%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI008^4 : 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 : 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 08:20:18 AM UTC 2026
% Result : Theorem 0.20s 0.35s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 75 ( 46 unt; 0 typ; 2 def)
% Number of atoms : 347 ( 90 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 561 ( 45 ~; 39 |; 0 &; 384 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 138 ( 138 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 27 usr; 8 con; 0-4 aty)
% ( 58 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 184 ( 100 ^; 82 !; 2 ?; 184 :)
% 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,
vNOT: $o > $o ).
thf(func_def_8,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_20,type,
sF0: $o ).
thf(func_def_21,type,
sF1: $o ).
thf(func_def_22,type,
sK2: qML_i > qML_mu ).
thf(func_def_23,type,
sK3: qML_i > $o ).
thf(func_def_24,type,
sK4: qML_i ).
thf(func_def_25,type,
sK5: qML_i > qML_mu > qML_mu > qML_i > $o ).
thf(func_def_26,type,
sK6: ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_mu ).
thf(func_def_27,type,
sK7: qML_i ).
thf(func_def_28,type,
sK8: ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_i ).
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(f2,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_1_A4) ).
thf(f3,axiom,
! [X1: qML_i,X0: qML_i] :
? [X2: qML_mu] : ( scott_G @ X2 @ X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_T3) ).
thf(f7,axiom,
! [X1: qML_mu > qML_i > $o,X0: qML_i] :
( ~ ( scott_P @ X1 @ X0 )
=> ( scott_P
@ ^ [X2: qML_mu,X3: qML_i] :
~ ( X1 @ X2 @ X3 )
@ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_A1b) ).
thf(f12,conjecture,
! [X0: qML_i,X1: qML_i > $o] :
( ~ ( X1 @ X0 )
| ! [X2: qML_i] : ( X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f13,negated_conjecture,
~ ! [X0: qML_i,X1: qML_i > $o] :
( ~ ( X1 @ X0 )
| ! [X2: qML_i] : ( X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
thf(f16,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(f17,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,[],[f16]) ).
thf(f18,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ~ ( scott_P @ X0 @ X1 )
=> ( scott_P
@ ^ [X2: qML_mu,X3: qML_i] :
~ ( X0 @ X2 @ X3 )
@ X1 ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ~ ( scott_P @ Y1 @ Y0 )
=> ( scott_P
@ ^ [Y2: qML_mu,Y3: qML_i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f18]) ).
thf(f28,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( scott_P @ X0 @ X1 )
=> ! [X2: qML_i] : ( scott_P @ X0 @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f29,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( !! @ qML_i
@ ^ [Y2: qML_i] : ( scott_P @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
! [X0: qML_i] :
? [X2: qML_mu] : ( scott_G @ X2 @ X0 ),
inference(rectify,[],[f3]) ).
thf(f31,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( ?? @ qML_mu
@ ^ [Y1: qML_mu] : ( scott_G @ Y1 @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f30]) ).
thf(f36,plain,
~ ! [X0: qML_i,X1: qML_i > $o] :
( ~ ( X1 @ X0 )
| ! [X2: qML_i] : ( X1 @ X2 ) ),
inference(rectify,[],[f13]) ).
thf(f37,plain,
( ( ~ ( !! @ ( qML_i > $o )
@ ^ [Y0: qML_i > $o] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ qML_i
@ ^ [Y2: qML_i] : ( Y0 @ Y2 ) )
| ~ ( Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( !! @ qML_i
@ ^ [Y2: qML_i] : ( scott_P @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f39,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ~ ( scott_P @ Y1 @ Y0 )
=> ( scott_P
@ ^ [Y2: qML_mu,Y3: qML_i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f40,plain,
( ( ~ ( !! @ ( qML_i > $o )
@ ^ [Y0: qML_i > $o] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ qML_i
@ ^ [Y2: qML_i] : ( Y0 @ Y2 ) )
| ~ ( Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f37]) ).
thf(f42,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,[],[f17]) ).
thf(f45,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( ?? @ qML_mu
@ ^ [Y1: qML_mu] : ( scott_G @ Y1 @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f53,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( ?? @ qML_mu
@ ^ [Y1: qML_mu] :
( ^ [Y2: qML_mu,Y3: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y4: qML_mu > qML_i > $o] :
( ( scott_P @ Y4 @ Y3 )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y1
@ Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f45,f42]) ).
thf(f57,definition,
( sF0
= ( !! @ ( qML_i > $o )
@ ^ [Y0: qML_i > $o] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ qML_i
@ ^ [Y2: qML_i] : ( Y0 @ Y2 ) )
| ~ ( Y0 @ Y1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f58,definition,
( sF1 = ( ~ sF0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f59,plain,
sF1 = $true,
inference(definition_folding,[],[f40,f58,f57]) ).
thf(f61,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 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f62,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( !! @ qML_i @ ( scott_P @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f63,plain,
( sF0
= ( !! @ ( qML_i > $o )
@ ^ [Y0: qML_i > $o] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ qML_i @ Y0 )
| ~ ( Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f70,plain,
! [X1: 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 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f61]) ).
thf(f71,plain,
! [X1: qML_i] :
( ( ?? @ qML_mu
@ ^ [Y0: qML_mu] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ X1 )
=> ( Y1 @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f73,plain,
( ( ( ~ sF0 ) = $true )
| ( sF1 = $false ) ),
inference(iff_proxy_clausification,[],[f58]) ).
thf(f74,plain,
! [X1: qML_i] :
( ( ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ~ ( scott_P @ Y1 @ Y0 )
=> ( scott_P
@ ^ [Y2: qML_mu,Y3: qML_i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f75,plain,
! [X1: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ~ ( scott_P @ Y0 @ X1 )
=> ( scott_P
@ ^ [Y1: qML_mu,Y2: qML_i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f78,plain,
! [X1: qML_i] :
( ( ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( !! @ qML_i @ ( scott_P @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f79,plain,
! [X1: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X1 )
=> ( !! @ qML_i @ ( scott_P @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
( ( sF0 = $true )
| ( ( !! @ ( qML_i > $o )
@ ^ [Y0: qML_i > $o] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ qML_i @ Y0 )
| ~ ( Y0 @ Y1 ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f63]) ).
thf(f88,plain,
! [X1: qML_i] :
( ( ^ [Y0: qML_mu] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ X1 )
=> ( Y1 @ Y0 @ X1 ) ) )
@ ( sK2 @ X1 ) )
= $true ),
inference(sigma_proxy_clausification,[],[f71]) ).
thf(f89,plain,
! [X1: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X1 )
=> ( Y0 @ ( sK2 @ X1 ) @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
( ( $false = $true )
| ( ( ~ sF0 ) = $true ) ),
inference(forward_demodulation,[],[f73,f59]) ).
thf(f91,plain,
( ( ~ sF0 ) = $true ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f92,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ^ [Y0: qML_mu > qML_i > $o] :
( ~ ( scott_P @ Y0 @ X1 )
=> ( scott_P
@ ^ [Y1: qML_mu,Y2: qML_i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f93,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ~ ( scott_P @ X2 @ X1 )
=> ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f96,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X1 )
=> ( !! @ qML_i @ ( scott_P @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f79]) ).
thf(f97,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X2 @ X1 )
=> ( !! @ qML_i @ ( scott_P @ X2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f100,plain,
( ( ( ^ [Y0: qML_i > $o] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ( !! @ qML_i @ Y0 )
| ~ ( Y0 @ Y1 ) ) )
@ sK3 )
= $false )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f80]) ).
thf(f101,plain,
( ( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( ( !! @ qML_i @ sK3 )
| ~ ( sK3 @ Y0 ) ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f105,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X1 )
=> ( Y0 @ ( sK2 @ X1 ) @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f89]) ).
thf(f106,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X2 @ X1 )
=> ( X2 @ ( sK2 @ X1 ) @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
sF0 = $false,
inference(not_proxy_clausification,[],[f91]) ).
thf(f108,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= $true )
| ( ( ~ ( scott_P @ X2 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f110,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X2 @ X1 )
= $false )
| ( ( !! @ qML_i @ ( scott_P @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f97]) ).
thf(f113,plain,
( ( sF0 = $true )
| ( ( ^ [Y0: qML_i] :
( ( !! @ qML_i @ sK3 )
| ~ ( sK3 @ Y0 ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f101]) ).
thf(f114,plain,
( ( sF0 = $true )
| ( ( ( !! @ qML_i @ sK3 )
| ~ ( sK3 @ sK4 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f118,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X2 @ X1 )
= $false )
| ( ( X2 @ ( sK2 @ X1 ) @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f119,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= $true )
| ( ( scott_P @ X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f108]) ).
thf(f121,plain,
! [X2: qML_mu > qML_i > $o,X3: qML_i,X1: qML_i] :
( ( ( scott_P @ X2 @ X3 )
= $true )
| ( ( scott_P @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f110]) ).
thf(f122,plain,
( ( ( ( !! @ qML_i @ sK3 )
| ~ ( sK3 @ sK4 ) )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f114,f107]) ).
thf(f123,plain,
( ( ( !! @ qML_i @ sK3 )
| ~ ( sK3 @ sK4 ) )
= $false ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f127,plain,
( ( ~ ( sK3 @ sK4 ) )
= $false ),
inference(or_proxy_clausification,[],[f123]) ).
thf(f128,plain,
( ( !! @ qML_i @ sK3 )
= $false ),
inference(or_proxy_clausification,[],[f123]) ).
thf(f133,plain,
( ( sK3 @ sK4 )
= $true ),
inference(not_proxy_clausification,[],[f127]) ).
thf(f134,plain,
( ( sK3 @ sK7 )
= $false ),
inference(sigma_proxy_clausification,[],[f128]) ).
thf(f177,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( $false
= ( scott_P @ X0 @ X2 ) )
| ( ( X0 @ ( sK2 @ X1 ) @ X1 )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f121,f118]) ).
thf(f180,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( $false
= ( scott_P @ X0 @ X2 ) )
| ( ( X0 @ ( sK2 @ X1 ) @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f177]) ).
thf(f189,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ ( sK2 @ X2 )
@ X2 )
= $true )
| ( $false = $true )
| ( ( scott_P @ X0 @ X1 )
= $true ) ),
inference(constrained_superposition,[],[f119,f180]) ).
thf(f193,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X0 @ X1 )
= $true )
| ( ( ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X0 @ Y0 @ Y1 )
@ ( sK2 @ X2 )
@ X2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f194,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X0 @ X1 )
= $true )
| ( ( ~ ( X0 @ ( sK2 @ X2 ) @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f201,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X0 @ X1 )
= $true )
| ( ( X0 @ ( sK2 @ X2 ) @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f206,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( X0 @ ( sK2 @ X2 ) @ X2 )
= $false )
| ( ( X0 @ ( sK2 @ X1 ) @ X1 )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f201,f118]) ).
thf(f210,plain,
! [X2: qML_i,X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( X0 @ ( sK2 @ X2 ) @ X2 )
= $false )
| ( ( X0 @ ( sK2 @ X1 ) @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f206]) ).
thf(f225,plain,
! [X0: qML_i] :
( ( $false = $true )
| ( ( ^ [Y0: qML_mu,Y1: qML_i] :
( sK3
@ ( ^ [Y2: qML_mu,Y3: qML_i] : Y3
@ Y0
@ Y1 ) )
@ ( sK2 @ X0 )
@ X0 )
= $true ) ),
inference(constrained_superposition,[],[f133,f210]) ).
thf(f252,plain,
! [X0: qML_i] :
( ( ^ [Y0: qML_mu,Y1: qML_i] :
( sK3
@ ( ^ [Y2: qML_mu,Y3: qML_i] : Y3
@ Y0
@ Y1 ) )
@ ( sK2 @ X0 )
@ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f253,plain,
! [X0: qML_i] :
( ( sK3 @ X0 )
= $true ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f271,plain,
$false = $true,
inference(backward_demodulation,[],[f134,f253]) ).
thf(f272,plain,
$false,
inference(trivial_inequality_removal,[],[f271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI008^4 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:20:02 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.20/0.35 % (70489)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (70498)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4156780868:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (70500)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (70500)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
% 0.20/0.35 % (70494)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1907403033:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (70495)lrs+10_16_si=on:nwc=1.5:random_seed=2394751484:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (70496)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2258164789:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (70497)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=3581185682: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)
% 0.20/0.35 % (70499)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2340266636:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (70498)Instruction limit reached!
% 0.20/0.35 % (70498)------------------------------
% 0.20/0.35 % (70498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (70498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (70498)CaDiCaL version: 2.1.3
% 0.20/0.35 % (70498)Termination reason: Instruction limit
% 0.20/0.35 % (70498)Termination phase: Saturation
% 0.20/0.35 % (70498)Time elapsed: 0.007 s
% 0.20/0.35 % (70498)Peak memory usage: 12 MB
% 0.20/0.35 % (70498)Instructions burned: 24 (million)
% 0.20/0.35 % (70500)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=2011700740:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (70496)Instruction limit reached!
% 0.20/0.35 % (70496)------------------------------
% 0.20/0.35 % (70496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (70496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (70496)CaDiCaL version: 2.1.3
% 0.20/0.35 % (70496)Termination reason: Instruction limit
% 0.20/0.35 % (70496)Termination phase: Saturation
% 0.20/0.35 % (70496)Time elapsed: 0.002 s
% 0.20/0.35 % (70496)Peak memory usage: 11 MB
% 0.20/0.35 % (70496)Instructions burned: 3 (million)
% 0.20/0.35 % (70495)Instruction limit reached!
% 0.20/0.35 % (70495)------------------------------
% 0.20/0.35 % (70495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (70495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (70495)CaDiCaL version: 2.1.3
% 0.20/0.35 % (70495)Termination reason: Instruction limit
% 0.20/0.35 % (70495)Termination phase: Saturation
% 0.20/0.35 % (70495)Time elapsed: 0.010 s
% 0.20/0.35 % (70495)Peak memory usage: 12 MB
% 0.20/0.35 % (70495)Instructions burned: 18 (million)
% 0.20/0.35 % (70508)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=437308899:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (70508)Instruction limit reached!
% 0.20/0.35 % (70508)------------------------------
% 0.20/0.35 % (70508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (70508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (70508)CaDiCaL version: 2.1.3
% 0.20/0.35 % (70508)Termination reason: Instruction limit
% 0.20/0.35 % (70508)Termination phase: Saturation
% 0.20/0.35 % (70508)Time elapsed: 0.001 s
% 0.20/0.35 % (70508)Peak memory usage: 10 MB
% 0.20/0.35 % (70508)Instructions burned: 3 (million)
% 0.20/0.35 % (70509)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3421704353:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.35 % (70512)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=652657817:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.35 % (70509)Instruction limit reached!
% 0.20/0.35 % (70509)------------------------------
% 0.20/0.35 % (70509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (70509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (70509)CaDiCaL version: 2.1.3
% 0.20/0.35 % (70509)Termination reason: Instruction limit
% 0.20/0.35 % (70509)Termination phase: Saturation
% 0.20/0.35 % (70509)Time elapsed: 0.003 s
% 0.20/0.35 % (70509)Peak memory usage: 11 MB
% 0.20/0.35 % (70509)Instructions burned: 5 (million)
% 0.20/0.35 % (70510)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (70512)Instruction limit reached!
% 0.20/0.35 % (70512)------------------------------
% 0.20/0.35 % (70512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (70512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (70512)CaDiCaL version: 2.1.3
% 0.20/0.35 % (70512)Termination reason: Instruction limit
% 0.20/0.35 % (70512)Termination phase: Saturation
% 0.20/0.35 % (70512)Time elapsed: 0.004 s
% 0.20/0.35 % (70512)Peak memory usage: 12 MB
% 0.20/0.35 % (70512)Instructions burned: 13 (million)
% 0.20/0.35 % (70510)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=202221850:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.35 % (70510)Instruction limit reached!
% 0.20/0.35 % (70510)------------------------------
% 0.20/0.35 % (70510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (70510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (70510)CaDiCaL version: 2.1.3
% 0.20/0.35 % (70510)Termination reason: Instruction limit
% 0.20/0.35 % (70510)Termination phase: Saturation
% 0.20/0.35 % (70510)Time elapsed: 0.004 s
% 0.20/0.35 % (70510)Peak memory usage: 12 MB
% 0.20/0.35 % (70510)Instructions burned: 7 (million)
% 0.20/0.35 % (70516)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2954521667:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.35 % (70515)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
% 0.20/0.35 % (70515)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (70499)Instruction limit reached!
% 0.20/0.35 % (70499)------------------------------
% 0.20/0.35 % (70499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (70499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (70499)CaDiCaL version: 2.1.3
% 0.20/0.35 % (70499)Termination reason: Instruction limit
% 0.20/0.35 % (70499)Termination phase: Saturation
% 0.20/0.35 % (70499)Time elapsed: 0.041 s
% 0.20/0.35 % (70499)Peak memory usage: 12 MB
% 0.20/0.35 % (70499)Instructions burned: 75 (million)
% 0.20/0.35 % (70494)Instruction limit reached!
% 0.20/0.35 % (70494)------------------------------
% 0.20/0.35 % (70494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (70494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (70494)CaDiCaL version: 2.1.3
% 0.20/0.35 % (70494)Termination reason: Instruction limit
% 0.20/0.35 % (70494)Termination phase: Saturation
% 0.20/0.35 % (70494)Time elapsed: 0.044 s
% 0.20/0.35 % (70494)Peak memory usage: 12 MB
% 0.20/0.35 % (70494)Instructions burned: 88 (million)
% 0.20/0.35 % (70515)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=387746985:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.35 % (70518)lrs+10_1_si=on:cs=on:random_seed=2783059790:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.20/0.35 % (70515) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-70489-70515"...
% 0.20/0.35 % (70520)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.20/0.35 % (70518)Instruction limit reached!
% 0.20/0.35 % (70518)------------------------------
% 0.20/0.35 % (70518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (70518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (70518)CaDiCaL version: 2.1.3
% 0.20/0.35 % (70518)Termination reason: Instruction limit
% 0.20/0.35 % (70518)Termination phase: Saturation
% 0.20/0.35 % (70518)Time elapsed: 0.004 s
% 0.20/0.35 % (70518)Peak memory usage: 11 MB
% 0.20/0.35 % (70518)Instructions burned: 8 (million)
% 0.20/0.35 % (70515)...printing done.
% 0.20/0.35 % (70515)Refutation found. Thanks to Tanya!
% 0.20/0.35 % SZS status Theorem for theBenchmark
% 0.20/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.36 % (70515)------------------------------
% 0.20/0.36 % (70515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (70515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (70515)CaDiCaL version: 2.1.3
% 0.20/0.36 % (70515)Termination reason: Refutation
% 0.20/0.36 % (70515)Time elapsed: 0.015 s
% 0.20/0.36 % (70515)Peak memory usage: 12 MB
% 0.20/0.36 % (70515)Instructions burned: 26 (million)
% 0.20/0.36 % (70489)Success in time 0.091 s
% 0.20/0.36 % Vampire exiting
%------------------------------------------------------------------------------