%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET924^1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 08:23:50 AM UTC 2026
% Result : Theorem 0.21s 0.33s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 39 unt; 0 typ; 2 def)
% Number of atoms : 379 ( 79 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 581 ( 47 ~; 28 |; 0 &; 488 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 35 usr; 8 con; 0-4 aty)
% ( 14 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 111 ( 0 sgn 18 !; 0 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_14,type,
in: $i > $i > mworld > $o ).
thf(func_def_15,type,
empty: $i > mworld > $o ).
thf(func_def_16,type,
singleton: $i > $i ).
thf(func_def_17,type,
set_difference: $i > $i > $i ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vOR: $o > $o > $o ).
thf(func_def_25,type,
vIMP: $o > $o > $o ).
thf(func_def_26,type,
vIFF: $o > $o > $o ).
thf(func_def_27,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db4:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(f6,axiom,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv_def) ).
thf(f9,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f23,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(f24,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f25,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(f26,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f27,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f28,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f35,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f36,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f41,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f9]) ).
thf(f42,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f69,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f70,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f72,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(flattening,[],[f70]) ).
thf(f74,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f75,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f79,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f82,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f96,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f97,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f112,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f96,f74,f82,f82,f79,f75]) ).
thf(f113,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f97,f74,f82,f82,f79,f75]) ).
thf(f114,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
= ( ~ ( in @ Y0 @ Y1 @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
= ( ~ ( in @ Y0 @ Y1 @ mactual ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) ) ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $false
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $true
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f119]) ).
thf(f122,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $false
= ( in @ X1 @ X2 @ mactual ) ) ),
inference(not_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $true
= ( in @ X1 @ X2 @ mactual ) ) ),
inference(not_proxy_clausification,[],[f120]) ).
thf(f124,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
= ( ~ ( in @ Y0 @ Y1 @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f125,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
= ( ~ ( in @ Y0 @ Y1 @ mactual ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ Y0 ) @ ( singleton @ sK0 ) @ mactual )
= ( ~ ( in @ sK0 @ Y0 @ mactual ) ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
( $false
= ( ^ [Y0: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ Y0 ) @ ( singleton @ sK0 ) @ mactual )
= ( ~ ( in @ sK0 @ Y0 @ mactual ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f126]) ).
thf(f128,plain,
( $false
= ( ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ sK1 ) @ ( singleton @ sK0 ) @ mactual )
= ( ~ ( in @ sK0 @ sK1 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f127]) ).
thf(f129,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ sK1 ) @ ( singleton @ sK0 ) @ mactual )
!= ( ~ ( in @ sK0 @ sK1 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f128]) ).
thf(f130,plain,
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ sK1 ) @ ( singleton @ sK0 ) @ mactual ) )
| ( $true
= ( ~ ( in @ sK0 @ sK1 @ mactual ) ) ) ),
inference(xor_proxy_clausification,[],[f129]) ).
thf(f131,plain,
( ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ sK1 ) @ ( singleton @ sK0 ) @ mactual ) )
| ( $false
= ( ~ ( in @ sK0 @ sK1 @ mactual ) ) ) ),
inference(xor_proxy_clausification,[],[f129]) ).
thf(f132,plain,
( ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ sK1 ) @ ( singleton @ sK0 ) @ mactual ) )
| ( $true
= ( in @ sK0 @ sK1 @ mactual ) ) ),
inference(not_proxy_clausification,[],[f131]) ).
thf(f133,plain,
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ sK1 ) @ ( singleton @ sK0 ) @ mactual ) )
| ( $false
= ( in @ sK0 @ sK1 @ mactual ) ) ),
inference(not_proxy_clausification,[],[f130]) ).
thf(f249,definition,
( spl4_3
<=> ( $true
= ( in @ sK0 @ sK1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f250,plain,
( ( $true
!= ( in @ sK0 @ sK1 @ mactual ) )
| spl4_3 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f251,plain,
( ( $true
= ( in @ sK0 @ sK1 @ mactual ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f253,definition,
( spl4_4
<=> ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ sK1 ) @ ( singleton @ sK0 ) @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f255,plain,
( ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ sK1 ) @ ( singleton @ sK0 ) @ mactual ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f256,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f132,f253,f249]) ).
thf(f257,plain,
( ( $true = $false )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ sK1 ) @ ( singleton @ sK0 ) @ mactual ) )
| ~ spl4_3 ),
inference(forward_demodulation,[],[f133,f251]) ).
thf(f258,plain,
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ sK0 ) @ sK1 ) @ ( singleton @ sK0 ) @ mactual ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f443,plain,
( ( $true = $false )
| ( $false
= ( in @ sK0 @ sK1 @ mactual ) )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f258,f122]) ).
thf(f446,plain,
( ( $false
= ( in @ sK0 @ sK1 @ mactual ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f443]) ).
thf(f451,plain,
( ( $true = $false )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f446,f251]) ).
thf(f455,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f451]) ).
thf(f456,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f455]) ).
thf(f511,plain,
( ( $true = $false )
| ( $true
= ( in @ sK0 @ sK1 @ mactual ) )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f123,f255]) ).
thf(f528,plain,
( ( $true
= ( in @ sK0 @ sK1 @ mactual ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f511]) ).
thf(f536,plain,
( $false
| spl4_3
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f528,f250]) ).
thf(f537,plain,
( spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f536]) ).
cnf(s30,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f256]) ).
cnf(s111,plain,
~ spl4_3,
inference(sat_conversion,[],[f456]) ).
cnf(s142,plain,
( spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f537]) ).
cnf(s145,plain,
~ spl4_4,
inference(rat,[],[s142,s111]) ).
cnf(s147,plain,
$false,
inference(rat,[],[s30,s145,s111]) ).
thf(f538,plain,
$false,
inference(avatar_sat_refutation,[],[s147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET924^1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:39:26 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.21/0.33 % (3374854)Will run a generic schedule for satisfiability detection.
% 0.21/0.33 % (3374859)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1844495896_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.33 % Exception at run slice level
% 0.21/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.33 % (3374860)% WARNING: option uhcvi not known.
% 0.21/0.33 % (3374860)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=63139640:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.33 % (3374861)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2270413130:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.33 % (3374862)dis+10_1_sil=32000:sp=arity:random_seed=1848495307:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.33 % (3374864)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1175865317:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.33 % (3374860)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.33 % (3374867)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1039620445:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.33 % (3374860)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.33 % Exception at run slice level
% 0.21/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.33 % (3374873)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1841181842:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.33 % (3374863)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1544025990:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.33 % (3374865)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=349641405:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.33 % (3374861) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3374854-3374861"...
% 0.21/0.33 % (3374863)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.33 % (3374861)...printing done.
% 0.21/0.33 % (3374861)Refutation found. Thanks to Tanya!
% 0.21/0.33 % SZS status Theorem for theBenchmark
% 0.21/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.34 % (3374861)------------------------------
% 0.21/0.34 % (3374861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3374861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3374861)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3374861)Termination reason: Refutation
% 0.21/0.34 % (3374861)Time elapsed: 0.040 s
% 0.21/0.34 % (3374861)Peak memory usage: 13 MB
% 0.21/0.34 % (3374861)Instructions burned: 42 (million)
% 0.21/0.34 % (3374854)Success in time 0.088 s
% 0.21/0.34 % Vampire exiting
%------------------------------------------------------------------------------