%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU700^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:30:50 AM UTC 2026
% Result : Theorem 0.09s 0.20s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 110 ( 35 unt; 0 typ; 16 def)
% Number of atoms : 630 ( 158 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 649 ( 99 ~; 112 |; 43 &; 311 @)
% ( 11 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 37 usr; 25 con; 0-4 aty)
% ( 24 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 116 ( 0 sgn 56 !; 12 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrI: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vOR: $o > $o > $o ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_19,type,
sK2: $o ).
thf(func_def_21,type,
sF4: $o ).
thf(func_def_22,type,
sF5: $o ).
thf(func_def_23,type,
sF6: $o ).
thf(func_def_25,type,
sF8: $o ).
thf(func_def_26,type,
sF9: $o ).
thf(func_def_27,type,
sK10: $i > $o ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f2,conjecture,
( dsetconstrI
=> ! [X1: $o,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( in @ X3
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( X1
& ( X4 = X2 ) )
| ( ~ X1
& ( X4 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(f3,negated_conjecture,
~ ( dsetconstrI
=> ! [X1: $o,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( in @ X3
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( X1
& ( X4 = X2 ) )
| ( ~ X1
& ( X4 = X3 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( dsetconstrI
=> ! [X0: $o,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ X0
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] :
( ( X0
& ( X4 = X2 ) )
| ( ~ X0
& ( X4 = X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( dsetconstrI = $true )
=> ! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true != X0 )
=> ( $true
= ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& ~ X0 )
| ( ( X2 = Y0 )
& X0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( ( dsetconstrI = $true )
=> ! [X2: $i,X1: $i,X0: $o] :
( ( ( in @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true != X0 )
=> ( $true
= ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& ~ X0 )
| ( ( X2 = Y0 )
& X0 ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
( ? [X2: $i,X1: $i,X0: $o] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& ~ X0 )
| ( ( X2 = Y0 )
& X0 ) ) ) ) )
& ( $true != X0 )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f10,plain,
( ? [X2: $i,X1: $i,X0: $o] :
( ( ( in @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& ~ X0 )
| ( ( X2 = Y0 )
& X0 ) ) ) ) )
& ( $true != X0 ) ) )
& ( dsetconstrI = $true ) ),
inference(flattening,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $o] :
( ( $true
= ( in @ X0 @ X1 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& ~ X2 )
| ( ( X0 = Y0 )
& X2 ) ) ) )
!= $true )
& ( $true != X2 ) ) )
& ( dsetconstrI = $true ) ),
inference(rectify,[],[f10]) ).
thf(f12,plain,
( ( $true
= ( in @ sK0 @ sK1 ) )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( $true
!= ( in @ sK3
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] :
( ( ( sK3 = Y0 )
& ~ sK2 )
| ( ( sK0 = Y0 )
& sK2 ) ) ) ) )
& ( sK2 != $true )
& ( dsetconstrI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f11]) ).
thf(f13,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f12]) ).
thf(f14,plain,
sK2 != $true,
inference(cnf_transformation,[],[f12]) ).
thf(f15,plain,
( $true
!= ( in @ sK3
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] :
( ( ( sK3 = Y0 )
& ~ sK2 )
| ( ( sK0 = Y0 )
& sK2 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
( ( in @ sK3 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f18,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f21,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f18,f13]) ).
thf(f24,definition,
( sF5
= ( in @ sK3 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f25,plain,
sF5 = $true,
inference(definition_folding,[],[f16,f24]) ).
thf(f26,definition,
( sF6 = ( ~ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f27,definition,
( sF7
= ( dsetconstr @ sK1
@ ^ [Y0: $i] :
( ( ( sK3 = Y0 )
& sF6 )
| ( ( sK0 = Y0 )
& sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f28,definition,
( sF8
= ( in @ sK3 @ sF7 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f29,plain,
sF8 != $true,
inference(definition_folding,[],[f15,f28,f27,f26]) ).
thf(f30,definition,
( sF9
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f31,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) )
= sF9 ),
inference(reorient_equations,[],[f30]) ).
thf(f32,plain,
sF9 = $true,
inference(definition_folding,[],[f21,f31]) ).
thf(f33,plain,
( ( sF8 = $true )
| ( ( in @ sK3 @ sF7 )
= $false ) ),
inference(iff_proxy_clausification,[],[f28]) ).
thf(f35,plain,
( ( $false = ( ~ sK2 ) )
| ( $true = sF6 ) ),
inference(iff_proxy_clausification,[],[f26]) ).
thf(f38,plain,
( ( $true = sF6 )
| ( sK2 = $true ) ),
inference(not_proxy_clausification,[],[f35]) ).
thf(f42,plain,
( ( ( in @ sK3 @ sK1 )
= $true )
| ( sF5 = $false ) ),
inference(iff_proxy_clausification,[],[f24]) ).
thf(f43,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $true )
| ( sF9 = $false ) ),
inference(iff_proxy_clausification,[],[f31]) ).
thf(f55,plain,
! [X1: $i > $o] :
( ( sF9 = $false )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f56,plain,
! [X1: $i > $o] :
( ( sF9 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X1: $i > $o] :
( ( sF9 = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i > $o] :
( ( sF9 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) ) ) )
@ X3 )
= $true )
| ( sF9 = $false ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( sF9 = $false )
| ( ( ( in @ X3 @ X2 )
=> ( ( X1 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( sF9 = $false )
| ( $true
= ( ( X1 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( sF9 = $false )
| ( ( in @ X3 @ X2 )
= $false )
| ( ( X1 @ X3 )
= $false )
| ( $true
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f73,definition,
( spl13_3
<=> ( sF8 = $true ) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
thf(f77,definition,
( spl13_4
<=> ( ( in @ sK3 @ sF7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
thf(f79,plain,
( ( ( in @ sK3 @ sF7 )
= $false )
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f80,plain,
( spl13_3
| spl13_4 ),
inference(avatar_split_clause,[],[f33,f77,f73]) ).
thf(f82,definition,
( spl13_5
<=> ( $false = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
thf(f83,plain,
( ( $false != sF6 )
| spl13_5 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f84,plain,
( ( $false = sF6 )
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f91,definition,
( spl13_7
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
thf(f93,plain,
( ( $true = sF6 )
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f95,definition,
( spl13_8
<=> ( sK2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
thf(f98,plain,
( spl13_7
| spl13_8 ),
inference(avatar_split_clause,[],[f38,f95,f91]) ).
thf(f118,definition,
( spl13_13
<=> ( ( in @ sK3 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl13_13])],[avatar_definition]) ).
thf(f120,plain,
( ( ( in @ sK3 @ sK1 )
= $true )
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f122,definition,
( spl13_14
<=> ( sF5 = $false ) ),
introduced(definition,[new_symbols(definition,[spl13_14])],[avatar_definition]) ).
thf(f124,plain,
( ( sF5 = $false )
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f125,plain,
( spl13_13
| spl13_14 ),
inference(avatar_split_clause,[],[f42,f122,f118]) ).
thf(f127,definition,
( spl13_15
<=> ( sF5 = $true ) ),
introduced(definition,[new_symbols(definition,[spl13_15])],[avatar_definition]) ).
thf(f129,plain,
( ( sF5 = $true )
| ~ spl13_15 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f136,plain,
spl13_15,
inference(avatar_split_clause,[],[f25,f127]) ).
thf(f137,plain,
~ spl13_8,
inference(avatar_split_clause,[],[f14,f95]) ).
thf(f143,definition,
( spl13_18
<=> ( sF9 = $true ) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
thf(f145,plain,
( ( sF9 = $true )
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f158,definition,
( spl13_21
<=> ! [X2: $i,X1: $i > $o,X3: $i] :
( ( ( in @ X3 @ X2 )
= $false )
| ( $true
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( ( X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl13_21])],[avatar_definition]) ).
thf(f159,plain,
( ! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( ( in @ X3 @ X2 )
= $false )
| ( ( X1 @ X3 )
= $false ) )
| ~ spl13_21 ),
inference(avatar_component_clause,[],[f158]) ).
thf(f161,definition,
( spl13_22
<=> ( sF9 = $false ) ),
introduced(definition,[new_symbols(definition,[spl13_22])],[avatar_definition]) ).
thf(f163,plain,
( ( sF9 = $false )
| ~ spl13_22 ),
inference(avatar_component_clause,[],[f161]) ).
thf(f164,plain,
( spl13_21
| spl13_22 ),
inference(avatar_split_clause,[],[f62,f161,f158]) ).
thf(f165,plain,
~ spl13_3,
inference(avatar_split_clause,[],[f29,f73]) ).
thf(f166,plain,
spl13_18,
inference(avatar_split_clause,[],[f32,f143]) ).
thf(f168,plain,
( ( $false = $true )
| ~ spl13_5
| ~ spl13_7 ),
inference(forward_demodulation,[],[f93,f84]) ).
thf(f169,plain,
( $false
| ~ spl13_5
| ~ spl13_7 ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f170,plain,
( ~ spl13_5
| ~ spl13_7 ),
inference(avatar_contradiction_clause,[],[f169]) ).
thf(f194,plain,
( ! [X0: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK3 = Y0 )
& sF6 )
| ( ( sK0 = Y0 )
& sK2 ) )
@ X0 ) )
| ( ( in @ X0 @ sF7 )
= $true )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl13_21 ),
inference(constrained_superposition,[],[f159,f27]) ).
thf(f195,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF7 )
= $true )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( ( ( ( sK3 = X0 )
& sF6 )
| ( ( sK0 = X0 )
& sK2 ) )
= $false ) )
| ~ spl13_21 ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f197,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( ( ( sK3 = X0 )
& sF6 )
= $false )
| ( ( in @ X0 @ sF7 )
= $true ) )
| ~ spl13_21 ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f198,plain,
( ! [X0: $i] :
( ( $false = sF6 )
| ( ( in @ X0 @ sF7 )
= $true )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( sK3 = X0 ) ) )
| ~ spl13_21 ),
inference(and_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF7 )
= $true )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( sK3 != X0 )
| ( $false = sF6 ) )
| ~ spl13_21 ),
inference(equality_proxy_clausification,[],[f198]) ).
thf(f202,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( sK3 != X0 )
| ( ( in @ X0 @ sF7 )
= $true ) )
| spl13_5
| ~ spl13_21 ),
inference(forward_subsumption_resolution,[],[f199,f83]) ).
thf(f206,plain,
( ( sK3 != sK3 )
| ( ( in @ sK3 @ sF7 )
= $true )
| ( $false = $true )
| spl13_5
| ~ spl13_13
| ~ spl13_21 ),
inference(constrained_superposition,[],[f120,f202]) ).
thf(f211,plain,
( ( ( in @ sK3 @ sF7 )
= $true )
| spl13_5
| ~ spl13_13
| ~ spl13_21 ),
inference(trivial_inequality_removal,[],[f206]) ).
thf(f225,plain,
( ( $false = $true )
| ~ spl13_4
| spl13_5
| ~ spl13_13
| ~ spl13_21 ),
inference(forward_demodulation,[],[f211,f79]) ).
thf(f226,plain,
( $false
| ~ spl13_4
| spl13_5
| ~ spl13_13
| ~ spl13_21 ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f227,plain,
( ~ spl13_4
| spl13_5
| ~ spl13_13
| ~ spl13_21 ),
inference(avatar_contradiction_clause,[],[f226]) ).
thf(f229,plain,
( ( $false = $true )
| ~ spl13_14
| ~ spl13_15 ),
inference(forward_demodulation,[],[f124,f129]) ).
thf(f230,plain,
( $false
| ~ spl13_14
| ~ spl13_15 ),
inference(trivial_inequality_removal,[],[f229]) ).
thf(f231,plain,
( ~ spl13_14
| ~ spl13_15 ),
inference(avatar_contradiction_clause,[],[f230]) ).
thf(f232,plain,
( ( $false = $true )
| ~ spl13_18
| ~ spl13_22 ),
inference(forward_demodulation,[],[f163,f145]) ).
thf(f233,plain,
( $false
| ~ spl13_18
| ~ spl13_22 ),
inference(trivial_inequality_removal,[],[f232]) ).
thf(f234,plain,
( ~ spl13_18
| ~ spl13_22 ),
inference(avatar_contradiction_clause,[],[f233]) ).
cnf(s2,plain,
( spl13_3
| spl13_4 ),
inference(sat_conversion,[],[f80]) ).
cnf(s4,plain,
( spl13_7
| spl13_8 ),
inference(sat_conversion,[],[f98]) ).
cnf(s7,plain,
( spl13_13
| spl13_14 ),
inference(sat_conversion,[],[f125]) ).
cnf(s10,plain,
spl13_15,
inference(sat_conversion,[],[f136]) ).
cnf(s11,plain,
~ spl13_8,
inference(sat_conversion,[],[f137]) ).
cnf(s15,plain,
( spl13_21
| spl13_22 ),
inference(sat_conversion,[],[f164]) ).
cnf(s16,plain,
~ spl13_3,
inference(sat_conversion,[],[f165]) ).
cnf(s17,plain,
spl13_18,
inference(sat_conversion,[],[f166]) ).
cnf(s18,plain,
( ~ spl13_5
| ~ spl13_7 ),
inference(sat_conversion,[],[f170]) ).
cnf(s22,plain,
( ~ spl13_4
| spl13_5
| ~ spl13_13
| ~ spl13_21 ),
inference(sat_conversion,[],[f227]) ).
cnf(s24,plain,
( ~ spl13_14
| ~ spl13_15 ),
inference(sat_conversion,[],[f231]) ).
cnf(s25,plain,
( ~ spl13_18
| ~ spl13_22 ),
inference(sat_conversion,[],[f234]) ).
cnf(s26,plain,
~ spl13_22,
inference(rat,[],[s25,s17]) ).
cnf(s27,plain,
spl13_21,
inference(rat,[],[s15,s26]) ).
cnf(s28,plain,
~ spl13_14,
inference(rat,[],[s24,s10]) ).
cnf(s30,plain,
spl13_13,
inference(rat,[],[s7,s28]) ).
cnf(s32,plain,
spl13_7,
inference(rat,[],[s4,s11]) ).
cnf(s33,plain,
~ spl13_5,
inference(rat,[],[s18,s32]) ).
cnf(s34,plain,
~ spl13_4,
inference(rat,[],[s22,s27,s30,s33]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s2,s34,s16]) ).
thf(f236,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU700^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.14 % Computer : n012.cluster.edu
% 0.09/0.14 % Model : x86_64 x86_64
% 0.09/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.14 % Memory : 8046.5625MB
% 0.09/0.14 % OS : Linux 6.8.0-71-generic
% 0.09/0.14 % CPULimit : 300
% 0.09/0.14 % WCLimit : 300
% 0.09/0.14 % DateTime : Tue Sep 29 14:11:48 UTC 2026
% 0.09/0.14 % CPUTime :
% 0.09/0.14 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 Running higher-order theorem proving
% 0.09/0.18 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.20 % (165111)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.20 % (165122)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.20 % (165122)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.09/0.20 % (165122)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2559732789:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_3000 on theBenchmark for (3000ds/157Mi)
% 0.09/0.20 % (165122) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-165111-165122"...
% 0.09/0.20 % (165122)...printing done.
% 0.09/0.20 % (165116)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1166234834:s2a=on:i=87:rtra=on:ntd=on_3000 on theBenchmark for (3000ds/87Mi)
% 0.09/0.20 % (165120)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3849277060:i=24:av=off:rtra=on_3000 on theBenchmark for (3000ds/24Mi)
% 0.09/0.20 % (165118)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3441348120:i=3:rtra=on:inj=on:ntd=on_3000 on theBenchmark for (3000ds/3Mi)
% 0.09/0.20 % (165117)lrs+10_16_si=on:nwc=1.5:random_seed=2442290973:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_3000 on theBenchmark for (3000ds/18Mi)
% 0.09/0.20 % (165121)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3839178927:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_3000 on theBenchmark for (3000ds/75Mi)
% 0.09/0.20 % (165119)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3888478376:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_3000 on theBenchmark for (3000ds/634Mi)
% 0.09/0.20 % (165122)Refutation found. Thanks to Tanya!
% 0.09/0.20 % SZS status Theorem for theBenchmark
% 0.09/0.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.20 % (165122)------------------------------
% 0.09/0.20 % (165122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.20 % (165122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.20 % (165122)CaDiCaL version: 2.1.3
% 0.09/0.20 % (165122)Termination reason: Refutation
% 0.09/0.20 % (165122)Time elapsed: 0.004 s
% 0.09/0.20 % (165122)Peak memory usage: 13 MB
% 0.09/0.20 % (165122)Instructions burned: 10 (million)
% 0.09/0.20 % (165111)Success in time 0.02 s
% 0.09/0.20 % Vampire exiting
%------------------------------------------------------------------------------