%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI004^4 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:20:17 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of formulae : 130 ( 23 unt; 0 typ; 7 def)
% Number of atoms : 659 ( 156 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 979 ( 95 ~; 129 |; 8 &; 612 @)
% ( 7 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 220 ( 220 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 15 con; 0-4 aty)
% ( 53 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 182 ( 0 sgn 73 !; 2 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
qML_mu: $tType ).
thf(type_def_6,type,
qML_i: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
scott_G: qML_mu > qML_i > $o ).
thf(func_def_1,type,
scott_NE_QML_mu: qML_mu > qML_i > $o ).
thf(func_def_2,type,
scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
thf(func_def_3,type,
scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
thf(func_def_5,type,
vNOT: $o > $o ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_15,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
sK0: qML_i > qML_mu ).
thf(func_def_18,type,
sK1: ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_mu ).
thf(func_def_19,type,
sK2: ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_i ).
thf(func_def_20,type,
sK3: qML_mu ).
thf(func_def_21,type,
sK4: qML_i ).
thf(func_def_22,type,
sK5: qML_mu > qML_i > $o ).
thf(func_def_23,type,
sK6: qML_mu > qML_i > $o ).
thf(func_def_24,type,
sK7: qML_i ).
thf(func_def_25,type,
sK8: qML_mu ).
thf(func_def_26,type,
sK9: qML_mu ).
thf(func_def_27,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db4:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( ( ^ [X0: qML_mu,X1: qML_i] :
! [X2: qML_mu > qML_i > $o] :
( ( scott_P @ X2 @ X1 )
=> ( X2 @ X0 @ X1 ) ) )
= scott_G ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_G__def) ).
thf(f3,axiom,
! [X1: qML_mu > qML_i > $o,X0: qML_i] :
( ( scott_P @ X1 @ X0 )
=> ! [X2: qML_i] : ( scott_P @ X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_A4) ).
thf(f5,axiom,
( ( ^ [X0: qML_mu > qML_i > $o,X1: qML_mu,X2: qML_i] :
( ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X1 @ X2 )
=> ! [X5: qML_mu,X4: qML_i] :
( ( X0 @ X5 @ X4 )
=> ( X3 @ X5 @ X4 ) ) )
& ( X0 @ X1 @ X2 ) ) )
= scott_ess_QML_mu ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_ess__def) ).
thf(f6,axiom,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X1 @ X0 )
=> ( scott_P
@ ^ [X2: qML_mu,X3: qML_i] :
~ ( X1 @ X2 @ X3 )
@ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_A1b) ).
thf(f11,conjecture,
! [X1: qML_mu,X0: qML_i] :
( ( scott_ess_QML_mu @ scott_G @ X1 @ X0 )
| ~ ( scott_G @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f12,negated_conjecture,
~ ! [X1: qML_mu,X0: qML_i] :
( ( scott_ess_QML_mu @ scott_G @ X1 @ X0 )
| ~ ( scott_G @ X1 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f17,plain,
~ ! [X0: qML_mu,X1: qML_i] :
( ( scott_ess_QML_mu @ scott_G @ X0 @ X1 )
| ~ ( scott_G @ X0 @ X1 ) ),
inference(rectify,[],[f12]) ).
thf(f18,plain,
~ ! [X0: qML_mu,X1: qML_i] :
( ( $true
= ( scott_ess_QML_mu @ scott_G @ X0 @ X1 ) )
| ( $true
!= ( scott_G @ X0 @ X1 ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f23,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( scott_P @ X0 @ X1 )
=> ! [X2: qML_i] : ( scott_P @ X0 @ X2 ) ),
inference(rectify,[],[f3]) ).
thf(f24,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( $true
= ( scott_P @ X0 @ X1 ) )
=> ! [X2: qML_i] :
( $true
= ( scott_P @ X0 @ X2 ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( ( ^ [X0: qML_mu,X1: qML_i] :
! [X2: qML_mu > qML_i > $o] :
( ( scott_P @ X2 @ X1 )
=> ( X2 @ X0 @ X1 ) ) )
= scott_G ),
inference(rectify,[],[f1]) ).
thf(f26,plain,
( scott_G
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X1 @ X0 )
=> ( scott_P
@ ^ [X2: qML_mu,X3: qML_i] :
~ ( X1 @ X2 @ X3 )
@ X0 ) ),
inference(rectify,[],[f6]) ).
thf(f28,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( ( scott_P @ X1 @ X0 )
!= $true )
=> ( $true
= ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X1 @ Y0 @ Y1 )
@ X0 ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
( ( ^ [X0: qML_mu > qML_i > $o,X1: qML_mu,X2: qML_i] :
( ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X1 @ X2 )
=> ! [X4: qML_mu,X5: qML_i] :
( ( X0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
& ( X0 @ X1 @ X2 ) ) )
= scott_ess_QML_mu ),
inference(rectify,[],[f5]) ).
thf(f30,plain,
( scott_ess_QML_mu
= ( ^ [Y0: qML_mu > qML_i > $o,Y1: qML_mu,Y2: qML_i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( Y3 @ Y1 @ Y2 )
=> ( !! @ qML_i
@ ^ [Y4: qML_i] :
( !! @ qML_mu
@ ^ [Y5: qML_mu] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f36,plain,
~ ! [X0: qML_mu,X1: qML_i] :
( ( $true
!= ( scott_G @ X0 @ X1 ) )
| ( $true
= ( scott_ess_QML_mu @ scott_G @ X0 @ X1 ) ) ),
inference(flattening,[],[f18]) ).
thf(f37,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( ( scott_P @ X1 @ X0 )
!= $true )
=> ( $true
= ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X1 @ Y0 @ Y1 )
@ X0 ) ) ),
inference(flattening,[],[f28]) ).
thf(f41,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( $true
= ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X1 @ Y0 @ Y1 )
@ X0 ) )
| ( ( scott_P @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f37]) ).
thf(f42,plain,
? [X0: qML_mu,X1: qML_i] :
( ( $true
= ( scott_G @ X0 @ X1 ) )
& ( $true
!= ( scott_ess_QML_mu @ scott_G @ X0 @ X1 ) ) ),
inference(ennf_transformation,[],[f36]) ).
thf(f43,plain,
! [X1: qML_i,X0: qML_mu > qML_i > $o] :
( ! [X2: qML_i] :
( $true
= ( scott_P @ X0 @ X2 ) )
| ( $true
!= ( scott_P @ X0 @ X1 ) ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f47,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ! [X2: qML_i] :
( ( scott_P @ X1 @ X2 )
= $true )
| ( ( scott_P @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f43]) ).
thf(f50,plain,
( ( $true
= ( scott_G @ sK3 @ sK4 ) )
& ( $true
!= ( scott_ess_QML_mu @ scott_G @ sK3 @ sK4 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f42]) ).
thf(f52,plain,
( scott_G
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f54,plain,
( scott_ess_QML_mu
= ( ^ [Y0: qML_mu > qML_i > $o,Y1: qML_mu,Y2: qML_i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( Y3 @ Y1 @ Y2 )
=> ( !! @ qML_i
@ ^ [Y4: qML_i] :
( !! @ qML_mu
@ ^ [Y5: qML_mu] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f57,plain,
! [X2: qML_i,X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( ( scott_P @ X1 @ X0 )
!= $true )
| ( ( scott_P @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f61,plain,
( $true
!= ( scott_ess_QML_mu @ scott_G @ sK3 @ sK4 ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f62,plain,
( $true
= ( scott_G @ sK3 @ sK4 ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f63,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( $true
= ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X1 @ Y0 @ Y1 )
@ X0 ) )
| ( ( scott_P @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f70,plain,
( $true
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK3
@ sK4 ) ),
inference(definition_unfolding,[],[f62,f52]) ).
thf(f71,plain,
( $true
!= ( ^ [Y0: qML_mu > qML_i > $o,Y1: qML_mu,Y2: qML_i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( Y3 @ Y1 @ Y2 )
=> ( !! @ qML_i
@ ^ [Y4: qML_i] :
( !! @ qML_mu
@ ^ [Y5: qML_mu] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) )
@ ^ [Y0: qML_mu,Y1: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK3
@ sK4 ) ),
inference(definition_unfolding,[],[f61,f54,f52]) ).
thf(f72,plain,
( $true
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK4 )
=> ( Y0 @ sK3 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f73,plain,
! [X1: qML_mu > qML_i > $o] :
( $true
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK4 )
=> ( Y0 @ sK3 @ sK4 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X1: qML_mu > qML_i > $o] :
( $true
= ( ( scott_P @ X1 @ sK4 )
=> ( X1 @ sK3 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( scott_P @ X1 @ sK4 ) )
| ( ( X1 @ sK3 @ sK4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( $true
!= ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK4 )
=> ( Y0 @ sK3 @ sK4 ) ) )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK3 @ sK4 )
=> ( !! @ qML_i
@ ^ [Y1: qML_i] :
( !! @ qML_mu
@ ^ [Y2: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f77,plain,
( ( $false
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK4 )
=> ( Y0 @ sK3 @ sK4 ) ) ) )
| ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK3 @ sK4 )
=> ( !! @ qML_i
@ ^ [Y1: qML_i] :
( !! @ qML_mu
@ ^ [Y2: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( ( $false
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK4 )
=> ( Y0 @ sK3 @ sK4 ) )
@ sK5 ) )
| ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK3 @ sK4 )
=> ( !! @ qML_i
@ ^ [Y1: qML_i] :
( !! @ qML_mu
@ ^ [Y2: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( $false
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK4 )
=> ( Y0 @ sK3 @ sK4 ) )
@ sK5 ) )
| ( ( ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK3 @ sK4 )
=> ( !! @ qML_i
@ ^ [Y1: qML_i] :
( !! @ qML_mu
@ ^ [Y2: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( ( ( ( sK6 @ sK3 @ sK4 )
=> ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ( scott_P @ sK5 @ sK4 )
=> ( sK5 @ sK3 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
( ( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( scott_P @ sK5 @ sK4 )
=> ( sK5 @ sK3 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( ( ( sK6 @ sK3 @ sK4 )
= $true )
| ( $false
= ( ( scott_P @ sK5 @ sK4 )
=> ( sK5 @ sK3 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f83,plain,
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ( ( sK6 @ sK3 @ sK4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ( $true
= ( scott_P @ sK5 @ sK4 ) )
| ( ( sK6 @ sK3 @ sK4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f85,plain,
( ( $false
= ( ( scott_P @ sK5 @ sK4 )
=> ( sK5 @ sK3 @ sK4 ) ) )
| ( $false
= ( ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f81]) ).
thf(f86,plain,
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ( $false
= ( ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( $false
= ( ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK7 ) )
| ( $true
= ( scott_P @ sK5 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f88,plain,
( ( ( !! @ qML_mu
@ ^ [Y0: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ sK7 )
=> ( Y1 @ Y0 @ sK7 ) ) )
=> ( sK6 @ Y0 @ sK7 ) ) )
= $false )
| ( $true
= ( scott_P @ sK5 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
( ( ( ^ [Y0: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ sK7 )
=> ( Y1 @ Y0 @ sK7 ) ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK8 )
= $false )
| ( $true
= ( scott_P @ sK5 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f88]) ).
thf(f90,plain,
( ( $true
= ( scott_P @ sK5 @ sK4 ) )
| ( $false
= ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK7 )
=> ( Y0 @ sK8 @ sK7 ) ) )
=> ( sK6 @ sK8 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
( ( $true
= ( scott_P @ sK5 @ sK4 ) )
| ( ( sK6 @ sK8 @ sK7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f92,plain,
( ( $true
= ( scott_P @ sK5 @ sK4 ) )
| ( $true
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK7 )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f93,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK7 )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 ) )
| ( $true
= ( scott_P @ sK5 @ sK4 ) ) ),
inference(pi_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( scott_P @ sK5 @ sK4 ) )
| ( ( ( scott_P @ X1 @ sK7 )
=> ( X1 @ sK8 @ sK7 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( scott_P @ sK5 @ sK4 ) )
| ( $true
= ( X1 @ sK8 @ sK7 ) )
| ( $false
= ( scott_P @ X1 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( ( ( !! @ qML_mu
@ ^ [Y0: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ sK7 )
=> ( Y1 @ Y0 @ sK7 ) ) )
=> ( sK6 @ Y0 @ sK7 ) ) )
= $false )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f97,plain,
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ( ( ^ [Y0: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ sK7 )
=> ( Y1 @ Y0 @ sK7 ) ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK9 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f96]) ).
thf(f98,plain,
( ( ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK7 )
=> ( Y0 @ sK9 @ sK7 ) ) )
=> ( sK6 @ sK9 @ sK7 ) )
= $false )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ( $false
= ( sK6 @ sK9 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( ( $true
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK7 )
=> ( Y0 @ sK9 @ sK7 ) ) ) )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f98]) ).
thf(f101,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK7 )
=> ( Y0 @ sK9 @ sK7 ) )
@ X1 ) )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(pi_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( ( scott_P @ X1 @ sK7 )
=> ( X1 @ sK9 @ sK7 ) ) )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f103,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ( $true
= ( X1 @ sK9 @ sK7 ) )
| ( $false
= ( scott_P @ X1 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f110,definition,
( spl10_1
<=> ( ( sK6 @ sK3 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f112,plain,
( ( ( sK6 @ sK3 @ sK4 )
= $true )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f114,definition,
( spl10_2
<=> ( $true
= ( scott_P @ sK5 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f116,plain,
( ( $true
= ( scott_P @ sK5 @ sK4 ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f114]) ).
thf(f117,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f84,f114,f110]) ).
thf(f119,definition,
( spl10_3
<=> ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f121,plain,
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f122,plain,
( spl10_3
| spl10_1 ),
inference(avatar_split_clause,[],[f83,f110,f119]) ).
thf(f124,definition,
( spl10_4
<=> ! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( X1 @ sK8 @ sK7 ) )
| ( $false
= ( scott_P @ X1 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f125,plain,
( ! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( scott_P @ X1 @ sK7 ) )
| ( $true
= ( X1 @ sK8 @ sK7 ) ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f126,plain,
( spl10_4
| spl10_2 ),
inference(avatar_split_clause,[],[f95,f114,f124]) ).
thf(f128,definition,
( spl10_5
<=> ( ( sK6 @ sK8 @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f130,plain,
( ( ( sK6 @ sK8 @ sK7 )
= $false )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f131,plain,
( spl10_5
| spl10_2 ),
inference(avatar_split_clause,[],[f91,f114,f128]) ).
thf(f133,definition,
( spl10_6
<=> ! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( X1 @ sK9 @ sK7 ) )
| ( $false
= ( scott_P @ X1 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f134,plain,
( ! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( scott_P @ X1 @ sK7 ) )
| ( $true
= ( X1 @ sK9 @ sK7 ) ) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f133]) ).
thf(f135,plain,
( spl10_3
| spl10_6 ),
inference(avatar_split_clause,[],[f103,f133,f119]) ).
thf(f137,definition,
( spl10_7
<=> ( $false
= ( sK6 @ sK9 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f139,plain,
( ( $false
= ( sK6 @ sK9 @ sK7 ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f140,plain,
( spl10_7
| spl10_3 ),
inference(avatar_split_clause,[],[f99,f119,f137]) ).
thf(f141,plain,
( ( $true = $false )
| ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ~ spl10_2 ),
inference(constrained_superposition,[],[f116,f75]) ).
thf(f142,plain,
( ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ( $true = $false )
| ~ spl10_2 ),
inference(constrained_superposition,[],[f75,f116]) ).
thf(f143,plain,
( ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f141]) ).
thf(f144,plain,
( ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f142]) ).
thf(f145,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_3 ),
inference(forward_demodulation,[],[f143,f121]) ).
thf(f146,plain,
( $false
| ~ spl10_2
| ~ spl10_3 ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f147,plain,
( ~ spl10_2
| ~ spl10_3 ),
inference(avatar_contradiction_clause,[],[f146]) ).
thf(f148,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_3 ),
inference(forward_demodulation,[],[f144,f121]) ).
thf(f149,plain,
( $false
| ~ spl10_2
| ~ spl10_3 ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f150,plain,
( ~ spl10_2
| ~ spl10_3 ),
inference(avatar_contradiction_clause,[],[f149]) ).
thf(f210,plain,
! [X0: qML_mu > qML_i > $o] :
( ( $true = $false )
| ( $true
= ( scott_P @ X0 @ sK4 ) )
| ( $true
= ( ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ sK3
@ sK4 ) ) ),
inference(constrained_superposition,[],[f63,f75]) ).
thf(f223,plain,
! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ sK3
@ sK4 ) )
| ( $true
= ( scott_P @ X0 @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f210]) ).
thf(f224,plain,
! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( ~ ( X0 @ sK3 @ sK4 ) ) )
| ( $true
= ( scott_P @ X0 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f225,plain,
! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( scott_P @ X0 @ sK4 ) )
| ( ( X0 @ sK3 @ sK4 )
= $false ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f243,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( X0 @ sK3 @ sK4 )
= $false )
| ( $true != $true )
| ( $true
= ( scott_P @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f57,f225]) ).
thf(f259,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( $true
= ( scott_P @ X0 @ X1 ) )
| ( ( X0 @ sK3 @ sK4 )
= $false ) ),
inference(trivial_inequality_removal,[],[f243]) ).
thf(f341,plain,
( ! [X0: qML_mu > qML_i > $o] :
( ( ( X0 @ sK3 @ sK4 )
= $false )
| ( $true
= ( X0 @ sK9 @ sK7 ) )
| ( $true = $false ) )
| ~ spl10_6 ),
inference(constrained_superposition,[],[f259,f134]) ).
thf(f351,plain,
( ! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( X0 @ sK9 @ sK7 ) )
| ( ( X0 @ sK3 @ sK4 )
= $false ) )
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f341]) ).
thf(f385,plain,
( ( $true = $false )
| ( ( sK6 @ sK3 @ sK4 )
= $false )
| ~ spl10_6
| ~ spl10_7 ),
inference(constrained_superposition,[],[f139,f351]) ).
thf(f392,plain,
( ( ( sK6 @ sK3 @ sK4 )
= $false )
| ~ spl10_6
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f385]) ).
thf(f396,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_6
| ~ spl10_7 ),
inference(forward_demodulation,[],[f392,f112]) ).
thf(f397,plain,
( $false
| ~ spl10_1
| ~ spl10_6
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f396]) ).
thf(f398,plain,
( ~ spl10_1
| ~ spl10_6
| ~ spl10_7 ),
inference(avatar_contradiction_clause,[],[f397]) ).
thf(f418,plain,
( ! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( X0 @ sK8 @ sK7 ) )
| ( $true = $false )
| ( ( X0 @ sK3 @ sK4 )
= $false ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f125,f259]) ).
thf(f428,plain,
( ! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( X0 @ sK8 @ sK7 ) )
| ( ( X0 @ sK3 @ sK4 )
= $false ) )
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f418]) ).
thf(f457,plain,
( ( ( sK6 @ sK3 @ sK4 )
= $false )
| ( $true = $false )
| ~ spl10_4
| ~ spl10_5 ),
inference(constrained_superposition,[],[f130,f428]) ).
thf(f461,plain,
( ( ( sK6 @ sK3 @ sK4 )
= $false )
| ~ spl10_4
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f457]) ).
thf(f468,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_4
| ~ spl10_5 ),
inference(forward_demodulation,[],[f461,f112]) ).
thf(f469,plain,
( $false
| ~ spl10_1
| ~ spl10_4
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f468]) ).
thf(f470,plain,
( ~ spl10_1
| ~ spl10_4
| ~ spl10_5 ),
inference(avatar_contradiction_clause,[],[f469]) ).
cnf(s1,plain,
( spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f117]) ).
cnf(s2,plain,
( spl10_1
| spl10_3 ),
inference(sat_conversion,[],[f122]) ).
cnf(s3,plain,
( spl10_2
| spl10_4 ),
inference(sat_conversion,[],[f126]) ).
cnf(s4,plain,
( spl10_2
| spl10_5 ),
inference(sat_conversion,[],[f131]) ).
cnf(s5,plain,
( spl10_3
| spl10_6 ),
inference(sat_conversion,[],[f135]) ).
cnf(s6,plain,
( spl10_3
| spl10_7 ),
inference(sat_conversion,[],[f140]) ).
cnf(s7,plain,
( ~ spl10_2
| ~ spl10_3 ),
inference(sat_conversion,[],[f147]) ).
cnf(s8,plain,
( ~ spl10_2
| ~ spl10_3 ),
inference(sat_conversion,[],[f150]) ).
cnf(s10,plain,
( ~ spl10_1
| ~ spl10_6
| ~ spl10_7 ),
inference(sat_conversion,[],[f398]) ).
cnf(s13,plain,
( ~ spl10_1
| ~ spl10_4
| ~ spl10_5 ),
inference(sat_conversion,[],[f470]) ).
cnf(s14,plain,
spl10_1,
inference(rat,[],[s7,s1,s2]) ).
cnf(s15,plain,
spl10_3,
inference(rat,[],[s10,s5,s6,s14]) ).
cnf(s16,plain,
~ spl10_2,
inference(rat,[],[s8,s15]) ).
cnf(s17,plain,
spl10_5,
inference(rat,[],[s4,s16]) ).
cnf(s18,plain,
spl10_4,
inference(rat,[],[s3,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s13,s14,s17,s18]) ).
thf(f471,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI004^4 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:16:51 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.29 % (2082408)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (2082415)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1449326545:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (2082415)Instruction limit reached!
% 0.21/0.29 % (2082415)------------------------------
% 0.21/0.29 % (2082415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2082415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2082415)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2082415)Termination reason: Instruction limit
% 0.21/0.29 % (2082415)Termination phase: Saturation
% 0.21/0.29 % (2082415)Time elapsed: 0.003 s
% 0.21/0.29 % (2082415)Peak memory usage: 12 MB
% 0.21/0.29 % (2082415)Instructions burned: 9 (million)
% 0.21/0.29 % (2082419)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (2082419)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
% 0.21/0.29 % (2082414)lrs+10_16_si=on:nwc=1.5:random_seed=1209343978:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (2082413)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2712974806:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (2082416)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=501392032: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)
% 0.21/0.29 % (2082417)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1824566854:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (2082419)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=3025696599:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (2082414)Instruction limit reached!
% 0.21/0.29 % (2082414)------------------------------
% 0.21/0.29 % (2082414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2082414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2082414)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2082414)Termination reason: Instruction limit
% 0.21/0.29 % (2082414)Termination phase: Saturation
% 0.21/0.29 % (2082414)Time elapsed: 0.010 s
% 0.21/0.29 % (2082414)Peak memory usage: 12 MB
% 0.21/0.29 % (2082414)Instructions burned: 19 (million)
% 0.21/0.29 % (2082413) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2082408-2082413"...
% 0.21/0.29 % (2082419) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2082408-2082419"...
% 0.21/0.29 % (2082418)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=795765306:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (2082417)Instruction limit reached!
% 0.21/0.29 % (2082417)------------------------------
% 0.21/0.29 % (2082417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2082417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2082417)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2082417)Termination reason: Instruction limit
% 0.21/0.29 % (2082417)Termination phase: Saturation
% 0.21/0.29 % (2082417)Time elapsed: 0.014 s
% 0.21/0.29 % (2082417)Peak memory usage: 12 MB
% 0.21/0.29 % (2082417)Instructions burned: 25 (million)
% 0.21/0.29 % (2082413)...printing done.
% 0.21/0.29 % (2082413)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (2082413)------------------------------
% 0.21/0.29 % (2082413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2082413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2082413)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2082413)Termination reason: Refutation
% 0.21/0.29 % (2082413)Time elapsed: 0.016 s
% 0.21/0.29 % (2082413)Peak memory usage: 13 MB
% 0.21/0.29 % (2082413)Instructions burned: 27 (million)
% 0.21/0.29 % (2082408)Success in time 0.052 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------