%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n011.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 08:20:20 AM UTC 2026
% Result : Theorem 2.79s 0.68s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 12
% Syntax : Number of formulae : 129 ( 23 unt; 0 typ; 7 def)
% Number of atoms : 666 ( 162 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 1042 ( 102 ~; 137 |; 8 &; 660 @)
% ( 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 : 230 ( 230 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 37 usr; 15 con; 0-4 aty)
% ( 53 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 205 ( 6 sgn 76 !; 2 ?; 205 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vNOT: $o > $o ).
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_i ).
thf(func_def_19,type,
sK2: ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_mu ).
thf(func_def_20,type,
sK3: qML_i ).
thf(func_def_21,type,
sK4: qML_mu ).
thf(func_def_22,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sK5: qML_mu > qML_i > $o ).
thf(func_def_24,type,
sK6: qML_mu > qML_i > $o ).
thf(func_def_25,type,
sK7: qML_mu ).
thf(func_def_26,type,
sK8: qML_i ).
thf(func_def_27,type,
sK9: qML_i ).
thf(func_def_28,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
sK11: qML_i > ( qML_mu > qML_i > qML_mu > qML_i > $o ) > qML_mu ).
thf(func_def_31,type,
sK12: ( qML_mu > qML_i > qML_mu > qML_i > $o ) > qML_i > qML_mu ).
thf(func_def_32,type,
sK13: ( qML_mu > qML_i > qML_mu > qML_i > $o ) > qML_i > qML_mu ).
thf(f1,axiom,
( scott_G
= ( ^ [X0: qML_mu,X1: qML_i] :
! [X2: qML_mu > qML_i > $o] :
( ( scott_P @ X2 @ X1 )
=> ( X2 @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_G__def) ).
thf(f3,axiom,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( scott_P @ X1 @ X0 )
=> ! [X2: qML_i] : ( scott_P @ X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_A4) ).
thf(f5,axiom,
( scott_ess_QML_mu
= ( ^ [X0: qML_mu > qML_i > $o,X1: qML_mu,X2: qML_i] :
( ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X1 @ X2 )
=> ! [X4: qML_i,X5: qML_mu] :
( ( X0 @ X5 @ X4 )
=> ( X3 @ X5 @ X4 ) ) )
& ( X0 @ X1 @ X2 ) ) ) ),
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,
! [X0: qML_i,X1: qML_mu] :
( ( 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,
~ ! [X0: qML_i,X1: qML_mu] :
( ( scott_ess_QML_mu @ scott_G @ X1 @ X0 )
| ~ ( scott_G @ X1 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f13,plain,
( scott_G
= ( ^ [X0: qML_mu,X1: qML_i] :
! [X2: qML_mu > qML_i > $o] :
( ( scott_P @ X2 @ X1 )
=> ( X2 @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f14,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,[],[f13]) ).
thf(f17,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( scott_P @ X1 @ X0 )
=> ! [X2: qML_i] : ( scott_P @ X1 @ X2 ) ),
inference(rectify,[],[f3]) ).
thf(f18,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( ( scott_P @ X1 @ X0 )
= $true )
=> ! [X2: qML_i] :
( ( scott_P @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f17]) ).
thf(f21,plain,
( scott_ess_QML_mu
= ( ^ [X0: qML_mu > qML_i > $o,X1: qML_mu,X2: qML_i] :
( ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X1 @ X2 )
=> ! [X4: qML_i,X5: qML_mu] :
( ( X0 @ X5 @ X4 )
=> ( X3 @ X5 @ X4 ) ) )
& ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f22,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_mu
@ ^ [Y4: qML_mu] :
( !! @ qML_i
@ ^ [Y5: qML_i] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,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(f24,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,[],[f23]) ).
thf(f33,plain,
~ ! [X0: qML_i,X1: qML_mu] :
( ( scott_ess_QML_mu @ scott_G @ X1 @ X0 )
| ~ ( scott_G @ X1 @ X0 ) ),
inference(rectify,[],[f12]) ).
thf(f34,plain,
~ ! [X0: qML_i,X1: qML_mu] :
( ( ( scott_ess_QML_mu @ scott_G @ X1 @ X0 )
= $true )
| ( ( scott_G @ X1 @ X0 )
!= $true ) ),
inference(fool_elimination,[],[f33]) ).
thf(f36,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,[],[f24]) ).
thf(f38,plain,
~ ! [X0: qML_i,X1: qML_mu] :
( ( ( scott_ess_QML_mu @ scott_G @ X1 @ X0 )
= $true )
| ( ( scott_G @ X1 @ X0 )
!= $true ) ),
inference(flattening,[],[f34]) ).
thf(f39,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ! [X2: qML_i] :
( ( scott_P @ X1 @ X2 )
= $true )
| ( ( scott_P @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f40,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,[],[f36]) ).
thf(f44,plain,
? [X0: qML_i,X1: qML_mu] :
( ( ( scott_ess_QML_mu @ scott_G @ X1 @ X0 )
!= $true )
& ( ( scott_G @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f38]) ).
thf(f47,plain,
( ( $true
!= ( scott_ess_QML_mu @ scott_G @ sK4 @ sK3 ) )
& ( $true
= ( scott_G @ sK4 @ sK3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f44]) ).
thf(f48,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,[],[f14]) ).
thf(f50,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,[],[f39]) ).
thf(f52,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_mu
@ ^ [Y4: qML_mu] :
( !! @ qML_i
@ ^ [Y5: qML_i] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f53,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,[],[f40]) ).
thf(f59,plain,
( $true
= ( scott_G @ sK4 @ sK3 ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f60,plain,
( $true
!= ( scott_ess_QML_mu @ scott_G @ sK4 @ sK3 ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f67,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_mu
@ ^ [Y4: qML_mu] :
( !! @ qML_i
@ ^ [Y5: qML_i] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
@ ^ [Y0: qML_mu,Y1: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4
@ sK3 ) ),
inference(definition_unfolding,[],[f60,f52,f48]) ).
thf(f68,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 ) ) )
@ sK4
@ sK3 ) ),
inference(definition_unfolding,[],[f59,f48]) ).
thf(f69,plain,
( $true
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X1: qML_mu > qML_i > $o] :
( $true
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X1: qML_mu > qML_i > $o] :
( $true
= ( ( scott_P @ X1 @ sK3 )
=> ( X1 @ sK4 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( scott_P @ X1 @ sK3 ) )
| ( $true
= ( X1 @ sK4 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( $true
!= ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) ) )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK4 @ sK3 )
=> ( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( !! @ qML_i
@ ^ [Y2: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f74,plain,
( ( $false
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK4 @ sK3 )
=> ( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( !! @ qML_i
@ ^ [Y2: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( $false
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK4 @ sK3 )
=> ( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( !! @ qML_i
@ ^ [Y2: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK5 ) )
| ( $false
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( ( $false
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK4 @ sK3 )
=> ( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( !! @ qML_i
@ ^ [Y2: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( ( $false
= ( ( sK5 @ sK4 @ sK3 )
=> ( !! @ qML_mu
@ ^ [Y0: qML_mu] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( ( scott_P @ sK6 @ sK3 )
=> ( sK6 @ sK4 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
( ( $false
= ( !! @ qML_mu
@ ^ [Y0: qML_mu] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( ( scott_P @ sK6 @ sK3 )
=> ( sK6 @ sK4 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( $true
= ( sK5 @ sK4 @ sK3 ) )
| ( $false
= ( ( scott_P @ sK6 @ sK3 )
=> ( sK6 @ sK4 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( ( $true
= ( sK5 @ sK4 @ sK3 ) )
| ( $false
= ( sK6 @ sK4 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( ( $true
= ( sK5 @ sK4 @ sK3 ) )
| ( $true
= ( scott_P @ sK6 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f82,plain,
( ( $false
= ( ^ [Y0: qML_mu] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ sK7 ) )
| ( $false
= ( ( scott_P @ sK6 @ sK3 )
=> ( sK6 @ sK4 @ sK3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f78]) ).
thf(f83,plain,
( ( $false
= ( ^ [Y0: qML_mu] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ sK7 ) )
| ( $false
= ( sK6 @ sK4 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ( $false
= ( ^ [Y0: qML_mu] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ sK7 ) )
| ( $true
= ( scott_P @ sK6 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f85,plain,
( ( $false
= ( !! @ qML_i
@ ^ [Y0: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( Y1 @ sK7 @ Y0 ) ) )
=> ( sK5 @ sK7 @ Y0 ) ) ) )
| ( $true
= ( scott_P @ sK6 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
( ( $false
= ( ^ [Y0: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( Y1 @ sK7 @ Y0 ) ) )
=> ( sK5 @ sK7 @ Y0 ) )
@ sK8 ) )
| ( $true
= ( scott_P @ sK6 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( $false
= ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK8 )
=> ( Y0 @ sK7 @ sK8 ) ) )
=> ( sK5 @ sK7 @ sK8 ) ) )
| ( $true
= ( scott_P @ sK6 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f88,plain,
( ( $false
= ( sK5 @ sK7 @ sK8 ) )
| ( $true
= ( scott_P @ sK6 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f89,plain,
( ( $true
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK8 )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
| ( $true
= ( scott_P @ sK6 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f90,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK8 )
=> ( Y0 @ sK7 @ sK8 ) )
@ X1 ) )
| ( $true
= ( scott_P @ sK6 @ sK3 ) ) ),
inference(pi_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( ( scott_P @ X1 @ sK8 )
=> ( X1 @ sK7 @ sK8 ) ) )
| ( $true
= ( scott_P @ sK6 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( scott_P @ X1 @ sK8 ) )
| ( $true
= ( scott_P @ sK6 @ sK3 ) )
| ( $true
= ( X1 @ sK7 @ sK8 ) ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f93,plain,
( ( $false
= ( !! @ qML_i
@ ^ [Y0: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( Y1 @ sK7 @ Y0 ) ) )
=> ( sK5 @ sK7 @ Y0 ) ) ) )
| ( $false
= ( sK6 @ sK4 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f94,plain,
( ( $false
= ( ^ [Y0: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( Y1 @ sK7 @ Y0 ) ) )
=> ( sK5 @ sK7 @ Y0 ) )
@ sK9 ) )
| ( $false
= ( sK6 @ sK4 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f93]) ).
thf(f95,plain,
( ( $false
= ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK9 )
=> ( Y0 @ sK7 @ sK9 ) ) )
=> ( sK5 @ sK7 @ sK9 ) ) )
| ( $false
= ( sK6 @ sK4 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
( ( $false
= ( sK5 @ sK7 @ sK9 ) )
| ( $false
= ( sK6 @ sK4 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f95]) ).
thf(f97,plain,
( ( $true
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK9 )
=> ( Y0 @ sK7 @ sK9 ) ) ) )
| ( $false
= ( sK6 @ sK4 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f95]) ).
thf(f98,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK9 )
=> ( Y0 @ sK7 @ sK9 ) )
@ X1 ) )
| ( $false
= ( sK6 @ sK4 @ sK3 ) ) ),
inference(pi_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $true
= ( ( scott_P @ X1 @ sK9 )
=> ( X1 @ sK7 @ sK9 ) ) )
| ( $false
= ( sK6 @ sK4 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( scott_P @ X1 @ sK9 ) )
| ( $false
= ( sK6 @ sK4 @ sK3 ) )
| ( $true
= ( X1 @ sK7 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f107,definition,
( spl10_1
<=> ( $true
= ( scott_P @ sK6 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f109,plain,
( ( $true
= ( scott_P @ sK6 @ sK3 ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f107]) ).
thf(f111,definition,
( spl10_2
<=> ( $true
= ( sK5 @ sK4 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f113,plain,
( ( $true
= ( sK5 @ sK4 @ sK3 ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f114,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f81,f111,f107]) ).
thf(f116,definition,
( spl10_3
<=> ( $false
= ( sK6 @ sK4 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f118,plain,
( ( $false
= ( sK6 @ sK4 @ sK3 ) )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f116]) ).
thf(f119,plain,
( spl10_3
| spl10_2 ),
inference(avatar_split_clause,[],[f80,f111,f116]) ).
thf(f121,definition,
( spl10_4
<=> ! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( scott_P @ X1 @ sK8 ) )
| ( $true
= ( X1 @ sK7 @ sK8 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f122,plain,
( ! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( scott_P @ X1 @ sK8 ) )
| ( $true
= ( X1 @ sK7 @ sK8 ) ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f121]) ).
thf(f123,plain,
( spl10_1
| spl10_4 ),
inference(avatar_split_clause,[],[f92,f121,f107]) ).
thf(f125,definition,
( spl10_5
<=> ( $false
= ( sK5 @ sK7 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f127,plain,
( ( $false
= ( sK5 @ sK7 @ sK8 ) )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f125]) ).
thf(f128,plain,
( spl10_1
| spl10_5 ),
inference(avatar_split_clause,[],[f88,f125,f107]) ).
thf(f130,definition,
( spl10_6
<=> ! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( scott_P @ X1 @ sK9 ) )
| ( $true
= ( X1 @ sK7 @ sK9 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f131,plain,
( ! [X1: qML_mu > qML_i > $o] :
( ( $false
= ( scott_P @ X1 @ sK9 ) )
| ( $true
= ( X1 @ sK7 @ sK9 ) ) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f130]) ).
thf(f132,plain,
( spl10_3
| spl10_6 ),
inference(avatar_split_clause,[],[f100,f130,f116]) ).
thf(f134,definition,
( spl10_7
<=> ( $false
= ( sK5 @ sK7 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f136,plain,
( ( $false
= ( sK5 @ sK7 @ sK9 ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f134]) ).
thf(f137,plain,
( spl10_3
| spl10_7 ),
inference(avatar_split_clause,[],[f96,f134,f116]) ).
thf(f148,plain,
( ( $true = $false )
| ( $true
= ( sK6 @ sK4 @ sK3 ) )
| ~ spl10_1 ),
inference(constrained_superposition,[],[f72,f109]) ).
thf(f155,plain,
( ( $true
= ( sK6 @ sK4 @ sK3 ) )
| ~ spl10_1 ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f160,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_3 ),
inference(forward_demodulation,[],[f155,f118]) ).
thf(f161,plain,
( $false
| ~ spl10_1
| ~ spl10_3 ),
inference(trivial_inequality_removal,[],[f160]) ).
thf(f162,plain,
( ~ spl10_1
| ~ spl10_3 ),
inference(avatar_contradiction_clause,[],[f161]) ).
thf(f599,plain,
! [X0: qML_mu > qML_i > $o] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ sK4
@ sK3 ) )
| ( $true
= ( scott_P @ X0 @ sK3 ) ) ),
inference(constrained_superposition,[],[f72,f53]) ).
thf(f606,plain,
! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ sK4
@ sK3 ) )
| ( $true
= ( scott_P @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f599]) ).
thf(f607,plain,
! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( ~ ( X0 @ sK4 @ sK3 ) ) )
| ( $true
= ( scott_P @ X0 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f606]) ).
thf(f608,plain,
! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( scott_P @ X0 @ sK3 ) )
| ( $false
= ( X0 @ sK4 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f607]) ).
thf(f633,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( $true != $true )
| ( $true
= ( scott_P @ X0 @ X1 ) )
| ( $false
= ( X0 @ sK4 @ sK3 ) ) ),
inference(constrained_superposition,[],[f50,f608]) ).
thf(f650,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( $true
= ( scott_P @ X0 @ X1 ) )
| ( $false
= ( X0 @ sK4 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f633]) ).
thf(f772,plain,
( ! [X0: qML_mu > qML_i > $o] :
( ( $true = $false )
| ( $true
= ( X0 @ sK7 @ sK9 ) )
| ( $false
= ( X0 @ sK4 @ sK3 ) ) )
| ~ spl10_6 ),
inference(constrained_superposition,[],[f131,f650]) ).
thf(f783,plain,
( ! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( X0 @ sK7 @ sK9 ) )
| ( $false
= ( X0 @ sK4 @ sK3 ) ) )
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f772]) ).
thf(f889,plain,
( ! [X0: qML_mu > qML_i > qML_mu] :
( ( $true = $false )
| ( $false
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( sK5 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: qML_mu,Y3: qML_i] : Y3
@ Y0
@ Y1 ) )
@ sK4
@ sK3 ) )
| ( sK7
!= ( X0 @ sK7 @ sK9 ) ) )
| ~ spl10_6
| ~ spl10_7 ),
inference(constrained_superposition,[],[f136,f783]) ).
thf(f916,plain,
( ! [X0: qML_mu > qML_i > qML_mu] :
( ( $false
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( sK5 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: qML_mu,Y3: qML_i] : Y3
@ Y0
@ Y1 ) )
@ sK4
@ sK3 ) )
| ( sK7
!= ( X0 @ sK7 @ sK9 ) ) )
| ~ spl10_6
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f889]) ).
thf(f917,plain,
( ! [X0: qML_mu > qML_i > qML_mu] :
( ( sK7
!= ( X0 @ sK7 @ sK9 ) )
| ( $false
= ( sK5 @ ( X0 @ sK4 @ sK3 ) @ sK3 ) ) )
| ~ spl10_6
| ~ spl10_7 ),
inference(beta-eta_normalization,[],[f916]) ).
thf(f4968,plain,
( ( $false
= ( sK5
@ ( ^ [Y0: qML_mu,Y1: qML_i] : Y0
@ sK4
@ sK3 )
@ sK3 ) )
| ~ spl10_6
| ~ spl10_7 ),
inference(equality_resolution,[],[f917]) ).
thf(f4971,plain,
( ( $false
= ( sK5 @ sK4 @ sK3 ) )
| ~ spl10_6
| ~ spl10_7 ),
inference(beta-eta_normalization,[],[f4968]) ).
thf(f4979,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_6
| ~ spl10_7 ),
inference(constrained_superposition,[],[f4971,f113]) ).
thf(f5089,plain,
( $false
| ~ spl10_2
| ~ spl10_6
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f4979]) ).
thf(f5090,plain,
( ~ spl10_2
| ~ spl10_6
| ~ spl10_7 ),
inference(avatar_contradiction_clause,[],[f5089]) ).
thf(f5375,plain,
( ! [X0: qML_mu > qML_i > $o] :
( ( $true = $false )
| ( $false
= ( X0 @ sK4 @ sK3 ) )
| ( $true
= ( X0 @ sK7 @ sK8 ) ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f650,f122]) ).
thf(f5424,plain,
( ! [X0: qML_mu > qML_i > $o] :
( ( $true
= ( X0 @ sK7 @ sK8 ) )
| ( $false
= ( X0 @ sK4 @ sK3 ) ) )
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f5375]) ).
thf(f5480,plain,
( ! [X0: qML_mu > qML_i > qML_mu] :
( ( $true = $false )
| ( $false
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( sK5 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: qML_mu,Y3: qML_i] : Y3
@ Y0
@ Y1 ) )
@ sK4
@ sK3 ) )
| ( sK7
!= ( X0 @ sK7 @ sK8 ) ) )
| ~ spl10_4
| ~ spl10_5 ),
inference(constrained_superposition,[],[f127,f5424]) ).
thf(f5495,plain,
( ! [X0: qML_mu > qML_i > qML_mu] :
( ( $false
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( sK5 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: qML_mu,Y3: qML_i] : Y3
@ Y0
@ Y1 ) )
@ sK4
@ sK3 ) )
| ( sK7
!= ( X0 @ sK7 @ sK8 ) ) )
| ~ spl10_4
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f5480]) ).
thf(f5496,plain,
( ! [X0: qML_mu > qML_i > qML_mu] :
( ( sK7
!= ( X0 @ sK7 @ sK8 ) )
| ( $false
= ( sK5 @ ( X0 @ sK4 @ sK3 ) @ sK3 ) ) )
| ~ spl10_4
| ~ spl10_5 ),
inference(beta-eta_normalization,[],[f5495]) ).
thf(f7819,plain,
( ( $false
= ( sK5
@ ( ^ [Y0: qML_mu,Y1: qML_i] : Y0
@ sK4
@ sK3 )
@ sK3 ) )
| ~ spl10_4
| ~ spl10_5 ),
inference(equality_resolution,[],[f5496]) ).
thf(f7822,plain,
( ( $false
= ( sK5 @ sK4 @ sK3 ) )
| ~ spl10_4
| ~ spl10_5 ),
inference(beta-eta_normalization,[],[f7819]) ).
thf(f7950,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_5 ),
inference(constrained_superposition,[],[f7822,f113]) ).
thf(f8054,plain,
( $false
| ~ spl10_2
| ~ spl10_4
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f7950]) ).
thf(f8055,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_5 ),
inference(avatar_contradiction_clause,[],[f8054]) ).
cnf(s1,plain,
( spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f114]) ).
cnf(s2,plain,
( spl10_2
| spl10_3 ),
inference(sat_conversion,[],[f119]) ).
cnf(s3,plain,
( spl10_1
| spl10_4 ),
inference(sat_conversion,[],[f123]) ).
cnf(s4,plain,
( spl10_1
| spl10_5 ),
inference(sat_conversion,[],[f128]) ).
cnf(s5,plain,
( spl10_3
| spl10_6 ),
inference(sat_conversion,[],[f132]) ).
cnf(s6,plain,
( spl10_3
| spl10_7 ),
inference(sat_conversion,[],[f137]) ).
cnf(s8,plain,
( ~ spl10_1
| ~ spl10_3 ),
inference(sat_conversion,[],[f162]) ).
cnf(s10,plain,
( ~ spl10_2
| ~ spl10_6
| ~ spl10_7 ),
inference(sat_conversion,[],[f5090]) ).
cnf(s12,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_5 ),
inference(sat_conversion,[],[f8055]) ).
cnf(s13,plain,
spl10_1,
inference(rat,[],[s12,s1,s3,s4]) ).
cnf(s14,plain,
~ spl10_3,
inference(rat,[],[s8,s13]) ).
cnf(s15,plain,
spl10_7,
inference(rat,[],[s6,s14]) ).
cnf(s16,plain,
spl10_6,
inference(rat,[],[s5,s14]) ).
cnf(s17,plain,
spl10_2,
inference(rat,[],[s2,s14]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s10,s15,s16,s17]) ).
thf(f8069,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI004^4 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.19 % Computer : n011.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 13:17:31 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.23 Running first-order model finding
% 0.11/0.23 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
% 2.79/0.68 % (68996)Will run a generic schedule for satisfiability detection.
% 2.79/0.68 % (69002)% WARNING: option uhcvi not known.
% 2.79/0.68 % (69002)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1502990847:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.79/0.68 % (69002)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.79/0.68 % (69002)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.79/0.68 % (69003)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2131828117:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.79/0.68 % (69001)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3632116353_2999 on theBenchmark for (2999ds/0Mi)
% 2.79/0.68 % (69004)dis+10_1_sil=32000:sp=arity:random_seed=3000579600:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.79/0.68 % (69005)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3917244807:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.79/0.68 % (69005)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.79/0.68 % Exception at run slice level
% 2.79/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.79/0.68 % (69007)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1559854451:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.79/0.68 % (69006)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3288349974:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.79/0.68 % (69013)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3538635939:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.79/0.68 % Exception at run slice level
% 2.79/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.79/0.68 % (69017)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=617857852:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.79/0.68 % (69004)Instruction limit reached!
% 2.79/0.68 % (69004)------------------------------
% 2.79/0.68 % (69004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.68 % (69004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.68 % (69004)CaDiCaL version: 2.1.3
% 2.79/0.68 % (69004)Termination reason: Instruction limit
% 2.79/0.68 % (69004)Termination phase: Saturation
% 2.79/0.68 % (69004)Time elapsed: 0.054 s
% 2.79/0.68 % (69004)Peak memory usage: 12 MB
% 2.79/0.68 % (69004)Instructions burned: 104 (million)
% 2.79/0.68 % (69005)Instruction limit reached!
% 2.79/0.68 % (69005)------------------------------
% 2.79/0.68 % (69005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.68 % (69005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.68 % (69005)CaDiCaL version: 2.1.3
% 2.79/0.68 % (69005)Termination reason: Instruction limit
% 2.79/0.68 % (69005)Termination phase: Saturation
% 2.79/0.68 % (69005)Time elapsed: 0.058 s
% 2.79/0.68 % (69005)Peak memory usage: 13 MB
% 2.79/0.68 % (69005)Instructions burned: 116 (million)
% 2.79/0.68 % (69019)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3545088533:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.79/0.68 % (69019)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.79/0.68 % (69019)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.79/0.68 % (69020)ott-21_1_sil=16000:fs=off:random_seed=942479681:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.79/0.68 % (69007)Instruction limit reached!
% 2.79/0.68 % (69007)------------------------------
% 2.79/0.68 % (69007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.68 % (69007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.68 % (69007)CaDiCaL version: 2.1.3
% 2.79/0.68 % (69007)Termination reason: Instruction limit
% 2.79/0.68 % (69007)Termination phase: Saturation
% 2.79/0.68 % (69007)Time elapsed: 0.084 s
% 2.79/0.68 % (69007)Peak memory usage: 13 MB
% 2.79/0.68 % (69007)Instructions burned: 160 (million)
% 2.79/0.68 % (69023)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3577415010:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.79/0.68 % (69017)Instruction limit reached!
% 2.79/0.68 % (69017)------------------------------
% 2.79/0.68 % (69017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.68 % (69017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.68 % (69017)CaDiCaL version: 2.1.3
% 2.79/0.68 % (69017)Termination reason: Instruction limit
% 2.79/0.68 % (69017)Termination phase: Saturation
% 2.79/0.68 % (69017)Time elapsed: 0.070 s
% 2.79/0.68 % (69017)Peak memory usage: 13 MB
% 2.79/0.68 % (69017)Instructions burned: 131 (million)
% 2.79/0.68 % (69006)Instruction limit reached!
% 2.79/0.68 % (69006)------------------------------
% 2.79/0.68 % (69006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.68 % (69006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.68 % (69006)CaDiCaL version: 2.1.3
% 2.79/0.68 % (69006)Termination reason: Instruction limit
% 2.79/0.68 % (69006)Termination phase: Saturation
% 2.79/0.68 % (69006)Time elapsed: 0.108 s
% 2.79/0.68 % (69006)Peak memory usage: 13 MB
% 2.79/0.68 % (69006)Instructions burned: 133 (million)
% 2.79/0.68 % (69025)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2323002808:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.79/0.68 % Exception at run slice level
% 2.79/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.79/0.68 % (69026)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2136595817:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.79/0.68 % (69028)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=342744153:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.79/0.68 % Exception at run slice level
% 2.79/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.79/0.68 % (69020)Instruction limit reached!
% 2.79/0.68 % (69020)------------------------------
% 2.79/0.68 % (69020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.68 % (69020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.68 % (69020)CaDiCaL version: 2.1.3
% 2.79/0.68 % (69020)Termination reason: Instruction limit
% 2.79/0.68 % (69020)Termination phase: Saturation
% 2.79/0.68 % (69020)Time elapsed: 0.089 s
% 2.79/0.68 % (69020)Peak memory usage: 12 MB
% 2.79/0.68 % (69020)Instructions burned: 181 (million)
% 2.79/0.68 % (69031)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=4238769428:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 2.79/0.68 % (69031)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.79/0.68 % (69032)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3721828332:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.79/0.68 % (69032)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.79/0.68 % (69023)Instruction limit reached!
% 2.79/0.68 % (69023)------------------------------
% 2.79/0.68 % (69023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.68 % (69023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.68 % (69023)CaDiCaL version: 2.1.3
% 2.79/0.68 % (69023)Termination reason: Instruction limit
% 2.79/0.68 % (69023)Termination phase: Saturation
% 2.79/0.68 % (69023)Time elapsed: 0.252 s
% 2.79/0.68 % (69023)Peak memory usage: 13 MB
% 2.79/0.68 % (69023)Instructions burned: 477 (million)
% 2.79/0.68 % (69035)fmb+10_1_sil=64000:random_seed=3022357117:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 2.79/0.68 % (69035)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.79/0.68 % Exception at run slice level
% 2.79/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.79/0.68 % (69019) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-68996-69019"...
% 2.79/0.68 % (69019)...printing done.
% 2.79/0.68 % (69019)Refutation found. Thanks to Tanya!
% 2.79/0.68 % SZS status Theorem for theBenchmark
% 2.79/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.79/0.68 % (69019)------------------------------
% 2.79/0.68 % (69019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.68 % (69019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.68 % (69019)CaDiCaL version: 2.1.3
% 2.79/0.68 % (69019)Termination reason: Refutation
% 2.79/0.68 % (69019)Time elapsed: 0.330 s
% 2.79/0.68 % (69019)Peak memory usage: 15 MB
% 2.79/0.68 % (69019)Instructions burned: 670 (million)
% 2.79/0.68 % (68996)Success in time 0.437 s
% 2.79/0.68 % Vampire exiting
%------------------------------------------------------------------------------