%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI003^2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:20:16 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 331 ( 61 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 609 ( 6 ~; 0 |; 24 &; 474 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 222 ( 222 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 42 usr; 5 con; 0-4 aty)
% ( 34 !!; 40 ??; 0 @@+; 0 @@-)
% Number of variables : 218 ( 194 ^; 20 !; 4 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
mtrue: $i > $o ).
thf(func_def_2,type,
mfalse: $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_19,type,
rel: $i > $i > $o ).
thf(func_def_20,type,
mbox: ( $i > $o ) > $i > $o ).
thf(func_def_21,type,
mdia: ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_23,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_24,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(func_def_25,type,
god: mu > $i > $o ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_27,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_31,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vIFF: $o > $o > $o ).
thf(func_def_36,type,
vOR: $o > $o > $o ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
sK1: $i > $i ).
thf(f7,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mimplies) ).
thf(f12,axiom,
( ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_indset ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mforall_indset) ).
thf(f14,axiom,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mexists_ind) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) )
= mdia_generic ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mdia_generic) ).
thf(f20,axiom,
( mdia
= ( mdia_generic @ rel ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mdia) ).
thf(f21,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mvalid) ).
thf(f23,axiom,
( ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) )
= god ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD1) ).
thf(f24,axiom,
mvalid @ ( positive @ god ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA3) ).
thf(f25,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( positive @ X0 )
@ ( mdia
@ ( mexists_ind
@ ^ [X1: mu] : ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT1) ).
thf(f26,conjecture,
( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corC) ).
thf(f27,negated_conjecture,
~ ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
thf(f28,plain,
~ ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f29,plain,
( $true
= ( ~ ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [Y0: mu] : ( god @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f21]) ).
thf(f31,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f33,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f14]) ).
thf(f34,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f37,plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(fool_elimination,[],[f20]) ).
thf(f46,plain,
( ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) )
= god ),
inference(rectify,[],[f23]) ).
thf(f47,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) )
= mdia_generic ),
inference(rectify,[],[f18]) ).
thf(f49,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_indset ),
inference(rectify,[],[f12]) ).
thf(f51,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f54,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( positive @ X0 )
@ ( mdia
@ ( mexists_ind
@ ^ [X1: mu] : ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f55,plain,
( ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( positive @ Y0 )
@ ( mdia
@ ( mexists_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
mvalid @ ( positive @ god ),
inference(rectify,[],[f24]) ).
thf(f57,plain,
( ( mvalid @ ( positive @ god ) )
= $true ),
inference(fool_elimination,[],[f56]) ).
thf(f60,plain,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f61,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f75,plain,
( $true
= ( ~ ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [Y0: mu] : ( god @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f77,plain,
( ( mvalid @ ( positive @ god ) )
= $true ),
inference(cnf_transformation,[],[f57]) ).
thf(f79,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f80,plain,
( ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( positive @ Y0 )
@ ( mdia
@ ( mexists_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f55]) ).
thf(f83,plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f87,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f88,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f91,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f92,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f100,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f104,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f83,f92]) ).
thf(f105,plain,
( god
= ( ^ [Y0: mu] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( positive @ Y1 )
@ ( Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f100,f91,f79]) ).
thf(f106,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) )
@ rel
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu] :
( ^ [Y2: ( mu > $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( positive @ Y2 )
@ ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f75,f88,f104,f87,f105]) ).
thf(f107,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( positive
@ ^ [Y0: mu] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( positive @ Y1 )
@ ( Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f77,f88,f105]) ).
thf(f108,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( positive @ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y1 @ Y3 @ Y4 ) ) )
@ rel
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( ?? @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f80,f88,f91,f79,f104,f87]) ).
thf(f109,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ?? @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
& ( rel @ Y0 @ Y2 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f110,plain,
( ( !! @ $i
@ ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f111,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mu
@ ^ [Y2: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
& ( rel @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f112,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mu
@ ^ [Y2: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
& ( rel @ Y0 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f111]) ).
thf(f113,plain,
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mu
@ ^ [Y2: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
& ( rel @ Y0 @ Y1 ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f112]) ).
thf(f116,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& ( rel @ sK0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f117,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& ( rel @ sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X1: $i] :
( $false
= ( ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ X1 )
=> ( Y1 @ Y0 @ X1 ) ) ) )
& ( rel @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f117]) ).
thf(f120,plain,
! [X1: $i] :
( $true
= ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f110]) ).
thf(f121,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ?? @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
& ( rel @ Y0 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f109]) ).
thf(f122,plain,
! [X1: $i] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
& ( rel @ X1 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f123,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
& ( rel @ X1 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( ( positive @ X2 @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] : ( X2 @ Y1 @ Y0 ) )
& ( rel @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f126,plain,
! [X0: $i] :
( ( $true
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] :
( ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y3 )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y1
@ Y0 ) )
& ( rel @ X0 @ Y0 ) ) ) )
= $true ),
inference(constrained_superposition,[],[f124,f120]) ).
thf(f127,plain,
! [X0: $i] :
( $true
= ( $true
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& ( rel @ X0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f126]) ).
thf(f128,plain,
! [X0: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& ( rel @ X0 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[],[f127]) ).
thf(f129,plain,
! [X0: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& ( rel @ X0 @ Y0 ) )
@ ( sK1 @ X0 ) ) ),
inference(sigma_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X0: $i] :
( $true
= ( ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK1 @ X0 ) )
=> ( Y1 @ Y0 @ ( sK1 @ X0 ) ) ) ) )
& ( rel @ X0 @ ( sK1 @ X0 ) ) ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
! [X0: $i] :
( ( rel @ X0 @ ( sK1 @ X0 ) )
= $true ),
inference(and_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X0: $i] :
( ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK1 @ X0 ) )
=> ( Y1 @ Y0 @ ( sK1 @ X0 ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f130]) ).
thf(f134,plain,
( $false
= ( ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK1 @ sK0 ) )
=> ( Y1 @ Y0 @ ( sK1 @ sK0 ) ) ) ) )
& $true ) ),
inference(constrained_superposition,[],[f118,f131]) ).
thf(f135,plain,
( $false
= ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK1 @ sK0 ) )
=> ( Y1 @ Y0 @ ( sK1 @ sK0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f134]) ).
thf(f137,plain,
$false = $true,
inference(forward_demodulation,[],[f135,f132]) ).
thf(f138,plain,
$false,
inference(trivial_inequality_removal,[],[f137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI003^2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n001.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 13:23:06 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.29 % (1221643)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (1221661)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=402171288:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (1221663)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (1221663)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
% 0.20/0.29 % (1221658)lrs+10_16_si=on:nwc=1.5:random_seed=168599690:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (1221659)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2684078074:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (1221657)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4189547593:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (1221660)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=974283348: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)
% 0.20/0.29 % (1221663)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=4102379140:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (1221662)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4027243268:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (1221661)Instruction limit reached!
% 0.20/0.29 % (1221661)------------------------------
% 0.20/0.29 % (1221661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1221661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1221661)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1221661)Termination reason: Instruction limit
% 0.20/0.29 % (1221661)Termination phase: Saturation
% 0.20/0.29 % (1221661)Time elapsed: 0.008 s
% 0.20/0.29 % (1221661)Peak memory usage: 11 MB
% 0.20/0.29 % (1221661)Instructions burned: 26 (million)
% 0.20/0.29 % (1221659)Instruction limit reached!
% 0.20/0.29 % (1221659)------------------------------
% 0.20/0.29 % (1221659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1221659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1221659)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1221659)Termination reason: Instruction limit
% 0.20/0.29 % (1221659)Termination phase: Function definition elimination
% 0.20/0.29 % (1221659)Time elapsed: 0.002 s
% 0.20/0.29 % (1221659)Peak memory usage: 10 MB
% 0.20/0.29 % (1221659)Instructions burned: 3 (million)
% 0.20/0.29 % (1221657)Refutation not found, incomplete strategy
% 0.20/0.29 % (1221657)------------------------------
% 0.20/0.29 % (1221657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1221657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1221657)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1221657)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1221657)Time elapsed: 0.005 s
% 0.20/0.29 % (1221657)Peak memory usage: 12 MB
% 0.20/0.29 % (1221657)Instructions burned: 9 (million)
% 0.20/0.29 % (1221657)------------------------------
% 0.20/0.29 % (1221657)------------------------------
% 0.20/0.29 % (1221663)Refutation not found, incomplete strategy
% 0.20/0.29 % (1221663)------------------------------
% 0.20/0.29 % (1221663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1221663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1221663)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1221663)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1221663)Time elapsed: 0.006 s
% 0.20/0.29 % (1221663)Peak memory usage: 12 MB
% 0.20/0.29 % (1221663)Instructions burned: 10 (million)
% 0.20/0.29 % (1221663)------------------------------
% 0.20/0.29 % (1221663)------------------------------
% 0.20/0.29 % (1221658)Instruction limit reached!
% 0.20/0.29 % (1221658)------------------------------
% 0.20/0.29 % (1221658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1221658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1221658)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1221658)Termination reason: Instruction limit
% 0.20/0.30 % (1221658)Termination phase: Saturation
% 0.20/0.30 % (1221658)Time elapsed: 0.009 s
% 0.20/0.30 % (1221658)Peak memory usage: 12 MB
% 0.20/0.30 % (1221658)Instructions burned: 18 (million)
% 0.20/0.30 % (1221676)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2112280626:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.30 % (1221676)Instruction limit reached!
% 0.20/0.30 % (1221676)------------------------------
% 0.20/0.30 % (1221676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1221676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1221676)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1221676)Termination reason: Instruction limit
% 0.20/0.30 % (1221676)Termination phase: Function definition elimination
% 0.20/0.30 % (1221676)Time elapsed: 0.001 s
% 0.20/0.30 % (1221676)Peak memory usage: 10 MB
% 0.20/0.30 % (1221676)Instructions burned: 3 (million)
% 0.20/0.30 % (1221678)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1795920037:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.30 % (1221681)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.30 % (1221686)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=992821550:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.30 % (1221678)Instruction limit reached!
% 0.20/0.30 % (1221678)------------------------------
% 0.20/0.30 % (1221678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1221678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1221678)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1221678)Termination reason: Instruction limit
% 0.20/0.30 % (1221678)Termination phase: Saturation
% 0.20/0.30 % (1221678)Time elapsed: 0.003 s
% 0.20/0.30 % (1221678)Peak memory usage: 11 MB
% 0.20/0.30 % (1221678)Instructions burned: 6 (million)
% 0.20/0.30 % (1221684)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
% 0.20/0.30 % (1221684)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.30 % (1221681)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1341426895:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.30 % (1221686) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1221643-1221686"...
% 0.20/0.30 % (1221683)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3152180696:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.30 % (1221684)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=580368109:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.30 % (1221686)...printing done.
% 0.20/0.30 % (1221686)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (1221686)------------------------------
% 0.20/0.30 % (1221686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1221686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1221686)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1221686)Termination reason: Refutation
% 0.20/0.30 % (1221686)Time elapsed: 0.004 s
% 0.20/0.30 % (1221686)Peak memory usage: 12 MB
% 0.20/0.30 % (1221686)Instructions burned: 14 (million)
% 0.20/0.30 % (1221643)Success in time 0.07 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------