % (1344233)CaDiCaL version: 2.1.3
% 3.78/0.95 % (1344233)Termination reason: Instruction limit
% 3.78/0.95 % (1344233)Termination phase: Saturation
% 3.78/0.95 % (1344233)Time elapsed: 0.055 s
% 3.78/0.95 % (1344233)Peak memory usage: 12 MB
% 3.78/0.95 % (1344233)Instructions burned: 116 (million)
% 3.78/0.95 % (1344232)Instruction limit reached!
% 3.78/0.95 % (1344232)------------------------------
% 3.78/0.95 % (1344232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.78/0.95 % (1344232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/0.95 % (1344232)CaDiCaL version: 2.1.3
% 3.78/0.95 % (1344232)Termination reason: Instruction limit
% 3.78/0.95 % (1344232)Termination phase: Saturation
% 3.78/0.95 % (1344232)Time elapsed: 0.060 s
% 3.78/0.95 % (1344232)Peak memory usage: 12 MB
% 3.78/0.95 % (1344232)Instructions burned: 104 (million)
% 3.78/0.95 % (1344245)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2148073698:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.78/0.95 % (1344248)ott-21_1_sil=16000:fs=off:random_seed=2258987774:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.78/0.95 % (1344249)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3364081638:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 15.75/2.52 % (1344235)Instruction limit reached!
% 15.75/2.52 % (1344235)------------------------------
% 15.75/2.52 % (1344235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.75/2.52 % (1344235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.75/2.52 % (1344235)CaDiCaL version: 2.1.3
% 15.75/2.52 % (1344235)Termination reason: Instruction limit
% 15.75/2.52 % (1344235)Termination phase: Saturation
% 15.75/2.52 % (1344235)Time elapsed: 0.107 s
% 15.75/2.52 % (1344235)Peak memory usage: 12 MB
% 15.75/2.52 % (1344235)Instructions burned: 161 (million)
% 15.75/2.52 % (1344253)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=476093310:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 15.75/2.52 % Exception at run slice level
% 15.75/2.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 15.75/2.52 % (1344255)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=608334695:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 15.75/2.52 % (1344245)Instruction limit reached!
% 15.75/2.52 % (1344245)------------------------------
% 15.75/2.52 % (1344245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.75/2.52 % (1344245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.75/2.52 % (1344245)CaDiCaL version: 2.1.3
% 15.75/2.52 % (1344245)Termination reason: Instruction limit
% 15.75/2.52 % (1344245)Termination phase: Saturation
% 15.75/2.52 % (1344245)Time elapsed: 0.099 s
% 15.75/2.52 % (1344245)Peak memory usage: 12 MB
% 15.75/2.52 % (1344245)Instructions burned: 132 (million)
% 15.75/2.52 % (1344257)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=811719835:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 15.75/2.52 % Exception at run slice level
% 15.75/2.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 15.75/2.52 % (1344246)Instruction limit reached!
% 15.75/2.52 % (1344246)------------------------------
% 15.75/2.52 % (1344246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.75/2.52 % (1344246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.75/2.52 % (1344246)CaDiCaL version: 2.1.3
% 15.75/2.52 % (1344246)Termination reason: Instruction limit
% 15.75/2.52 % (1344246)Termination phase: Saturation
% 15.75/2.52 % (1344246)Time elapsed: 0.159 s
% 15.75/2.52 % (1344246)Peak memory usage: 14 MB
% 15.75/2.52 % (1344246)Instructions burned: 687 (million)
% 15.75/2.52 % (1344260)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2758585240:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 15.75/2.52 % (1344260)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 15.75/2.52 % (1344259)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=727119425:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 15.75/2.52 % (1344259)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 15.75/2.52 % (1344248)Instruction limit reached!
% 15.75/2.52 % (1344248)------------------------------
% 15.75/2.52 % (1344248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.75/2.52 % (1344248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.75/2.52 % (1344248)CaDiCaL version: 2.1.3
% 15.75/2.52 % (1344248)Termination reason: Instruction limit
% 15.75/2.52 % (1344248)Termination phase: Saturation
% 15.75/2.52 % (1344248)Time elapsed: 0.149 s
% 15.75/2.52 % (1344248)Peak memory usage: 12 MB
% 15.75/2.52 % (1344248)Instructions burned: 181 (million)
% 15.75/2.52 % (1344263)fmb+10_1_sil=64000:random_seed=1602288285:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 15.75/2.52 % (1344263)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 15.75/2.52 % Exception at run slice level
% 15.75/2.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 15.75/2.52 % (1344265)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=273626590:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 15.75/2.52 % Exception at run slice level
% 15.75/2.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/2.92 % (1344249)Instruction limit reached!
% 17.66/2.92 % (1344249)------------------------------
% 17.66/2.92 % (1344249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344249)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344249)Termination reason: Instruction limit
% 17.66/2.92 % (1344249)Termination phase: Saturation
% 17.66/2.92 % (1344249)Time elapsed: 0.243 s
% 17.66/2.92 % (1344249)Peak memory usage: 12 MB
% 17.66/2.92 % (1344249)Instructions burned: 478 (million)
% 17.66/2.92 % (1344267)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=946677789:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 17.66/2.92 % Exception at run slice level
% 17.66/2.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/2.92 % (1344268)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1576060450:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 17.66/2.92 % (1344268)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.66/2.92 % (1344270)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2948347916:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 17.66/2.92 % (1344270)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 17.66/2.92 % (1344270)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.66/2.92 % (1344260)Instruction limit reached!
% 17.66/2.92 % (1344260)------------------------------
% 17.66/2.92 % (1344260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344260)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344260)Termination reason: Instruction limit
% 17.66/2.92 % (1344260)Termination phase: Saturation
% 17.66/2.92 % (1344260)Time elapsed: 0.223 s
% 17.66/2.92 % (1344260)Peak memory usage: 14 MB
% 17.66/2.92 % (1344260)Instructions burned: 883 (million)
% 17.66/2.92 % (1344273)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=4029350717:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 17.66/2.92 % Exception at run slice level
% 17.66/2.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/2.92 % (1344275)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=684467250:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 17.66/2.92 % Exception at run slice level
% 17.66/2.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/2.92 % (1344277)ott-2_1_sil=16000:newcnf=on:random_seed=2592319511:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 17.66/2.92 % (1344277)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.66/2.92 % (1344259)Instruction limit reached!
% 17.66/2.92 % (1344259)------------------------------
% 17.66/2.92 % (1344259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344259)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344259)Termination reason: Instruction limit
% 17.66/2.92 % (1344259)Termination phase: Saturation
% 17.66/2.92 % (1344259)Time elapsed: 0.430 s
% 17.66/2.92 % (1344259)Peak memory usage: 14 MB
% 17.66/2.92 % (1344259)Instructions burned: 693 (million)
% 17.66/2.92 % (1344277)Instruction limit reached!
% 17.66/2.92 % (1344277)------------------------------
% 17.66/2.92 % (1344277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344277)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344277)Termination reason: Instruction limit
% 17.66/2.92 % (1344277)Termination phase: Saturation
% 17.66/2.92 % (1344277)Time elapsed: 0.207 s
% 17.66/2.92 % (1344277)Peak memory usage: 15 MB
% 17.66/2.92 % (1344277)Instructions burned: 872 (million)
% 17.66/2.92 % (1344279)ott+10_1_sil=32000:tgt=ground:random_seed=3193726576:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 17.66/2.92 % (1344280)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=909323246:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 17.66/2.92 % Exception at run slice level
% 17.66/2.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/2.92 % (1344255)Instruction limit reached!
% 17.66/2.92 % (1344255)------------------------------
% 17.66/2.92 % (1344255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344255)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344255)Termination reason: Instruction limit
% 17.66/2.92 % (1344255)Termination phase: Saturation
% 17.66/2.92 % (1344255)Time elapsed: 0.533 s
% 17.66/2.92 % (1344255)Peak memory usage: 14 MB
% 17.66/2.92 % (1344255)Instructions burned: 1179 (million)
% 17.66/2.92 % (1344283)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1002433630:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 17.66/2.92 % (1344283)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.66/2.92 % (1344284)dis+21_1_sil=32000:sas=cadical:random_seed=715910489:i=3773:amm=off_2992 on theBenchmark for (2992ds/3773Mi)
% 17.66/2.92 % (1344270)Instruction limit reached!
% 17.66/2.92 % (1344270)------------------------------
% 17.66/2.92 % (1344270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344270)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344270)Termination reason: Instruction limit
% 17.66/2.92 % (1344270)Termination phase: Saturation
% 17.66/2.92 % (1344270)Time elapsed: 0.806 s
% 17.66/2.92 % (1344270)Peak memory usage: 16 MB
% 17.66/2.92 % (1344270)Instructions burned: 1473 (million)
% 17.66/2.92 % (1344288)ott+11_1_sil=16000:gs=on:random_seed=129252981:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 17.66/2.92 % (1344288)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.66/2.92 % (1344283)Instruction limit reached!
% 17.66/2.92 % (1344283)------------------------------
% 17.66/2.92 % (1344283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344283)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344283)Termination reason: Instruction limit
% 17.66/2.92 % (1344283)Termination phase: Saturation
% 17.66/2.92 % (1344283)Time elapsed: 0.748 s
% 17.66/2.92 % (1344283)Peak memory usage: 16 MB
% 17.66/2.92 % (1344283)Instructions burned: 3513 (million)
% 17.66/2.92 % (1344290)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=4124441803:fmbsr=1.6:i=67534_2985 on theBenchmark for (2985ds/67534Mi)
% 17.66/2.92 % Exception at run slice level
% 17.66/2.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/2.92 % (1344292)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=3397763475:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2984 on theBenchmark for (2984ds/4591Mi)
% 17.66/2.92 % (1344288)Instruction limit reached!
% 17.66/2.92 % (1344288)------------------------------
% 17.66/2.92 % (1344288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344288)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344288)Termination reason: Instruction limit
% 17.66/2.92 % (1344288)Termination phase: Saturation
% 17.66/2.92 % (1344288)Time elapsed: 0.943 s
% 17.66/2.92 % (1344288)Peak memory usage: 15 MB
% 17.66/2.92 % (1344288)Instructions burned: 2253 (million)
% 17.66/2.92 % (1344294)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=3266452450:i=29340_2978 on theBenchmark for (2978ds/29340Mi)
% 17.66/2.92 % (1344284)Instruction limit reached!
% 17.66/2.92 % (1344284)------------------------------
% 17.66/2.92 % (1344284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344284)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344284)Termination reason: Instruction limit
% 17.66/2.92 % (1344284)Termination phase: Saturation
% 17.66/2.92 % (1344284)Time elapsed: 1.534 s
% 17.66/2.92 % (1344284)Peak memory usage: 17 MB
% 17.66/2.92 % (1344284)Instructions burned: 3774 (million)
% 17.66/2.92 % (1344296)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=3661281666:i=5211_2977 on theBenchmark for (2977ds/5211Mi)
% 17.66/2.92 % (1344292)Instruction limit reached!
% 17.66/2.92 % (1344292)------------------------------
% 17.66/2.92 % (1344292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344292)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344292)Termination reason: Instruction limit
% 17.66/2.92 % (1344292)Termination phase: Saturation
% 17.66/2.92 % (1344292)Time elapsed: 1.020 s
% 17.66/2.92 % (1344292)Peak memory usage: 17 MB
% 17.66/2.92 % (1344292)Instructions burned: 4595 (million)
% 17.66/2.92 % (1344298)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=1622769238:i=5497:nm=2_2974 on theBenchmark for (2974ds/5497Mi)
% 17.66/2.92 % Exception at run slice level
% 17.66/2.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/2.92 % (1344300)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=2237213690:fmbsr=2:i=46332_2974 on theBenchmark for (2974ds/46332Mi)
% 17.66/2.92 % Exception at run slice level
% 17.66/2.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/2.92 % (1344302)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=371382658:i=14071_2974 on theBenchmark for (2974ds/14071Mi)
% 17.66/2.92 % Exception at run slice level
% 17.66/2.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/2.92 % (1344304)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2486631888:i=22565:add=on:rawr=on_2974 on theBenchmark for (2974ds/22565Mi)
% 17.66/2.92 % (1344294) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1344224-1344294"...
% 17.66/2.92 % (1344294)...printing done.
% 17.66/2.92 % (1344294)Refutation found. Thanks to Tanya!
% 17.66/2.92 % SZS status Theorem for theBenchmark
% 17.66/2.92 % SZS output start Proof for theBenchmark
% See solution above
% 17.66/2.92 % (1344294)------------------------------
% 17.66/2.92 % (1344294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/2.92 % (1344294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/2.92 % (1344294)CaDiCaL version: 2.1.3
% 17.66/2.92 % (1344294)Termination reason: Refutation
% 17.66/2.92 % (1344294)Time elapsed: 0.488 s
% 17.66/2.92 % (1344294)Peak memory usage: 14 MB
% 17.66/2.92 % (1344294)Instructions burned: 1106 (million)
% 17.66/2.92 % (1344224)Success in time 2.706 s
% 17.66/2.92 % Vampire exiting
%------------------------------------------------------------------------------