%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU823^2 : 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 : n016.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 08:34:14 AM UTC 2026
% Result : Theorem 2.27s 0.64s
% Output : Refutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 86 ( 23 unt; 0 typ; 6 def)
% Number of atoms : 597 ( 137 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 584 ( 65 ~; 97 |; 12 &; 309 @)
% ( 6 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 42 usr; 13 con; 0-8 aty)
% ( 26 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 99 ( 0 sgn 64 !; 4 ?; 99 :)
% 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,
ordinalTransSet: $o ).
thf(func_def_9,type,
ordinalIrrefl: $o ).
thf(func_def_10,type,
vAND: $o > $o > $o ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vIMP: $o > $o > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vOR: $o > $o > $o ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
sF7: ( $i > $o ) > $i > $o ).
thf(func_def_33,type,
sF9:
!>[X0: $tType] : ( ( X0 > $o ) > ( $i > $o ) > X0 > $i > $o ) ).
thf(func_def_34,type,
sF10: $i > $i > $o ).
thf(func_def_35,type,
sF11: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_36,type,
sF12:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > X0 > X1 > ( X1 > $o ) > $i > $o ) ).
thf(func_def_37,type,
sF13:
!>[X0: $tType,X1: $tType] : ( X0 > ( $i > $o ) > ( ( $i > $o ) > X0 > X1 ) > X1 ) ).
thf(func_def_38,type,
sF14:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X0 > X1 > X2 ) ).
thf(func_def_39,type,
sF15:
!>[X0: $tType] : ( X0 > ( X0 > $i > $o ) > $i > $o ) ).
thf(func_def_40,type,
sF16:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X0 > ( X0 > X1 > X2 > X3 ) > X2 > X1 > X3 ) ).
thf(func_def_41,type,
sF17: $i > $o ).
thf(func_def_42,type,
sF18: $i > $o ).
thf(func_def_43,type,
sF19:
!>[X0: $tType,X1: $tType,X2: $tType] : ( X0 > ( $i > $o ) > X1 > ( ( $i > $o ) > X0 > X1 > X2 ) > X2 ) ).
thf(f4,axiom,
( ordinalTransSet
= ( ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalTransSet) ).
thf(f5,axiom,
( ordinalIrrefl
= ( ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalIrrefl) ).
thf(f6,conjecture,
( ordinalTransSet
=> ( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalNoCycle) ).
thf(f7,negated_conjecture,
~ ( ordinalTransSet
=> ( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f14,plain,
( ordinalTransSet
= ( ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( ordinalTransSet
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( ordinalIrrefl
= ( ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( ordinalIrrefl
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ( ordinalTransSet
=> ( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
~ ( ( ordinalTransSet = $true )
=> ( ( ordinalIrrefl = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
~ ( ( ordinalTransSet = $true )
=> ( ( ordinalIrrefl = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ) ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( ordinalIrrefl = $true )
& ( ordinalTransSet = $true ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f22,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( ordinalIrrefl = $true )
& ( ordinalTransSet = $true ) ),
inference(flattening,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( in @ sK1 @ sK0 ) )
& ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
= ( ordinal @ sK0 ) )
& ( ordinalIrrefl = $true )
& ( ordinalTransSet = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f22]) ).
thf(f27,plain,
( ordinalTransSet
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f28,plain,
( ordinalIrrefl
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f29,plain,
ordinalTransSet = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f30,plain,
ordinalIrrefl = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f31,plain,
( $true
= ( ordinal @ sK0 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f32,plain,
( $true
= ( in @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f33,plain,
( $true
= ( in @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f37,plain,
( ( ordinalIrrefl = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f28]) ).
thf(f38,plain,
! [X1: $i] :
( ( ordinalIrrefl = $false )
| ( $true
= ( ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X1: $i] :
( ( ordinalIrrefl = $false )
| ( $true
= ( ( ordinal @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X1: $i] :
( ( ordinalIrrefl = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ordinalIrrefl = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( ordinalIrrefl = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( $true
= ( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( ordinalIrrefl = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ( in @ X2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( ordinalIrrefl = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f43]) ).
thf(f55,plain,
( ( ordinalTransSet = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f27]) ).
thf(f56,plain,
! [X1: $i] :
( ( ordinalTransSet = $false )
| ( $true
= ( ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X1: $i] :
( ( ordinalTransSet = $false )
| ( $true
= ( ( ordinal @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X1: $i] :
( ( ordinalTransSet = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( ( ordinalTransSet = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( ordinalTransSet = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ordinalTransSet = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ordinalTransSet = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( $true
= ( ( in @ X2 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ordinalTransSet = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ordinalTransSet = $false )
| ( $false
= ( ordinal @ X1 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X3 @ X2 )
= $false )
| ( ( in @ X3 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f80,definition,
( spl8_1
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( ordinal @ X1 ) )
| ( ( in @ X2 @ X2 )
= $false )
| ( ( in @ X2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f81,plain,
( ! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X2 )
= $false )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( ordinal @ X1 ) ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f80]) ).
thf(f83,definition,
( spl8_2
<=> ( ordinalIrrefl = $false ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f85,plain,
( ( ordinalIrrefl = $false )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f86,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f44,f83,f80]) ).
thf(f92,definition,
( spl8_4
<=> ( ordinalIrrefl = $true ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f94,plain,
( ( ordinalIrrefl = $true )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f107,definition,
( spl8_7
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( ordinal @ X1 ) )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X2 )
= $false )
| ( ( in @ X2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
thf(f108,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ X2 )
= $false )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( ordinal @ X1 ) ) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f107]) ).
thf(f110,definition,
( spl8_8
<=> ( ordinalTransSet = $false ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
thf(f112,plain,
( ( ordinalTransSet = $false )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f113,plain,
( spl8_7
| spl8_8 ),
inference(avatar_split_clause,[],[f64,f110,f107]) ).
thf(f119,definition,
( spl8_10
<=> ( ordinalTransSet = $true ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
thf(f121,plain,
( ( ordinalTransSet = $true )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f138,plain,
spl8_10,
inference(avatar_split_clause,[],[f29,f119]) ).
thf(f139,plain,
spl8_4,
inference(avatar_split_clause,[],[f30,f92]) ).
thf(f144,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_10 ),
inference(forward_demodulation,[],[f121,f112]) ).
thf(f145,plain,
( $false
| ~ spl8_8
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f144]) ).
thf(f146,plain,
( ~ spl8_8
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f145]) ).
thf(f323,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( in @ X0 @ sK0 ) )
| ( ( ordinal @ sK0 )
= $false ) )
| ~ spl8_7 ),
inference(constrained_superposition,[],[f33,f108]) ).
thf(f328,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( in @ X0 @ sK0 ) )
| ( ( ordinal @ sK0 )
= $false ) )
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f323]) ).
thf(f351,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( in @ X0 @ sK0 ) ) )
| ~ spl8_7 ),
inference(forward_demodulation,[],[f328,f31]) ).
thf(f352,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( in @ X0 @ sK0 ) ) )
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f351]) ).
thf(f359,plain,
( ( $true = $false )
| ( $true
= ( in @ sK0 @ sK0 ) )
| ~ spl8_7 ),
inference(constrained_superposition,[],[f32,f352]) ).
thf(f360,plain,
( ( $true
= ( in @ sK0 @ sK0 ) )
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f359]) ).
thf(f375,plain,
( ( $true = $false )
| ( $true = $false )
| ( ( ordinal @ sK0 )
= $false )
| ~ spl8_1
| ~ spl8_7 ),
inference(constrained_superposition,[],[f81,f360]) ).
thf(f378,plain,
( ( $true = $false )
| ( ( ordinal @ sK0 )
= $false )
| ~ spl8_1
| ~ spl8_7 ),
inference(duplicate_literal_removal,[],[f375]) ).
thf(f379,plain,
( ( ( ordinal @ sK0 )
= $false )
| ~ spl8_1
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f378]) ).
thf(f389,plain,
( ( $true = $false )
| ~ spl8_1
| ~ spl8_7 ),
inference(constrained_superposition,[],[f379,f31]) ).
thf(f397,plain,
( $false
| ~ spl8_1
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f389]) ).
thf(f398,plain,
( ~ spl8_1
| ~ spl8_7 ),
inference(avatar_contradiction_clause,[],[f397]) ).
thf(f420,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_4 ),
inference(constrained_superposition,[],[f85,f94]) ).
thf(f424,plain,
( $false
| ~ spl8_2
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f420]) ).
thf(f425,plain,
( ~ spl8_2
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[],[f424]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f86]) ).
cnf(s5,plain,
( spl8_7
| spl8_8 ),
inference(sat_conversion,[],[f113]) ).
cnf(s10,plain,
spl8_10,
inference(sat_conversion,[],[f138]) ).
cnf(s11,plain,
spl8_4,
inference(sat_conversion,[],[f139]) ).
cnf(s12,plain,
( ~ spl8_8
| ~ spl8_10 ),
inference(sat_conversion,[],[f146]) ).
cnf(s18,plain,
( ~ spl8_1
| ~ spl8_7 ),
inference(sat_conversion,[],[f398]) ).
cnf(s20,plain,
( ~ spl8_2
| ~ spl8_4 ),
inference(sat_conversion,[],[f425]) ).
cnf(s21,plain,
~ spl8_2,
inference(rat,[],[s20,s11]) ).
cnf(s22,plain,
~ spl8_8,
inference(rat,[],[s12,s10]) ).
cnf(s23,plain,
spl8_7,
inference(rat,[],[s5,s22]) ).
cnf(s24,plain,
~ spl8_1,
inference(rat,[],[s18,s23]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s1,s21,s24]) ).
thf(f427,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU823^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n016.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:39:49 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 2.27/0.64 % (438055)Will run a generic schedule for satisfiability detection.
% 2.27/0.64 % (438063)dis+10_1_sil=32000:sp=arity:random_seed=898892702:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.27/0.64 % (438061)% WARNING: option uhcvi not known.
% 2.27/0.64 % (438061)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1166423971:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.27/0.64 % (438060)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1414122407_2999 on theBenchmark for (2999ds/0Mi)
% 2.27/0.64 % (438062)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3308642692:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.27/0.64 % (438064)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=266873057:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.27/0.64 % (438066)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4145368607:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.27/0.64 % (438061)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.27/0.64 % (438064)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.27/0.64 % (438061)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.27/0.64 % Exception at run slice level
% 2.27/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.27/0.64 % (438065)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1439325937:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.27/0.64 % (438063)Instruction limit reached!
% 2.27/0.64 % (438063)------------------------------
% 2.27/0.64 % (438063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.64 % (438063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.64 % (438063)CaDiCaL version: 2.1.3
% 2.27/0.64 % (438063)Termination reason: Instruction limit
% 2.27/0.64 % (438063)Termination phase: Saturation
% 2.27/0.64 % (438063)Time elapsed: 0.023 s
% 2.27/0.64 % (438063)Peak memory usage: 12 MB
% 2.27/0.64 % (438063)Instructions burned: 103 (million)
% 2.27/0.64 % (438073)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1593746841:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.27/0.64 % Exception at run slice level
% 2.27/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.27/0.64 % (438075)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1103042964:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.27/0.64 % (438077)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=3267807429:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.27/0.64 % (438077)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.27/0.64 % (438077)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.27/0.64 % (438064)Instruction limit reached!
% 2.27/0.64 % (438064)------------------------------
% 2.27/0.64 % (438064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.64 % (438064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.64 % (438064)CaDiCaL version: 2.1.3
% 2.27/0.64 % (438064)Termination reason: Instruction limit
% 2.27/0.64 % (438064)Termination phase: Saturation
% 2.27/0.64 % (438064)Time elapsed: 0.049 s
% 2.27/0.64 % (438064)Peak memory usage: 12 MB
% 2.27/0.64 % (438064)Instructions burned: 118 (million)
% 2.27/0.64 % (438075)Instruction limit reached!
% 2.27/0.64 % (438075)------------------------------
% 2.27/0.64 % (438075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.64 % (438075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.64 % (438075)CaDiCaL version: 2.1.3
% 2.27/0.64 % (438075)Termination reason: Instruction limit
% 2.27/0.64 % (438075)Termination phase: Saturation
% 2.27/0.64 % (438075)Time elapsed: 0.030 s
% 2.27/0.64 % (438075)Peak memory usage: 12 MB
% 2.27/0.64 % (438075)Instructions burned: 142 (million)
% 2.27/0.64 % (438081)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=937386401:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 2.27/0.64 % (438080)ott-21_1_sil=16000:fs=off:random_seed=480933130:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.27/0.64 % (438066)Instruction limit reached!
% 2.27/0.64 % (438066)------------------------------
% 2.27/0.64 % (438066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.64 % (438066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.64 % (438066)CaDiCaL version: 2.1.3
% 2.27/0.64 % (438066)Termination reason: Instruction limit
% 2.27/0.64 % (438066)Termination phase: Saturation
% 2.27/0.64 % (438066)Time elapsed: 0.069 s
% 2.27/0.64 % (438066)Peak memory usage: 13 MB
% 2.27/0.64 % (438066)Instructions burned: 159 (million)
% 2.27/0.64 % (438084)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1475451233:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 2.27/0.64 % Exception at run slice level
% 2.27/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.27/0.64 % (438065)Instruction limit reached!
% 2.27/0.64 % (438065)------------------------------
% 2.27/0.64 % (438065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.64 % (438065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.64 % (438065)CaDiCaL version: 2.1.3
% 2.27/0.64 % (438065)Termination reason: Instruction limit
% 2.27/0.64 % (438065)Termination phase: Saturation
% 2.27/0.64 % (438065)Time elapsed: 0.104 s
% 2.27/0.64 % (438065)Peak memory usage: 12 MB
% 2.27/0.64 % (438065)Instructions burned: 132 (million)
% 2.27/0.64 % (438087)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1692668576:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.27/0.64 % Exception at run slice level
% 2.27/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.27/0.64 % (438086)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1145072335:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.27/0.64 % (438080)Instruction limit reached!
% 2.27/0.64 % (438080)------------------------------
% 2.27/0.64 % (438080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.64 % (438080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.64 % (438080)CaDiCaL version: 2.1.3
% 2.27/0.64 % (438080)Termination reason: Instruction limit
% 2.27/0.64 % (438080)Termination phase: Saturation
% 2.27/0.64 % (438080)Time elapsed: 0.077 s
% 2.27/0.64 % (438080)Peak memory usage: 13 MB
% 2.27/0.64 % (438080)Instructions burned: 182 (million)
% 2.27/0.64 % (438089)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=3549434323: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)
% 2.27/0.64 % (438089)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.27/0.64 % (438091)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=704923326:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.27/0.64 % (438091)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.27/0.64 % (438081)Instruction limit reached!
% 2.27/0.64 % (438081)------------------------------
% 2.27/0.64 % (438081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.64 % (438081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.64 % (438081)CaDiCaL version: 2.1.3
% 2.27/0.64 % (438081)Termination reason: Instruction limit
% 2.27/0.64 % (438081)Termination phase: Saturation
% 2.27/0.64 % (438081)Time elapsed: 0.109 s
% 2.27/0.64 % (438081)Peak memory usage: 13 MB
% 2.27/0.64 % (438081)Instructions burned: 478 (million)
% 2.27/0.64 % (438094)fmb+10_1_sil=64000:random_seed=3421854740:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.27/0.64 % (438094)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.27/0.64 % Exception at run slice level
% 2.27/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.27/0.64 % (438096)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4074530593:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 2.27/0.64 % Exception at run slice level
% 2.27/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.27/0.64 % (438098)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2304351221:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 2.27/0.64 % Exception at run slice level
% 2.27/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.27/0.64 % (438100)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3317176059:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 2.27/0.64 % (438100)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.27/0.64 % (438077)Instruction limit reached!
% 2.27/0.64 % (438077)------------------------------
% 2.27/0.64 % (438077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.64 % (438077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.64 % (438077)CaDiCaL version: 2.1.3
% 2.27/0.64 % (438077)Termination reason: Instruction limit
% 2.27/0.64 % (438077)Termination phase: Saturation
% 2.27/0.64 % (438077)Time elapsed: 0.289 s
% 2.27/0.64 % (438077)Peak memory usage: 14 MB
% 2.27/0.64 % (438077)Instructions burned: 686 (million)
% 2.27/0.64 % (438102)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4269131669:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 2.27/0.64 % (438102)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.27/0.64 % (438102)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.27/0.64 % (438102) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-438055-438102"...
% 2.27/0.64 % (438102)...printing done.
% 2.27/0.64 % (438102)Refutation found. Thanks to Tanya!
% 2.27/0.64 % SZS status Theorem for theBenchmark
% 2.27/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 2.27/0.64 % (438102)------------------------------
% 2.27/0.64 % (438102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.64 % (438102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.64 % (438102)CaDiCaL version: 2.1.3
% 2.27/0.64 % (438102)Termination reason: Refutation
% 2.27/0.64 % (438102)Time elapsed: 0.020 s
% 2.27/0.64 % (438102)Peak memory usage: 13 MB
% 2.27/0.64 % (438102)Instructions burned: 32 (million)
% 2.27/0.64 % (438055)Success in time 0.404 s
% 2.27/0.64 % Vampire exiting
%------------------------------------------------------------------------------