%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PHI043^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:20:21 AM UTC 2026
% Result : Theorem 6.56s 1.21s
% Output : Refutation 6.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 14
% Syntax : Number of formulae : 134 ( 76 unt; 0 typ; 0 def)
% Number of atoms : 1214 ( 357 equ; 0 cnn)
% Maximal formula atoms : 13 ( 9 avg)
% Number of connectives : 1980 ( 127 ~; 201 |; 14 &;1514 @)
% ( 2 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 400 ( 400 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 55 usr; 5 con; 0-4 aty)
% ( 62 !!; 10 ??; 0 @@+; 0 @@-)
% Number of variables : 623 ( 448 ^; 173 !; 2 ?; 623 :)
% 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,
eiw_ind: $i > mu > $o ).
thf(func_def_25,type,
mforall_eiw_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_26,type,
mexists_eiw_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_27,type,
p: ( mu > $i > $o ) > $i > $o ).
thf(func_def_28,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_31,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_34,type,
vNOT: $o > $o ).
thf(func_def_35,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vOR: $o > $o > $o ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
vIFF: $o > $o > $o ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
sK0: $i > mu ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK2: mu > $i > $o ).
thf(func_def_48,type,
sK3: ( mu > $i > $o ) > $i > ( mu > $i > $o ) > $i ).
thf(func_def_49,type,
sK4: ( mu > $i > $o ) > $i > ( mu > $i > $o ) > mu ).
thf(func_def_51,type,
sK6: $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_52,type,
sK7: ( mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_53,type,
sK8: $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_54,type,
sK9: ( mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_55,type,
sK10: ( mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > $i ).
thf(func_def_56,type,
sK11: ( mu > $i > $i ) > ( mu > $i > mu ) > mu ).
thf(func_def_57,type,
sK12: ( mu > $i > $o ) > mu ).
thf(f4,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mnot) ).
thf(f7,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL016^0.ax',mequiv) ).
thf(f12,axiom,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mforall_indset) ).
thf(f17,axiom,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox_generic) ).
thf(f18,axiom,
( mdia_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mdia_generic) ).
thf(f19,axiom,
( mbox
= ( mbox_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox) ).
thf(f20,axiom,
( mdia
= ( mdia_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mdia) ).
thf(f21,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mvalid) ).
thf(f24,axiom,
( mforall_eiw_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( eiw_ind @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL017^1.ax',mforall_eiw_ind) ).
thf(f25,axiom,
( mexists_eiw_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_eiw_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL017^1.ax',mexists_eiw_ind) ).
thf(f26,axiom,
( mvalid
@ ( mnot
@ ( p
@ ^ [X0: mu,X1: $i] : ( X0 != X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(f27,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies
@ ( mbox
@ ( mforall_eiw_ind
@ ^ [X2: mu] : ( mequiv @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) )
@ ( mequiv @ ( p @ X0 ) @ ( p @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axii) ).
thf(f28,conjecture,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( p @ X0 )
@ ( mdia
@ ( mexists_eiw_ind
@ ^ [X1: mu] : ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',possible_instantiation_of_the_positive_variable_domain) ).
thf(f29,negated_conjecture,
~ ( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( p @ X0 )
@ ( mdia
@ ( mexists_eiw_ind
@ ^ [X1: mu] : ( X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
thf(f33,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f34,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f39,plain,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f40,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f43,plain,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f44,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f49,plain,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f50,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f59,plain,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f60,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f61,plain,
( mdia_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f62,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f63,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f21]) ).
thf(f64,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f69,plain,
( mforall_eiw_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( eiw_ind @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f70,plain,
( mforall_eiw_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( eiw_ind @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( mexists_eiw_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_eiw_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f72,plain,
( mexists_eiw_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_eiw_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( mvalid
@ ( mnot
@ ( p
@ ^ [X0: mu,X1: $i] : ( X0 != X0 ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f74,plain,
( $true
= ( mvalid
@ ( mnot
@ ( p
@ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 ) ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f75,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies
@ ( mbox
@ ( mforall_eiw_ind
@ ^ [X2: mu] : ( mequiv @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) )
@ ( mequiv @ ( p @ X0 ) @ ( p @ X1 ) ) ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f76,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies
@ ( mbox
@ ( mforall_eiw_ind
@ ^ [Y2: mu] : ( mequiv @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) )
@ ( mequiv @ ( p @ Y0 ) @ ( p @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f77,plain,
~ ( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( p @ X0 )
@ ( mdia
@ ( mexists_eiw_ind
@ ^ [X1: mu] : ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f78,plain,
( $true
!= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( p @ Y0 )
@ ( mdia
@ ( mexists_eiw_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f79,plain,
( $true
!= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( p @ Y0 )
@ ( mdia
@ ( mexists_eiw_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(flattening,[],[f78]) ).
thf(f84,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f87,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f89,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f92,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f97,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f98,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f99,plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f100,plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f101,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f104,plain,
( mforall_eiw_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( eiw_ind @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f105,plain,
( mexists_eiw_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_eiw_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f106,plain,
( $true
= ( mvalid
@ ( mnot
@ ( p
@ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f107,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies
@ ( mbox
@ ( mforall_eiw_ind
@ ^ [Y2: mu] : ( mequiv @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) )
@ ( mequiv @ ( p @ Y0 ) @ ( p @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f108,plain,
( $true
!= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( p @ Y0 )
@ ( mdia
@ ( mexists_eiw_ind
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f111,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f99,f97]) ).
thf(f112,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f100,f98]) ).
thf(f113,plain,
( mexists_eiw_ind
= ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( eiw_ind @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f105,f84,f104,f84]) ).
thf(f114,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( p
@ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f106,f101,f84]) ).
thf(f115,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 > $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] :
( ( eiw_ind @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
= ( Y4 @ Y5 ) )
@ ( Y0 @ Y2 )
@ ( Y1 @ Y2 ) ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( p @ Y0 )
@ ( p @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f107,f101,f92,f92,f87,f111,f104,f89,f89]) ).
thf(f116,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 ) )
@ ( p @ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
& ( Y2 @ Y4 ) ) )
@ rel
@ ( ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( eiw_ind @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( Y1 @ Y2 ) ) ) )
@ ^ [Y1: mu] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f108,f101,f92,f87,f112,f113]) ).
thf(f117,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( p @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( rel @ Y0 @ Y2 )
& ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( eiw_ind @ Y2 @ Y3 )
=> ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( p @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( rel @ Y0 @ Y2 )
& ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( eiw_ind @ Y2 @ Y3 )
=> ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f117]) ).
thf(f119,plain,
( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( p @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( rel @ sK1 @ Y1 )
& ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( eiw_ind @ Y1 @ Y2 )
=> ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
( $false
= ( ^ [Y0: mu > $i > $o] :
( ( p @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( rel @ sK1 @ Y1 )
& ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( eiw_ind @ Y1 @ Y2 )
=> ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f119]) ).
thf(f121,plain,
( $false
= ( ( p @ sK2 @ sK1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
& ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ~ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
& ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ~ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f123,plain,
( $true
= ( p @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f124,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
& ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ~ ( sK2 @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f122]) ).
thf(f125,plain,
! [X1: $i] :
( $false
= ( ( rel @ sK1 @ X1 )
& ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( eiw_ind @ X1 @ Y0 )
=> ~ ( sK2 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( eiw_ind @ X1 @ Y0 )
=> ~ ( sK2 @ Y0 @ X1 ) ) ) ) )
| ( $false
= ( rel @ sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( eiw_ind @ X1 @ Y0 )
=> ~ ( sK2 @ Y0 @ X1 ) ) ) )
| ( $false
= ( rel @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( ^ [Y0: mu] :
( ( eiw_ind @ X1 @ Y0 )
=> ~ ( sK2 @ Y0 @ X1 ) )
@ X2 ) )
| ( $false
= ( rel @ sK1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( ( eiw_ind @ X1 @ X2 )
=> ~ ( sK2 @ X2 @ X1 ) ) )
| ( $false
= ( rel @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f130,plain,
! [X2: mu,X1: $i] :
( ( ( eiw_ind @ X1 @ X2 )
= $false )
| ( $false
= ( rel @ sK1 @ X1 ) )
| ( $true
= ( ~ ( sK2 @ X2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X2: mu,X1: $i] :
( ( ( eiw_ind @ X1 @ X2 )
= $false )
| ( $false
= ( rel @ sK1 @ X1 ) )
| ( $false
= ( sK2 @ X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f130]) ).
thf(f132,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] :
( ( eiw_ind @ Y3 @ Y4 )
=> ( ( Y1 @ Y4 @ Y3 )
= ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( p @ Y1 @ Y0 )
= ( p @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f133,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] :
( ( eiw_ind @ Y3 @ Y4 )
=> ( ( Y1 @ Y4 @ Y3 )
= ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( p @ Y1 @ Y0 )
= ( p @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f132]) ).
thf(f134,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] :
( ( eiw_ind @ Y2 @ Y3 )
=> ( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( p @ Y0 @ X1 )
= ( p @ Y1 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f135,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] :
( ( eiw_ind @ Y2 @ Y3 )
=> ( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( p @ Y0 @ X1 )
= ( p @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ X1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( eiw_ind @ Y1 @ Y2 )
=> ( ( X2 @ Y2 @ Y1 )
= ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( p @ X2 @ X1 )
= ( p @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,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] :
( ( eiw_ind @ Y1 @ Y2 )
=> ( ( X2 @ Y2 @ Y1 )
= ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( p @ X2 @ X1 )
= ( p @ Y0 @ X1 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( ( X2 @ Y1 @ Y0 )
= ( X3 @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( ( X2 @ Y1 @ Y0 )
= ( X3 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( ( X2 @ Y1 @ Y0 )
= ( X3 @ Y1 @ Y0 ) ) ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ~ ( rel @ X1 @ ( sK3 @ X3 @ X1 @ X2 ) )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( eiw_ind @ ( sK3 @ X3 @ X1 @ X2 ) @ Y0 )
=> ( ( X2 @ Y0 @ ( sK3 @ X3 @ X1 @ X2 ) )
= ( X3 @ Y0 @ ( sK3 @ X3 @ X1 @ X2 ) ) ) ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( eiw_ind @ ( sK3 @ X3 @ X1 @ X2 ) @ Y0 )
=> ( ( X2 @ Y0 @ ( sK3 @ X3 @ X1 @ X2 ) )
= ( X3 @ Y0 @ ( sK3 @ X3 @ X1 @ X2 ) ) ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ~ ( rel @ X1 @ ( sK3 @ X3 @ X1 @ X2 ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f144,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( p @ X2 @ X1 ) )
| ( $false
= ( p @ X3 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f145]) ).
thf(f148,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: mu] :
( ( eiw_ind @ ( sK3 @ X3 @ X1 @ X2 ) @ Y0 )
=> ( ( X2 @ Y0 @ ( sK3 @ X3 @ X1 @ X2 ) )
= ( X3 @ Y0 @ ( sK3 @ X3 @ X1 @ X2 ) ) ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f142]) ).
thf(f149,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ( eiw_ind @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK4 @ X3 @ X1 @ X2 ) )
=> ( ( X2 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) )
= ( X3 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ( X2 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) )
= ( X3 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( eiw_ind @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f152,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( eiw_ind @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( eiw_ind @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( p @ X2 @ X1 ) )
| ( $false
= ( p @ X3 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f152]) ).
thf(f155,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( X2 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) )
!= ( X3 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) ) ),
inference(iff_proxy_clausification,[],[f150]) ).
thf(f156,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) ) )
| ( $true
= ( X3 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) ) ),
inference(xor_proxy_clausification,[],[f155]) ).
thf(f161,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( ( p @ X2 @ X1 )
= ( p @ X3 @ X1 ) )
| ( $true
= ( X3 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) ) ),
inference(iff_proxy_clausification,[],[f156]) ).
thf(f162,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( X3 @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( p @ X2 @ X1 ) )
| ( $false
= ( p @ X3 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( p
@ ^ [Y1: mu,Y2: $i] : ( Y1 != Y1 )
@ Y0 ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f165,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( p
@ ^ [Y1: mu,Y2: $i] : ( Y1 != Y1 )
@ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( $true
= ( ~ ( p
@ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 )
@ X1 ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 )
@ X1 ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ~ $true
@ X1 ) ),
inference(boolean_simplification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X1 ) ),
inference(boolean_simplification,[],[f168]) ).
thf(f188,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel @ sK1 @ ( sK3 @ X0 @ X1 @ X2 ) ) )
| ( $false
= ( sK2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( sK3 @ X0 @ X1 @ X2 ) ) )
| ( $true
= ( p @ X2 @ X1 ) )
| ( $false
= ( p @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f131,f153]) ).
thf(f189,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( sK2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( sK3 @ X0 @ X1 @ X2 ) ) )
| ( $false
= ( rel @ sK1 @ ( sK3 @ X0 @ X1 @ X2 ) ) )
| ( $true
= ( p @ X2 @ X1 ) )
| ( $false
= ( p @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f658,plain,
! [X2: mu > $i > $o,X3: mu > $i > mu,X0: mu > $i > $o,X1: $i,X4: $i,X5: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( rel @ sK1 @ ( sK3 @ X0 @ X1 @ X2 ) ) )
| ( $true
= ( p @ X2 @ X1 ) )
| ( $false
= ( p @ X0 @ X1 ) )
| ( $true
= ( X5
@ ( sK4
@ ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X3 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X4
@ X5 )
@ ( sK3
@ ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X3 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X4
@ X5 ) ) )
| ( $true
= ( p @ X5 @ X4 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X3 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X4 ) )
| ( ( ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 ) )
!= X0 )
| ( X1 != X4 )
| ( X2 != X5 )
| ( ( sK4 @ X0 @ X1 @ X2 )
!= ( X3
@ ( sK4
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 )
@ X4
@ X5 )
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 )
@ X4
@ X5 ) ) ) ),
inference(constrained_superposition,[],[f189,f162]) ).
thf(f722,plain,
! [X2: mu > $i > $o,X3: mu > $i > mu,X0: mu > $i > $o,X1: $i,X4: $i,X5: mu > $i > $o] :
( ( $false
= ( rel @ sK1 @ ( sK3 @ X0 @ X1 @ X2 ) ) )
| ( $true
= ( p @ X2 @ X1 ) )
| ( $false
= ( p @ X0 @ X1 ) )
| ( $true
= ( X5
@ ( sK4
@ ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X3 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X4
@ X5 )
@ ( sK3
@ ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X3 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X4
@ X5 ) ) )
| ( $true
= ( p @ X5 @ X4 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X3 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X4 ) )
| ( ( ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 ) )
!= X0 )
| ( X1 != X4 )
| ( X2 != X5 )
| ( ( sK4 @ X0 @ X1 @ X2 )
!= ( X3
@ ( sK4
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 )
@ X4
@ X5 )
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 )
@ X4
@ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f658]) ).
thf(f723,plain,
! [X2: mu > $i > $o,X3: mu > $i > mu,X0: mu > $i > $o,X1: $i,X4: $i,X5: mu > $i > $o] :
( ( ( sK4 @ X0 @ X1 @ X2 )
!= ( X3
@ ( sK4
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 )
@ X4
@ X5 )
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 )
@ X4
@ X5 ) ) )
| ( $true
= ( p @ X2 @ X1 ) )
| ( $false
= ( p @ X0 @ X1 ) )
| ( $true
= ( X5
@ ( sK4
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 )
@ X4
@ X5 )
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 )
@ X4
@ X5 ) ) )
| ( $true
= ( p @ X5 @ X4 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 )
@ X4 ) )
| ( ( ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X3 @ Y0 @ Y1 ) @ Y1 ) )
!= X0 )
| ( $false
= ( rel @ sK1 @ ( sK3 @ X0 @ X1 @ X2 ) ) )
| ( X2 != X5 )
| ( X1 != X4 ) ),
inference(beta-eta_normalization,[],[f722]) ).
thf(f1067,plain,
! [X2: mu > $i > mu,X3: mu > $i > $i,X0: mu > $i > $o,X1: $i,X4: mu > $i > $o,X5: $i] :
( ( $true
= ( p @ X0 @ X1 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X1 ) )
| ( $true
= ( X4
@ ( sK4
@ ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ Y1 )
@ X5
@ X4 )
@ ( sK3
@ ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ Y1 )
@ X5
@ X4 ) ) )
| ( $true
= ( p @ X4 @ X5 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ Y1 )
@ X5 ) )
| ( ( ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ Y1 ) )
!= ( ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) ) ) )
| ( $false
= ( rel @ sK1
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X1
@ X0 ) ) )
| ( X0 != X4 )
| ( X1 != X5 )
| ( X0 != X4 )
| ( X1 != X5 )
| ( ( ^ [Y0: mu,Y1: $i] : Y1 )
!= X3 )
| ( ( ^ [Y0: mu,Y1: $i] : Y0 )
!= X2 ) ),
inference(equality_resolution,[],[f723]) ).
thf(f1070,plain,
! [X2: mu > $i > mu,X3: mu > $i > $i,X0: mu > $i > $o,X1: $i,X4: mu > $i > $o,X5: $i] :
( ( $true
= ( p @ X0 @ X1 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X1 ) )
| ( $true
= ( X4
@ ( sK4
@ ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ Y1 )
@ X5
@ X4 )
@ ( sK3
@ ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ Y1 )
@ X5
@ X4 ) ) )
| ( $true
= ( p @ X4 @ X5 ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ Y1 )
@ X5 ) )
| ( ( ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ Y1 ) )
!= ( ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) ) ) )
| ( $false
= ( rel @ sK1
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X1
@ X0 ) ) )
| ( X0 != X4 )
| ( X1 != X5 )
| ( ( ^ [Y0: mu,Y1: $i] : Y1 )
!= X3 )
| ( ( ^ [Y0: mu,Y1: $i] : Y0 )
!= X2 ) ),
inference(duplicate_literal_removal,[],[f1067]) ).
thf(f1071,plain,
! [X2: mu > $i > mu,X3: mu > $i > $i,X0: mu > $i > $o,X1: $i,X4: mu > $i > $o,X5: $i] :
( ( sK2
!= ( ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) ) ) )
| ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X1 ) )
| ( $true
= ( X4 @ ( sK4 @ sK2 @ X5 @ X4 ) @ ( sK3 @ sK2 @ X5 @ X4 ) ) )
| ( $true
= ( p @ X4 @ X5 ) )
| ( $false
= ( p @ sK2 @ X5 ) )
| ( $true
= ( p @ X0 @ X1 ) )
| ( $false
= ( rel @ sK1
@ ( sK3
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X2 @ Y0 @ Y1 ) @ ( X3 @ Y0 @ Y1 ) )
@ X1
@ X0 ) ) )
| ( ( ^ [Y0: mu,Y1: $i] : Y1 )
!= X3 )
| ( ( ^ [Y0: mu,Y1: $i] : Y0 )
!= X2 )
| ( X0 != X4 )
| ( X1 != X5 ) ),
inference(beta-eta_normalization,[],[f1070]) ).
thf(f1073,plain,
! [X2: $i,X3: mu > $i > $o,X0: $i,X1: mu > $i > $o] :
( ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X0 ) )
| ( $true
= ( X1 @ ( sK4 @ sK2 @ X2 @ X1 ) @ ( sK3 @ sK2 @ X2 @ X1 ) ) )
| ( $true
= ( p @ X1 @ X2 ) )
| ( $false
= ( p @ sK2 @ X2 ) )
| ( $true
= ( p @ X3 @ X0 ) )
| ( $false
= ( rel @ sK1
@ ( sK3
@ ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X0
@ X3 ) ) )
| ( ( ^ [Y0: mu,Y1: $i] : Y1 )
!= ( ^ [Y0: mu,Y1: $i] : Y1 ) )
| ( ( ^ [Y0: mu,Y1: $i] : Y0 )
!= ( ^ [Y0: mu,Y1: $i] : Y0 ) )
| ( X1 != X3 )
| ( X0 != X2 ) ),
inference(equality_resolution,[],[f1071]) ).
thf(f1074,plain,
! [X2: $i,X3: mu > $i > $o,X0: $i,X1: mu > $i > $o] :
( ( $false
= ( p
@ ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X0 ) )
| ( $true
= ( X1 @ ( sK4 @ sK2 @ X2 @ X1 ) @ ( sK3 @ sK2 @ X2 @ X1 ) ) )
| ( $true
= ( p @ X1 @ X2 ) )
| ( $false
= ( p @ sK2 @ X2 ) )
| ( $true
= ( p @ X3 @ X0 ) )
| ( $false
= ( rel @ sK1
@ ( sK3
@ ^ [Y0: mu,Y1: $i] :
( sK2
@ ( ^ [Y2: mu,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X0
@ X3 ) ) )
| ( X1 != X3 )
| ( X0 != X2 ) ),
inference(trivial_inequality_removal,[],[f1073]) ).
thf(f1075,plain,
! [X2: $i,X3: mu > $i > $o,X0: $i,X1: mu > $i > $o] :
( ( $true
= ( X1 @ ( sK4 @ sK2 @ X2 @ X1 ) @ ( sK3 @ sK2 @ X2 @ X1 ) ) )
| ( $false
= ( rel @ sK1 @ ( sK3 @ sK2 @ X0 @ X3 ) ) )
| ( $true
= ( p @ X1 @ X2 ) )
| ( $false
= ( p @ sK2 @ X2 ) )
| ( $true
= ( p @ X3 @ X0 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( X1 != X3 )
| ( X0 != X2 ) ),
inference(beta-eta_normalization,[],[f1074]) ).
thf(f1083,plain,
! [X2: $i,X3: mu > $i > $o,X0: $i] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] : $false
@ ( sK4 @ sK2 @ X2
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK3 @ sK2 @ X2
@ ^ [Y0: mu,Y1: $i] : $false ) ) )
| ( $false
= ( rel @ sK1 @ ( sK3 @ sK2 @ X0 @ X3 ) ) )
| ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X2 ) )
| ( $false
= ( p @ sK2 @ X2 ) )
| ( $true
= ( p @ X3 @ X0 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( ( ^ [Y0: mu,Y1: $i] : $false )
!= X3 )
| ( X0 != X2 ) ),
inference(primitive_instantiation,[],[f1075]) ).
thf(f1261,plain,
! [X2: $i,X3: mu > $i > $o,X0: $i] :
( ( $true = $false )
| ( $false
= ( rel @ sK1 @ ( sK3 @ sK2 @ X0 @ X3 ) ) )
| ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X2 ) )
| ( $false
= ( p @ sK2 @ X2 ) )
| ( $true
= ( p @ X3 @ X0 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( ( ^ [Y0: mu,Y1: $i] : $false )
!= X3 )
| ( X0 != X2 ) ),
inference(beta-eta_normalization,[],[f1083]) ).
thf(f1262,plain,
! [X2: $i,X3: mu > $i > $o,X0: $i] :
( ( $false
= ( rel @ sK1 @ ( sK3 @ sK2 @ X0 @ X3 ) ) )
| ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X2 ) )
| ( $false
= ( p @ sK2 @ X2 ) )
| ( $true
= ( p @ X3 @ X0 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( ( ^ [Y0: mu,Y1: $i] : $false )
!= X3 )
| ( X0 != X2 ) ),
inference(trivial_inequality_removal,[],[f1261]) ).
thf(f1271,plain,
! [X2: $i,X3: mu > $i > $o,X0: $i] :
( ( $true = $false )
| ( $false
= ( rel @ sK1 @ ( sK3 @ sK2 @ X0 @ X3 ) ) )
| ( $false
= ( p @ sK2 @ X2 ) )
| ( $true
= ( p @ X3 @ X0 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( ( ^ [Y0: mu,Y1: $i] : $false )
!= X3 )
| ( X0 != X2 ) ),
inference(forward_demodulation,[],[f1262,f169]) ).
thf(f1272,plain,
! [X2: $i,X3: mu > $i > $o,X0: $i] :
( ( ( ^ [Y0: mu,Y1: $i] : $false )
!= X3 )
| ( $false
= ( p @ sK2 @ X2 ) )
| ( $true
= ( p @ X3 @ X0 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( $false
= ( rel @ sK1 @ ( sK3 @ sK2 @ X0 @ X3 ) ) )
| ( X0 != X2 ) ),
inference(trivial_inequality_removal,[],[f1271]) ).
thf(f1279,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( p @ sK2 @ X0 ) )
| ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X1 ) )
| ( $false
= ( p @ sK2 @ X1 ) )
| ( $false
= ( rel @ sK1
@ ( sK3 @ sK2 @ X1
@ ^ [Y0: mu,Y1: $i] : $false ) ) )
| ( X0 != X1 ) ),
inference(equality_resolution,[],[f1272]) ).
thf(f1281,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( $false
= ( p @ sK2 @ X1 ) )
| ( $false
= ( rel @ sK1
@ ( sK3 @ sK2 @ X1
@ ^ [Y0: mu,Y1: $i] : $false ) ) )
| ( X0 != X1 ) ),
inference(forward_demodulation,[],[f1279,f169]) ).
thf(f1282,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( p @ sK2 @ X0 ) )
| ( $false
= ( rel @ sK1
@ ( sK3 @ sK2 @ X1
@ ^ [Y0: mu,Y1: $i] : $false ) ) )
| ( $false
= ( p @ sK2 @ X1 ) )
| ( X0 != X1 ) ),
inference(trivial_inequality_removal,[],[f1281]) ).
thf(f1313,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ sK1 ) )
| ( $false
= ( p @ sK2 @ sK1 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( $false
= ( p @ sK2 @ sK1 ) )
| ( sK1 != X0 ) ),
inference(constrained_superposition,[],[f146,f1282]) ).
thf(f1314,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ sK1 ) )
| ( $false
= ( p @ sK2 @ sK1 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( sK1 != X0 ) ),
inference(duplicate_literal_removal,[],[f1313]) ).
thf(f1315,plain,
! [X0: $i] :
( ( $true
= ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ sK1 ) )
| ( $false
= ( p @ sK2 @ sK1 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( sK1 != X0 ) ),
inference(trivial_inequality_removal,[],[f1314]) ).
thf(f1362,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p @ sK2 @ sK1 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( sK1 != X0 ) ),
inference(forward_demodulation,[],[f1315,f169]) ).
thf(f1363,plain,
! [X0: $i] :
( ( $false
= ( p @ sK2 @ sK1 ) )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( sK1 != X0 ) ),
inference(trivial_inequality_removal,[],[f1362]) ).
thf(f1366,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p @ sK2 @ X0 ) )
| ( sK1 != X0 ) ),
inference(forward_demodulation,[],[f1363,f123]) ).
thf(f1367,plain,
! [X0: $i] :
( ( $false
= ( p @ sK2 @ X0 ) )
| ( sK1 != X0 ) ),
inference(trivial_inequality_removal,[],[f1366]) ).
thf(f1377,plain,
( ( $true = $false )
| ( sK1 != sK1 ) ),
inference(constrained_superposition,[],[f123,f1367]) ).
thf(f1393,plain,
$false,
inference(trivial_inequality_removal,[],[f1377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI043^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:20:01 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 3.89/0.93 % (2633238)Will run a generic schedule for satisfiability detection.
% 3.89/0.93 % (2633244)% WARNING: option uhcvi not known.
% 3.89/0.93 % (2633243)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=637686_2999 on theBenchmark for (2999ds/0Mi)
% 3.89/0.93 % (2633244)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2005398737:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.89/0.93 % (2633244)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.89/0.93 % Exception at run slice level
% 3.89/0.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.89/0.93 % (2633244)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.89/0.93 % (2633245)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1801225131:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.89/0.93 % (2633247)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2198198046:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.89/0.93 % (2633247)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.89/0.93 % (2633246)dis+10_1_sil=32000:sp=arity:random_seed=1625460057:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.89/0.93 % (2633248)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1354060887:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.89/0.93 % (2633249)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=407415868:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.89/0.93 % (2633255)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3545498248:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.89/0.93 % Exception at run slice level
% 3.89/0.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.89/0.93 % (2633247)Instruction limit reached!
% 3.89/0.93 % (2633247)------------------------------
% 3.89/0.93 % (2633247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.89/0.93 % (2633247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/0.93 % (2633247)CaDiCaL version: 2.1.3
% 3.89/0.93 % (2633247)Termination reason: Instruction limit
% 3.89/0.93 % (2633247)Termination phase: Saturation
% 3.89/0.93 % (2633247)Time elapsed: 0.049 s
% 3.89/0.93 % (2633247)Peak memory usage: 12 MB
% 3.89/0.93 % (2633247)Instructions burned: 117 (million)
% 3.89/0.93 % (2633261)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3099643453:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.89/0.93 % (2633262)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=1922667334:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.89/0.93 % (2633262)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.89/0.93 % (2633262)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.89/0.93 % (2633246)Instruction limit reached!
% 3.89/0.93 % (2633246)------------------------------
% 3.89/0.93 % (2633246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.89/0.93 % (2633246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/0.93 % (2633246)CaDiCaL version: 2.1.3
% 3.89/0.93 % (2633246)Termination reason: Instruction limit
% 3.89/0.93 % (2633246)Termination phase: Saturation
% 3.89/0.93 % (2633246)Time elapsed: 0.072 s
% 3.89/0.93 % (2633246)Peak memory usage: 12 MB
% 3.89/0.93 % (2633246)Instructions burned: 104 (million)
% 3.89/0.93 % (2633248)Instruction limit reached!
% 3.89/0.93 % (2633248)------------------------------
% 3.89/0.93 % (2633248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.89/0.93 % (2633248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/0.93 % (2633248)CaDiCaL version: 2.1.3
% 3.89/0.93 % (2633248)Termination reason: Instruction limit
% 3.89/0.93 % (2633248)Termination phase: Saturation
% 3.89/0.93 % (2633248)Time elapsed: 0.079 s
% 3.89/0.93 % (2633248)Peak memory usage: 13 MB
% 3.89/0.93 % (2633248)Instructions burned: 132 (million)
% 3.89/0.93 % (2633265)ott-21_1_sil=16000:fs=off:random_seed=4097727661:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.89/0.93 % (2633266)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2880007968:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.56/1.21 % (2633261)Instruction limit reached!
% 6.56/1.21 % (2633261)------------------------------
% 6.56/1.21 % (2633261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.21 % (2633261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.21 % (2633261)CaDiCaL version: 2.1.3
% 6.56/1.21 % (2633261)Termination reason: Instruction limit
% 6.56/1.21 % (2633261)Termination phase: Saturation
% 6.56/1.21 % (2633261)Time elapsed: 0.062 s
% 6.56/1.21 % (2633261)Peak memory usage: 13 MB
% 6.56/1.21 % (2633261)Instructions burned: 132 (million)
% 6.56/1.21 % (2633249)Instruction limit reached!
% 6.56/1.21 % (2633249)------------------------------
% 6.56/1.21 % (2633249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.21 % (2633249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.21 % (2633249)CaDiCaL version: 2.1.3
% 6.56/1.21 % (2633249)Termination reason: Instruction limit
% 6.56/1.21 % (2633249)Termination phase: Saturation
% 6.56/1.21 % (2633249)Time elapsed: 0.120 s
% 6.56/1.21 % (2633249)Peak memory usage: 13 MB
% 6.56/1.21 % (2633249)Instructions burned: 159 (million)
% 6.56/1.21 % (2633269)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2708624929:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.56/1.21 % Exception at run slice level
% 6.56/1.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.56/1.21 % (2633270)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4166086516:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.56/1.21 % (2633272)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3836429294:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.56/1.21 % Exception at run slice level
% 6.56/1.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.56/1.21 % (2633265)Instruction limit reached!
% 6.56/1.21 % (2633265)------------------------------
% 6.56/1.21 % (2633265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.21 % (2633265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.21 % (2633265)CaDiCaL version: 2.1.3
% 6.56/1.21 % (2633265)Termination reason: Instruction limit
% 6.56/1.21 % (2633265)Termination phase: Saturation
% 6.56/1.21 % (2633265)Time elapsed: 0.081 s
% 6.56/1.21 % (2633265)Peak memory usage: 13 MB
% 6.56/1.21 % (2633265)Instructions burned: 182 (million)
% 6.56/1.21 % (2633276)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3174963814:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 6.56/1.21 % (2633276)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.56/1.21 % (2633275)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=615162493:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 6.56/1.21 % (2633275)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.56/1.21 % (2633262)Instruction limit reached!
% 6.56/1.21 % (2633262)------------------------------
% 6.56/1.21 % (2633262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.21 % (2633262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.21 % (2633262)CaDiCaL version: 2.1.3
% 6.56/1.21 % (2633262)Termination reason: Instruction limit
% 6.56/1.21 % (2633262)Termination phase: Saturation
% 6.56/1.21 % (2633262)Time elapsed: 0.174 s
% 6.56/1.21 % (2633262)Peak memory usage: 15 MB
% 6.56/1.21 % (2633262)Instructions burned: 685 (million)
% 6.56/1.21 % (2633279)fmb+10_1_sil=64000:random_seed=3574386815:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 6.56/1.21 % (2633279)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.56/1.21 % Exception at run slice level
% 6.56/1.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.56/1.21 % (2633281)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=295927200:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 6.56/1.21 % Exception at run slice level
% 6.56/1.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.56/1.21 % (2633283)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=50537213:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 6.56/1.21 % Exception at run slice level
% 6.56/1.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.56/1.21 % (2633285)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3567155082:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 6.56/1.21 % (2633285)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.56/1.21 % (2633266)Instruction limit reached!
% 6.56/1.21 % (2633266)------------------------------
% 6.56/1.21 % (2633266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.21 % (2633266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.21 % (2633266)CaDiCaL version: 2.1.3
% 6.56/1.21 % (2633266)Termination reason: Instruction limit
% 6.56/1.21 % (2633266)Termination phase: Saturation
% 6.56/1.21 % (2633266)Time elapsed: 0.231 s
% 6.56/1.21 % (2633266)Peak memory usage: 14 MB
% 6.56/1.21 % (2633266)Instructions burned: 477 (million)
% 6.56/1.21 % (2633287)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=897908950:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 6.56/1.21 % (2633287)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.56/1.21 % (2633287)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.56/1.21 % (2633270)Instruction limit reached!
% 6.56/1.21 % (2633270)------------------------------
% 6.56/1.21 % (2633270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.21 % (2633270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.21 % (2633270)CaDiCaL version: 2.1.3
% 6.56/1.21 % (2633270)Termination reason: Instruction limit
% 6.56/1.21 % (2633270)Termination phase: Saturation
% 6.56/1.21 % (2633270)Time elapsed: 0.341 s
% 6.56/1.21 % (2633270)Peak memory usage: 17 MB
% 6.56/1.21 % (2633270)Instructions burned: 1184 (million)
% 6.56/1.21 % (2633289)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1205356784:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 6.56/1.21 % Exception at run slice level
% 6.56/1.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.56/1.21 % (2633291)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1932158059:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 6.56/1.21 % Exception at run slice level
% 6.56/1.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.56/1.21 % (2633293)ott-2_1_sil=16000:newcnf=on:random_seed=978111945:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 6.56/1.21 % (2633293)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.56/1.21 % (2633276)Instruction limit reached!
% 6.56/1.21 % (2633276)------------------------------
% 6.56/1.21 % (2633276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.21 % (2633276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.21 % (2633276)CaDiCaL version: 2.1.3
% 6.56/1.21 % (2633276)Termination reason: Instruction limit
% 6.56/1.21 % (2633276)Termination phase: Saturation
% 6.56/1.21 % (2633276)Time elapsed: 0.398 s
% 6.56/1.21 % (2633276)Peak memory usage: 14 MB
% 6.56/1.21 % (2633276)Instructions burned: 880 (million)
% 6.56/1.21 % (2633295)ott+10_1_sil=32000:tgt=ground:random_seed=573870885:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 6.56/1.21 % (2633275)Instruction limit reached!
% 6.56/1.21 % (2633275)------------------------------
% 6.56/1.21 % (2633275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.21 % (2633275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.21 % (2633275)CaDiCaL version: 2.1.3
% 6.56/1.21 % (2633275)Termination reason: Instruction limit
% 6.56/1.21 % (2633275)Termination phase: Saturation
% 6.56/1.21 % (2633275)Time elapsed: 0.412 s
% 6.56/1.21 % (2633275)Peak memory usage: 21 MB
% 6.56/1.21 % (2633275)Instructions burned: 693 (million)
% 6.56/1.21 % (2633297)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2462937440:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 6.56/1.21 % Exception at run slice level
% 6.56/1.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.56/1.21 % (2633299)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=733479292:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 6.56/1.21 % (2633299)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.56/1.21 % (2633293)Instruction limit reached!
% 6.56/1.21 % (2633293)------------------------------
% 6.56/1.21 % (2633293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.21 % (2633293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.21 % (2633293)CaDiCaL version: 2.1.3
% 6.56/1.21 % (2633293)Termination reason: Instruction limit
% 6.56/1.21 % (2633293)Termination phase: Saturation
% 6.56/1.21 % (2633293)Time elapsed: 0.257 s
% 6.56/1.21 % (2633293)Peak memory usage: 16 MB
% 6.56/1.21 % (2633293)Instructions burned: 870 (million)
% 6.56/1.21 % (2633301)dis+21_1_sil=32000:sas=cadical:random_seed=3831940829:i=3773:amm=off_2991 on theBenchmark for (2991ds/3773Mi)
% 6.56/1.21 % (2633301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2633238-2633301"...
% 6.56/1.21 % (2633301)...printing done.
% 6.56/1.21 % (2633301)Refutation found. Thanks to Tanya!
% 6.56/1.21 % SZS status Theorem for theBenchmark
% 6.56/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 6.56/1.22 % (2633301)------------------------------
% 6.56/1.22 % (2633301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.22 % (2633301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.22 % (2633301)CaDiCaL version: 2.1.3
% 6.56/1.22 % (2633301)Termination reason: Refutation
% 6.56/1.22 % (2633301)Time elapsed: 0.120 s
% 6.56/1.22 % (2633301)Peak memory usage: 14 MB
% 6.56/1.22 % (2633301)Instructions burned: 424 (million)
% 6.56/1.22 % (2633238)Success in time 0.979 s
% 6.56/1.22 % Vampire exiting
%------------------------------------------------------------------------------