%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET027^3 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:23:11 AM UTC 2026
% Result : Theorem 0.23s 0.37s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 70 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 470 ( 105 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 708 ( 7 ~; 33 |; 13 &; 599 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 7 con; 0-4 aty)
% ( 29 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 199 ( 145 ^; 54 !; 0 ?; 199 :)
% 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,
member: $i > $i > mworld > $o ).
thf(func_def_14,type,
subset: $i > $i > mworld > $o ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vIFF: $o > $o > $o ).
thf(func_def_25,type,
vOR: $o > $o > $o ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
sK0: mworld > mworld ).
thf(func_def_29,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
sK4: $i > $i > $i ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f6,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv_def) ).
thf(f10,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(f12,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( subset @ X0 @ X1 )
@ ( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(f14,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X2 ) ) @ ( subset @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
thf(f15,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X2 ) ) @ ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
thf(f16,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X2 ) ) @ ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y2 ) ) @ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f20,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f21,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f23,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f26,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( subset @ X0 @ X1 )
@ ( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f27,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
inference(rectify,[],[f6]) ).
thf(f29,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f38,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f39,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f42,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f43,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y2 ) ) @ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(flattening,[],[f17]) ).
thf(f45,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f50,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f51,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f53,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y2 ) ) @ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f54,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f55,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f56,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f61,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 ) )
@ ( subset @ Y0 @ Y1 )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f45,f50,f56,f56,f54,f56,f51]) ).
thf(f62,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: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y2 ) )
@ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f53,f50,f56,f56,f56,f51,f55]) ).
thf(f64,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y2 @ mactual ) )
=> ( subset @ Y0 @ Y2 @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f65,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y2 @ mactual ) )
=> ( subset @ Y0 @ Y2 @ mactual ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f64]) ).
thf(f66,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ sK1 @ Y0 @ mactual )
& ( subset @ Y0 @ Y1 @ mactual ) )
=> ( subset @ sK1 @ Y1 @ mactual ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ sK1 @ Y0 @ mactual )
& ( subset @ Y0 @ Y1 @ mactual ) )
=> ( subset @ sK1 @ Y1 @ mactual ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ sK1 @ sK2 @ mactual )
& ( subset @ sK2 @ Y0 @ mactual ) )
=> ( subset @ sK1 @ Y0 @ mactual ) ) )
= $false ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( ( ^ [Y0: $i] :
( ( ( subset @ sK1 @ sK2 @ mactual )
& ( subset @ sK2 @ Y0 @ mactual ) )
=> ( subset @ sK1 @ Y0 @ mactual ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( $false
= ( ( ( subset @ sK1 @ sK2 @ mactual )
& ( subset @ sK2 @ sK3 @ mactual ) )
=> ( subset @ sK1 @ sK3 @ mactual ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( ( subset @ sK1 @ sK3 @ mactual )
= $false ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( $true
= ( ( subset @ sK1 @ sK2 @ mactual )
& ( subset @ sK2 @ sK3 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( $true
= ( subset @ sK2 @ sK3 @ mactual ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( ( subset @ sK1 @ sK2 @ mactual )
= $true ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f75,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y2 @ Y0 @ mactual )
=> ( member @ Y2 @ Y1 @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f76,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y2 @ Y0 @ mactual )
=> ( member @ Y2 @ Y1 @ mactual ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( member @ Y1 @ X1 @ mactual )
=> ( member @ Y1 @ Y0 @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( member @ Y1 @ X1 @ mactual )
=> ( member @ Y1 @ Y0 @ mactual ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( subset @ X1 @ X2 @ mactual )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) )
= ( subset @ X1 @ X2 @ mactual ) ),
inference(iff_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) ) )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 @ mactual ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f80]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) )
@ ( sK4 @ X1 @ X2 ) )
= $false )
| ( $true
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(sigma_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 @ mactual ) )
| ( ( ( member @ ( sK4 @ X1 @ X2 ) @ X1 @ mactual )
=> ( member @ ( sK4 @ X1 @ X2 ) @ X2 @ mactual ) )
= $false ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X1: $i] :
( ( ( member @ ( sK4 @ X1 @ X2 ) @ X2 @ mactual )
= $false )
| ( $true
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X1: $i] :
( ( ( member @ ( sK4 @ X1 @ X2 ) @ X1 @ mactual )
= $true )
| ( $true
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) )
@ X3 ) )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( member @ X3 @ X1 @ mactual )
=> ( member @ X3 @ X2 @ mactual ) ) )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( member @ X3 @ X2 @ mactual ) )
| ( ( member @ X3 @ X1 @ mactual )
= $false )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f99,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( member @ ( sK4 @ X0 @ X1 ) @ X2 @ mactual )
= $false )
| ( $true = $false )
| ( $false
= ( subset @ X2 @ X1 @ mactual ) ) ),
inference(constrained_superposition,[],[f89,f85]) ).
thf(f101,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( member @ ( sK4 @ X0 @ X1 ) @ X2 @ mactual ) )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( subset @ X0 @ X2 @ mactual )
= $false ) ),
inference(constrained_superposition,[],[f89,f86]) ).
thf(f108,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( member @ ( sK4 @ X0 @ X1 ) @ X2 @ mactual ) )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( subset @ X0 @ X2 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f109,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( member @ ( sK4 @ X0 @ X1 ) @ X2 @ mactual )
= $false )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( $false
= ( subset @ X2 @ X1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f123,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( $false
= ( subset @ X2 @ X1 @ mactual ) )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( subset @ X0 @ X2 @ mactual )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f109,f108]) ).
thf(f132,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ X2 @ mactual )
= $false )
| ( $false
= ( subset @ X2 @ X1 @ mactual ) )
| ( $true = $false )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) ) ),
inference(duplicate_literal_removal,[],[f123]) ).
thf(f133,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 @ mactual ) )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( subset @ X0 @ X2 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f148,plain,
! [X0: $i] :
( ( $false
= ( subset @ X0 @ sK2 @ mactual ) )
| ( $true
= ( subset @ X0 @ sK3 @ mactual ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f73,f133]) ).
thf(f154,plain,
! [X0: $i] :
( ( $true
= ( subset @ X0 @ sK3 @ mactual ) )
| ( $false
= ( subset @ X0 @ sK2 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f166,plain,
( ( $true = $false )
| ( ( subset @ sK1 @ sK2 @ mactual )
= $false ) ),
inference(constrained_superposition,[],[f154,f71]) ).
thf(f175,plain,
( ( subset @ sK1 @ sK2 @ mactual )
= $false ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f182,plain,
$true = $false,
inference(forward_demodulation,[],[f175,f74]) ).
thf(f183,plain,
$false,
inference(trivial_inequality_removal,[],[f182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET027^3 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n008.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 13:36:09 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.29 Running higher-order theorem proving
% 0.23/0.30 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
% 0.23/0.37 % (3155907)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.37 % (3155915)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=386329583: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_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.37 % (3155916)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1526119613:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.37 % (3155918)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.37 % (3155918)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
% 0.23/0.37 % (3155912)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4218958864:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.37 % (3155914)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1856671403:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.37 % (3155913)lrs+10_16_si=on:nwc=1.5:random_seed=1839722718:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.37 % (3155917)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2987425998:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.37 % (3155918)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=3525945406:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.37 % (3155914)Instruction limit reached!
% 0.23/0.37 % (3155914)------------------------------
% 0.23/0.37 % (3155914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3155914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3155914)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3155914)Termination reason: Instruction limit
% 0.23/0.37 % (3155914)Termination phase: Saturation
% 0.23/0.37 % (3155914)Time elapsed: 0.003 s
% 0.23/0.37 % (3155914)Peak memory usage: 11 MB
% 0.23/0.37 % (3155914)Instructions burned: 3 (million)
% 0.23/0.37 % (3155912) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3155907-3155912"...
% 0.23/0.37 % (3155918) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3155907-3155918"...
% 0.23/0.37 % (3155916)Instruction limit reached!
% 0.23/0.37 % (3155916)------------------------------
% 0.23/0.37 % (3155916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3155916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3155916)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3155916)Termination reason: Instruction limit
% 0.23/0.37 % (3155916)Termination phase: Saturation
% 0.23/0.37 % (3155916)Time elapsed: 0.024 s
% 0.23/0.37 % (3155916)Peak memory usage: 12 MB
% 0.23/0.37 % (3155916)Instructions burned: 24 (million)
% 0.23/0.37 % (3155913) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3155907-3155913"...
% 0.23/0.37 % (3155912)...printing done.
% 0.23/0.37 % (3155912)Refutation found. Thanks to Tanya!
% 0.23/0.37 % SZS status Theorem for theBenchmark
% 0.23/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.37 % (3155912)------------------------------
% 0.23/0.37 % (3155912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3155912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3155912)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3155912)Termination reason: Refutation
% 0.23/0.37 % (3155912)Time elapsed: 0.018 s
% 0.23/0.37 % (3155912)Peak memory usage: 12 MB
% 0.23/0.37 % (3155912)Instructions burned: 18 (million)
% 0.23/0.37 % (3155907)Success in time 0.056 s
% 0.23/0.37 % Vampire exiting
%------------------------------------------------------------------------------