%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI002^2 : 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 : n002.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 0.30s 0.41s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 15
% Syntax : Number of formulae : 111 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 639 ( 149 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 1060 ( 46 ~; 55 |; 27 &; 819 @)
% ( 2 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 355 ( 355 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 44 usr; 5 con; 0-4 aty)
% ( 56 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 372 ( 286 ^; 82 !; 4 ?; 372 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vAND: $o > $o > $o ).
thf(func_def_27,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_34,type,
vIMP: $o > $o > $o ).
thf(func_def_35,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
vIFF: $o > $o > $o ).
thf(func_def_40,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
sK1: mu > $i > $o ).
thf(func_def_43,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
sK2: ( mu > $i > $o ) > $i > ( mu > $i > $o ) > $i ).
thf(func_def_45,type,
sK3: ( mu > $i > $o ) > $i > ( mu > $i > $o ) > mu ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mnot) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mand) ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mimplies) ).
thf(f9,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mequiv) ).
thf(f11,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mforall_ind) ).
thf(f12,axiom,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mforall_indset) ).
thf(f14,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) )
= mexists_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mexists_ind) ).
thf(f17,axiom,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mbox_generic) ).
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(f19,axiom,
( mbox
= ( mbox_generic @ rel ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mbox) ).
thf(f20,axiom,
( mdia
= ( mdia_generic @ rel ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mdia) ).
thf(f21,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mvalid) ).
thf(f23,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA1) ).
thf(f24,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ X0 )
@ ( mbox
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) ) )
@ ( positive @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA2) ).
thf(f25,conjecture,
( 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,negated_conjecture,
~ ( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( positive @ X0 )
@ ( mdia
@ ( mexists_ind
@ ^ [X1: mu] : ( X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
thf(f27,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) )
= mdia_generic ),
inference(rectify,[],[f18]) ).
thf(f28,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f30,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f6]) ).
thf(f31,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f34,plain,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f35,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f39,plain,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f40,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f42,plain,
~ ( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( positive @ X0 )
@ ( mdia
@ ( mexists_ind
@ ^ [X1: mu] : ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f43,plain,
( $true
!= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( positive @ Y0 )
@ ( mdia
@ ( mexists_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f45,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f48,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
inference(rectify,[],[f11]) ).
thf(f49,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f21]) ).
thf(f51,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f54,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f7]) ).
thf(f55,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) )
= mexists_ind ),
inference(rectify,[],[f14]) ).
thf(f57,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f4]) ).
thf(f59,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f60,plain,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f61,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f62,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ X0 )
@ ( mbox
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) ) )
@ ( positive @ X1 ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f63,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ Y0 )
@ ( mbox
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) )
@ ( positive @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f70,plain,
( $true
!= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( positive @ Y0 )
@ ( mdia
@ ( mexists_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(flattening,[],[f43]) ).
thf(f71,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f72,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f76,plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f77,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f78,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f79,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f80,plain,
( $true
!= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( positive @ Y0 )
@ ( mdia
@ ( mexists_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f81,plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f82,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f84,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f85,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f90,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ Y0 )
@ ( mbox
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) )
@ ( positive @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f91,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f94,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f95,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f98,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f76,f84]) ).
thf(f99,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f81,f91]) ).
thf(f100,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,f82,f79,f78,f99,f94]) ).
thf(f101,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
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( positive @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f85,f82,f79,f95,f71,f71]) ).
thf(f102,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: ( 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 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( positive @ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( Y0 @ Y2 )
@ ( Y1 @ Y2 ) ) ) ) )
@ ( positive @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f90,f82,f79,f79,f78,f77,f98,f72,f78]) ).
thf(f103,plain,
( $true
!= ( !! @ $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 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f104,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ?? @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
& ( rel @ Y0 @ Y2 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f103]) ).
thf(f105,plain,
( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
& ( rel @ sK0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
( ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
& ( rel @ sK0 @ Y1 ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f105]) ).
thf(f107,plain,
( ( ( positive @ sK1 @ sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] : ( sK1 @ Y1 @ Y0 ) )
& ( rel @ sK0 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] : ( sK1 @ Y1 @ Y0 ) )
& ( rel @ sK0 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f109,plain,
( $true
= ( positive @ sK1 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f110,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] : ( sK1 @ Y1 @ Y0 ) )
& ( rel @ sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f108]) ).
thf(f111,plain,
! [X1: $i] :
( ( ( ?? @ mu
@ ^ [Y0: mu] : ( sK1 @ Y0 @ X1 ) )
& ( rel @ sK0 @ X1 ) )
= $false ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f112,plain,
! [X1: $i] :
( ( $false
= ( ?? @ mu
@ ^ [Y0: mu] : ( sK1 @ Y0 @ X1 ) ) )
| ( ( rel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( ^ [Y0: mu] : ( sK1 @ Y0 @ X1 )
@ X2 ) )
| ( ( rel @ sK0 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( sK1 @ X2 @ X1 ) )
| ( ( rel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y0 @ Y3 )
| ( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( positive @ Y1 @ Y0 ) )
=> ( positive @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f116,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y0 @ Y3 )
| ( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( positive @ Y1 @ Y0 ) )
=> ( positive @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ X1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( positive @ Y0 @ X1 ) )
=> ( positive @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ X1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( positive @ Y0 @ X1 ) )
=> ( positive @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ X1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ( positive @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ X1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ( positive @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ( positive @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( positive @ X3 @ X1 )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) ) )
& ( positive @ X2 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( positive @ X3 @ X1 )
= $true )
| ( ( positive @ X2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) )
@ ( sK2 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( positive @ X3 @ X1 )
= $true )
| ( ( positive @ X2 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( ~ ( rel @ X1 @ ( sK2 @ X3 @ X1 @ X2 ) )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) )
=> ( X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) ) ) ) )
= $false )
| ( ( positive @ X3 @ X1 )
= $true )
| ( ( positive @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( positive @ X2 @ X1 )
= $false )
| ( ( positive @ X3 @ X1 )
= $true )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) )
=> ( X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( positive @ X3 @ X1 )
= $true )
| ( ( positive @ X2 @ X1 )
= $false )
| ( $false
= ( ~ ( rel @ X1 @ ( sK2 @ X3 @ X1 @ X2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f125]) ).
thf(f128,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( rel @ X1 @ ( sK2 @ X3 @ X1 @ X2 ) )
= $true )
| ( ( positive @ X3 @ X1 )
= $true )
| ( ( positive @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) )
=> ( X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X2 ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( positive @ X3 @ X1 )
= $true )
| ( ( positive @ X2 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f126]) ).
thf(f130,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) )
=> ( X3 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) ) )
= $false )
| ( ( positive @ X2 @ X1 )
= $false )
| ( ( positive @ X3 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f132,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( ( positive @ X3 @ X1 )
= $true )
| ( ( positive @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f130]) ).
thf(f133,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive
@ ^ [Y2: mu,Y3: $i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 )
= ( ~ ( positive @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f134,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive
@ ^ [Y2: mu,Y3: $i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 )
= ( ~ ( positive @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive
@ ^ [Y1: mu,Y2: $i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 )
= ( ~ ( positive @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive
@ ^ [Y1: mu,Y2: $i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 )
= ( ~ ( positive @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= ( ~ ( positive @ X2 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= ( ~ ( positive @ X2 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f137]) ).
thf(f140,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $true
= ( ~ ( positive @ X2 @ X1 ) ) )
| ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f138]) ).
thf(f141,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= $false )
| ( ( positive @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f140]) ).
thf(f143,plain,
! [X2: mu,X0: mu > $i > $o,X1: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( positive @ X1 @ sK0 ) )
| ( $true
= ( positive @ X0 @ sK0 ) )
| ( $false
= ( sK1 @ X2 @ ( sK2 @ X0 @ sK0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f128,f114]) ).
thf(f145,plain,
! [X2: mu,X0: mu > $i > $o,X1: mu > $i > $o] :
( ( $false
= ( sK1 @ X2 @ ( sK2 @ X0 @ sK0 @ X1 ) ) )
| ( $false
= ( positive @ X1 @ sK0 ) )
| ( $true
= ( positive @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f178,plain,
! [X0: mu > $i > $o] :
( ( ( positive @ sK1 @ sK0 )
= $false )
| ( $true
= ( positive @ X0 @ sK0 ) )
| ( $true = $false )
| ( $true
= ( positive @ X0 @ sK0 ) )
| ( ( positive @ sK1 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f132,f145]) ).
thf(f184,plain,
! [X0: mu > $i > $o] :
( ( ( positive @ sK1 @ sK0 )
= $false )
| ( $true
= ( positive @ X0 @ sK0 ) )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[],[f178]) ).
thf(f185,plain,
! [X0: mu > $i > $o] :
( ( ( positive @ sK1 @ sK0 )
= $false )
| ( $true
= ( positive @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f184]) ).
thf(f196,plain,
! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $true
= ( positive @ X0 @ sK0 ) ) ),
inference(forward_demodulation,[],[f185,f109]) ).
thf(f197,plain,
! [X0: mu > $i > $o] :
( $true
= ( positive @ X0 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f196]) ).
thf(f202,plain,
! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( positive @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f141,f197]) ).
thf(f205,plain,
! [X0: mu > $i > $o] :
( $false
= ( positive @ X0 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f202]) ).
thf(f208,plain,
$true = $false,
inference(forward_demodulation,[],[f205,f197]) ).
thf(f209,plain,
$false,
inference(trivial_inequality_removal,[],[f208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : PHI002^2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n002.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 13:19:22 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running higher-order theorem proving
% 0.26/0.34 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
% 0.30/0.41 % (1255799)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.41 % (1255807)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=478323678: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)
% 0.30/0.41 % (1255810)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.41 % (1255810)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
% 0.30/0.41 % (1255805)lrs+10_16_si=on:nwc=1.5:random_seed=2944359179:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.41 % (1255804)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3718400503:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.41 % (1255806)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2563418844:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.41 % (1255809)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4247883239:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.41 % (1255808)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=739391240:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.41 % (1255810)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=1270751297:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.41 % (1255806)Instruction limit reached!
% 0.30/0.41 % (1255806)------------------------------
% 0.30/0.41 % (1255806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (1255806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (1255806)CaDiCaL version: 2.1.3
% 0.30/0.41 % (1255806)Termination reason: Instruction limit
% 0.30/0.41 % (1255806)Termination phase: Property scanning
% 0.30/0.41 % (1255806)Time elapsed: 0.003 s
% 0.30/0.41 % (1255806)Peak memory usage: 10 MB
% 0.30/0.41 % (1255806)Instructions burned: 3 (million)
% 0.30/0.41 % (1255804) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1255799-1255804"...
% 0.30/0.41 % (1255810) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1255799-1255810"...
% 0.30/0.41 % (1255805)Instruction limit reached!
% 0.30/0.41 % (1255805)------------------------------
% 0.30/0.41 % (1255805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (1255805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (1255805)CaDiCaL version: 2.1.3
% 0.30/0.41 % (1255805)Termination reason: Instruction limit
% 0.30/0.41 % (1255805)Termination phase: Saturation
% 0.30/0.41 % (1255805)Time elapsed: 0.016 s
% 0.30/0.41 % (1255805)Peak memory usage: 12 MB
% 0.30/0.41 % (1255805)Instructions burned: 18 (million)
% 0.30/0.41 % (1255804)...printing done.
% 0.30/0.41 % (1255804)Refutation found. Thanks to Tanya!
% 0.30/0.41 % SZS status Theorem for theBenchmark
% 0.30/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.41 % (1255804)------------------------------
% 0.30/0.41 % (1255804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (1255804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (1255804)CaDiCaL version: 2.1.3
% 0.30/0.41 % (1255804)Termination reason: Refutation
% 0.30/0.41 % (1255804)Time elapsed: 0.022 s
% 0.30/0.41 % (1255804)Peak memory usage: 12 MB
% 0.30/0.41 % (1255804)Instructions burned: 22 (million)
% 0.30/0.41 % (1255799)Success in time 0.061 s
% 0.30/0.41 % Vampire exiting
%------------------------------------------------------------------------------