%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU822^2 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:34:12 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 423 ( 61 equ; 0 cnn)
% Maximal formula atoms : 3 ( 12 avg)
% Number of connectives : 830 ( 23 ~; 32 |; 59 &; 536 @)
% ( 0 <=>; 110 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 83 usr; 6 con; 0-4 aty)
% ( 63 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 119 ( 91 ^; 25 !; 3 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
nonempty: $i > $o ).
thf(func_def_3,type,
transitiveset: $i > $o ).
thf(func_def_4,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_6,type,
wellorderedByIn: $i > $o ).
thf(func_def_7,type,
ordinal: $i > $o ).
thf(func_def_8,type,
ordinalIrrefl: $o ).
thf(func_def_9,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vIMP: $o > $o > $o ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vOR: $o > $o > $o ).
thf(func_def_18,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(func_def_20,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
sK1: $i > $i ).
thf(func_def_25,type,
sK2: $i > $i ).
thf(func_def_26,type,
sK3: $i > $i ).
thf(func_def_27,type,
sK4: $i > $i ).
thf(func_def_28,type,
sK5: $i > $i ).
thf(func_def_29,type,
sK6: $i > $i ).
thf(func_def_30,type,
sK7: $i > $i ).
thf(func_def_31,type,
sK8: $i > $i ).
thf(func_def_32,type,
sK9: $i > $i ).
thf(func_def_33,type,
sK10: $i > $i ).
thf(func_def_34,type,
sK11: $i > $i ).
thf(func_def_35,type,
sK12: $i > $i ).
thf(func_def_36,type,
sK13: $i > $i ).
thf(func_def_37,type,
sK14: $i > $i ).
thf(func_def_38,type,
sK15: $i > $i ).
thf(func_def_39,type,
sK16: $i > $i ).
thf(func_def_40,type,
sK17: $i > $i ).
thf(func_def_41,type,
sK18: $i > $i ).
thf(func_def_42,type,
sK19: $i > $i ).
thf(func_def_43,type,
sK20: $i > $i ).
thf(func_def_44,type,
sK21: $i > $i ).
thf(func_def_45,type,
sK22: $i > $i ).
thf(func_def_46,type,
sK23: $i > $i ).
thf(func_def_47,type,
sK24: $i > $i ).
thf(func_def_48,type,
sK25: $i > $i ).
thf(func_def_49,type,
sK26: $i > $i ).
thf(func_def_50,type,
sK27: $i > $i ).
thf(func_def_51,type,
sK28: $i > $i ).
thf(func_def_52,type,
sK29: $i > $i ).
thf(func_def_53,type,
sK30: $i > $i ).
thf(func_def_54,type,
sK31: $i > $i ).
thf(func_def_55,type,
sK32: $i > $i ).
thf(func_def_56,type,
sK33: $i > $i ).
thf(func_def_57,type,
sK34: $i > $i ).
thf(func_def_58,type,
sK35: $i > $i ).
thf(func_def_59,type,
sK36: $i > $i ).
thf(func_def_60,type,
sK37: $i > $i ).
thf(func_def_61,type,
sK38: $i > $i > $i ).
thf(func_def_62,type,
sK39: $i > $i ).
thf(func_def_63,type,
sK40: $i > $i > $i ).
thf(func_def_64,type,
sK41: $i > $i ).
thf(func_def_65,type,
sK42: $i > $i ).
thf(func_def_66,type,
sK43: $i > $i > $i ).
thf(func_def_67,type,
sK44: $i > $i ).
thf(func_def_68,type,
sK45: $i > $i > $i ).
thf(func_def_69,type,
sK46: $i > $i ).
thf(func_def_70,type,
sK47: $i > $i ).
thf(func_def_71,type,
sK48: $i > $i ).
thf(func_def_72,type,
sK49: $i > $i ).
thf(func_def_73,type,
sK50: $i > $i > $i ).
thf(func_def_74,type,
sK51: $i > $i ).
thf(func_def_75,type,
sK52: $i > $i > $i ).
thf(func_def_76,type,
sK53: $i > $i ).
thf(func_def_77,type,
sK54: $i > $i ).
thf(func_def_78,type,
sK55: $i > $i > $i ).
thf(func_def_79,type,
sK56: $i > $i ).
thf(func_def_80,type,
sK57: $i > $i > $i ).
thf(func_def_81,type,
sK58: $i > $i ).
thf(func_def_82,type,
sK59: $i > $i ).
thf(func_def_83,type,
sK60: $i > $i ).
thf(func_def_84,type,
sK61: $i > $i ).
thf(f1,axiom,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ X2 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
| ( in @ X2 @ X3 )
| ( X2 = X3 ) ) ) )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ( in @ X2 @ X3 )
& ( in @ X1 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(f2,axiom,
( wellorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 ) ) )
& ( in @ X2 @ X1 ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(f3,axiom,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal) ).
thf(f5,conjecture,
( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ~ ( in @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalIrrefl2) ).
thf(f6,negated_conjecture,
~ ( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ~ ( in @ X0 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
| ( in @ X2 @ X3 )
| ( X2 = X3 ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( ( in @ X5 @ X6 )
& ( in @ X4 @ X5 ) )
=> ( in @ X4 @ X6 ) ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( wellorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 ) ) )
& ( in @ X2 @ X1 ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f15,plain,
~ ( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ~ ( in @ X0 @ X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
~ ( ( ordinalIrrefl = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ( ( in @ X0 @ X0 )
!= $true ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
~ ( ( ordinalIrrefl = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ( ( in @ X0 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ? [X0: $i] :
( ( ( in @ X0 @ X0 )
= $true )
& ( ( ordinal @ X0 )
= $true ) )
& ( ordinalIrrefl = $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f19,plain,
( ( $true
= ( in @ sK0 @ sK0 ) )
& ( $true
= ( ordinal @ sK0 ) )
& ( ordinalIrrefl = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f18]) ).
thf(f20,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f21,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f22,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f25,plain,
( $true
= ( ordinal @ sK0 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
( $true
= ( in @ sK0 @ sK0 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f29,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y3 @ Y4 ) )
=> ( in @ Y2 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 )
| ( in @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ Y2 ) ) ) )
@ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f21,f20]) ).
thf(f30,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( nonempty @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f22,f29]) ).
thf(f32,plain,
( $true
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( nonempty @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f25,f30]) ).
thf(f33,plain,
( $true
= ( ( transitiveset @ sK0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f37,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f38,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f37]) ).
thf(f62,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f63,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ~ ( in @ X1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ~ ( in @ X1 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( ( in @ X1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f64]) ).
thf(f904,plain,
( ( $true = $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f65,f26]) ).
thf(f909,plain,
$true = $false,
inference(duplicate_literal_removal,[],[f904]) ).
thf(f910,plain,
$false,
inference(trivial_inequality_removal,[],[f909]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU822^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n009.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:35:00 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.29 % (4088446)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (4088453)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=595527721:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (4088452)% WARNING: option uhcvi not known.
% 0.20/0.29 % (4088451)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2768584556_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (4088452)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2590378777:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (4088452)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (4088452)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % (4088453) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4088446-4088453"...
% 0.20/0.29 % (4088453)...printing done.
% 0.20/0.29 % (4088453)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (4088453)------------------------------
% 0.20/0.29 % (4088453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (4088453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (4088453)CaDiCaL version: 2.1.3
% 0.20/0.29 % (4088453)Termination reason: Refutation
% 0.20/0.29 % (4088453)Time elapsed: 0.014 s
% 0.20/0.29 % (4088453)Peak memory usage: 12 MB
% 0.20/0.29 % (4088453)Instructions burned: 56 (million)
% 0.20/0.29 % (4088446)Success in time 0.049 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------