%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG014^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 07:49:26 AM UTC 2026
% Result : Theorem 0.84s 0.43s
% Output : Refutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 27
% Syntax : Number of formulae : 237 ( 113 unt; 0 typ; 10 def)
% Number of atoms : 1942 ( 324 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 3771 ( 221 ~; 277 |; 199 &;2510 @)
% ( 10 <=>; 223 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 96 ( 91 usr; 23 con; 0-4 aty)
% ( 240 !!; 91 ??; 0 @@+; 0 @@-)
% Number of variables : 866 ( 17 sgn 243 !; 10 ?; 866 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
reg: $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
c: reg > reg > $o ).
thf(func_def_33,type,
dc: reg > reg > $o ).
thf(func_def_34,type,
p: reg > reg > $o ).
thf(func_def_35,type,
eq: reg > reg > $o ).
thf(func_def_36,type,
o: reg > reg > $o ).
thf(func_def_37,type,
po: reg > reg > $o ).
thf(func_def_38,type,
ec: reg > reg > $o ).
thf(func_def_39,type,
pp: reg > reg > $o ).
thf(func_def_40,type,
tpp: reg > reg > $o ).
thf(func_def_41,type,
ntpp: reg > reg > $o ).
thf(func_def_42,type,
catalunya: reg ).
thf(func_def_43,type,
france: reg ).
thf(func_def_44,type,
spain: reg ).
thf(func_def_45,type,
paris: reg ).
thf(func_def_46,type,
a: $i > $i > $o ).
thf(func_def_47,type,
fool: $i > $i > $o ).
thf(func_def_48,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_51,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_53,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
vIMP: $o > $o > $o ).
thf(func_def_55,type,
vAND: $o > $o > $o ).
thf(func_def_56,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_58,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_61,type,
vNOT: $o > $o ).
thf(func_def_62,type,
vOR: $o > $o > $o ).
thf(func_def_63,type,
sK0: $i > ( $i > $o ) > $i ).
thf(func_def_64,type,
sK1: $i > ( $i > $o ) > $i ).
thf(func_def_65,type,
sK2: $i > ( $i > $o ) > $i ).
thf(func_def_66,type,
sK3: reg > reg ).
thf(func_def_67,type,
sK4: reg > reg ).
thf(func_def_70,type,
sK7: reg > reg > reg ).
thf(func_def_71,type,
sK8: reg > reg ).
thf(func_def_72,type,
sK9: reg > reg > reg ).
thf(func_def_73,type,
sK10: reg > reg ).
thf(func_def_74,type,
sK11: reg ).
thf(func_def_75,type,
sK12: reg ).
thf(func_def_76,type,
sK13: reg > reg ).
thf(func_def_77,type,
sK14: reg > reg ).
thf(func_def_78,type,
sK15: reg > reg ).
thf(func_def_79,type,
sK16: reg > reg ).
thf(func_def_80,type,
sK17: reg ).
thf(func_def_81,type,
sK18: reg > reg ).
thf(func_def_82,type,
sK19: reg > reg ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
! [X0: reg] : ( c @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_reflexive) ).
thf(f35,axiom,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f36,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ( p @ X1 @ X0 ) ) )
= eq ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',eq) ).
thf(f37,axiom,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) )
= ec ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f40,axiom,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(f42,axiom,
( ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) )
= ntpp ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(f43,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ fool @ X0 ) @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_axiom_for_fool) ).
thf(f47,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(f48,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f49,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X2: reg,X1: reg] :
( ( o @ X1 @ france )
& ( o @ X1 @ france )
& ~ ( eq @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X2: reg,X1: reg] :
( ( o @ X1 @ france )
& ( o @ X1 @ france )
& ~ ( eq @ X1 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f55,plain,
( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ fool @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f43]) ).
thf(f56,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ fool @ Y0 ) @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f58,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f66,plain,
( ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) )
= ec ),
inference(rectify,[],[f39]) ).
thf(f67,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
( ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) )
= ntpp ),
inference(rectify,[],[f42]) ).
thf(f69,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f71,plain,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f72,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f79,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X1: reg,X2: reg] :
( ( o @ X2 @ france )
& ( o @ X2 @ france )
& ~ ( eq @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f80,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( eq @ Y1 @ Y2 )
& ( o @ Y1 @ france )
& ( o @ Y1 @ france ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f79]) ).
thf(f84,plain,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
inference(rectify,[],[f47]) ).
thf(f85,plain,
( ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) )
= $true ),
inference(fool_elimination,[],[f84]) ).
thf(f103,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f106,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f107,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f106]) ).
thf(f110,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f111,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f110]) ).
thf(f114,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f115,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f114]) ).
thf(f118,plain,
( ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ( p @ X1 @ X0 ) ) )
= eq ),
inference(rectify,[],[f36]) ).
thf(f119,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f118]) ).
thf(f122,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f123,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f122]) ).
thf(f124,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f125,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f124]) ).
thf(f126,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f127,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f126]) ).
thf(f128,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f129,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(fool_elimination,[],[f128]) ).
thf(f134,plain,
! [X0: reg] : ( c @ X0 @ X0 ),
inference(rectify,[],[f32]) ).
thf(f135,plain,
! [X0: reg] :
( ( c @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f134]) ).
thf(f138,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( eq @ Y1 @ Y2 )
& ( o @ Y1 @ france )
& ( o @ Y1 @ france ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f80]) ).
thf(f140,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f141,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f143,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ fool @ Y0 ) @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f145,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f146,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f147,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( eq @ Y1 @ Y2 )
& ( o @ Y1 @ france )
& ( o @ Y1 @ france ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f138]) ).
thf(f149,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f150,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f151,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f111]) ).
thf(f152,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f153,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f115]) ).
thf(f154,plain,
! [X0: reg] :
( ( c @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f135]) ).
thf(f155,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f156,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f127]) ).
thf(f157,plain,
( ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f85]) ).
thf(f160,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f164,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f129]) ).
thf(f169,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f149,f145,f140]) ).
thf(f170,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f160,f153,f153]) ).
thf(f171,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f146,f170]) ).
thf(f172,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f151,f153,f153]) ).
thf(f174,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f152,f172,f171,f171]) ).
thf(f177,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 )
& ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f155,f153,f153]) ).
thf(f178,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ fool
@ Y0 )
@ Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f143,f156,f150,f169,f141]) ).
thf(f179,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y1
@ Y2 )
& ( ^ [Y3: reg,Y4: reg] :
( ?? @ reg
@ ^ [Y5: reg] :
( ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y3 )
& ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y4 ) ) )
@ Y1
@ france )
& ( ^ [Y3: reg,Y4: reg] :
( ?? @ reg
@ ^ [Y5: reg] :
( ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y3 )
& ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y4 ) ) )
@ Y1
@ france ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f147,f156,f141,f177,f170,f170]) ).
thf(f181,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ fool
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( c @ Y1 @ Y2 )
& ~ ( ^ [Y3: reg,Y4: reg] :
( ?? @ reg
@ ^ [Y5: reg] :
( ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y3 )
& ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y4 ) ) )
@ Y1
@ Y2 ) )
@ spain
@ france ) ) ) ),
inference(definition_unfolding,[],[f157,f156,f141,f171]) ).
thf(f184,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 ) ) ) )
@ paris
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f164,f156,f141,f174]) ).
thf(f225,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( fool @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f226,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( fool @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i > $o,X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) ) )
= $false )
| ( ( X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ ( sK2 @ X1 @ X2 ) )
= $false )
| ( ( X2 @ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( ( ~ ( fool @ X1 @ ( sK2 @ X1 @ X2 ) )
| ( X2 @ ( sK2 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ ( sK2 @ X1 @ X2 ) )
= $false )
| ( ( X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( fool @ X1 @ ( sK2 @ X1 @ X2 ) ) )
= $false )
| ( ( X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f236,plain,
! [X2: $i > $o,X1: $i] :
( ( ( fool @ X1 @ ( sK2 @ X1 @ X2 ) )
= $true )
| ( ( X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ Y0 @ Y1 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f238,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ Y0 @ Y1 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X1: $i] :
( ( ~ ( fool @ X1 @ X2 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) ) )
| ( $true
= ( ~ ( fool @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( fool @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f242]) ).
thf(f246,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) ) )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f247,plain,
! [X2: $i,X1: $i] :
( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) )
= $false )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false ) ),
inference(pi_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f250,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) )
@ ( sK3 @ X3 ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) )
@ ( sK4 @ X3 ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) )
@ ( sK3 @ X3 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ ( sK4 @ X3 ) @ X3 )
=> ( c @ ( sK4 @ X3 ) @ spain ) )
= $false )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( ( c @ ( sK3 @ X3 ) @ X3 )
=> ( c @ ( sK3 @ X3 ) @ france ) )
= $false ) ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK4 @ X3 ) @ spain )
= $false )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( ( c @ ( sK3 @ X3 ) @ X3 )
=> ( c @ ( sK3 @ X3 ) @ france ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK4 @ X3 ) @ X3 )
= $true )
| ( ( ( c @ ( sK3 @ X3 ) @ X3 )
=> ( c @ ( sK3 @ X3 ) @ france ) )
= $false )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f253]) ).
thf(f256,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( $false
= ( c @ ( sK3 @ X3 ) @ france ) )
| ( ( c @ ( sK4 @ X3 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f255]) ).
thf(f258,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK4 @ X3 ) @ spain )
= $false )
| ( $false
= ( c @ ( sK3 @ X3 ) @ france ) )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f254]) ).
thf(f260,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ?? @ reg
@ ^ [Y2: reg] :
( ?? @ reg
@ ^ [Y3: reg] :
( ~ ( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) ) )
& ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ france ) ) ) ) )
& ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ france ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f261,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ?? @ reg
@ ^ [Y2: reg] :
( ?? @ reg
@ ^ [Y3: reg] :
( ~ ( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) ) )
& ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ france ) ) ) ) )
& ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ france ) ) ) ) ) ) ) ) ) )
@ sK5 )
= $false ),
inference(sigma_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ sK5 @ Y0 )
| ( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ Y2 ) ) ) )
& ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) )
& ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f261]) ).
thf(f263,plain,
( ( ^ [Y0: $i] :
( ~ ( a @ sK5 @ Y0 )
| ( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ Y2 ) ) ) )
& ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) )
& ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) ) ) )
@ sK6 )
= $false ),
inference(sigma_proxy_clausification,[],[f262]) ).
thf(f264,plain,
( ( ~ ( a @ sK5 @ sK6 )
| ( ?? @ reg
@ ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f263]) ).
thf(f265,plain,
( ( ?? @ reg
@ ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f264]) ).
thf(f266,plain,
( ( ~ ( a @ sK5 @ sK6 ) )
= $false ),
inference(or_proxy_clausification,[],[f264]) ).
thf(f267,plain,
( ( a @ sK5 @ sK6 )
= $true ),
inference(not_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f265]) ).
thf(f269,plain,
! [X1: reg] :
( ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ X1 )
=> ( c @ Y1 @ Y0 ) ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f268]) ).
thf(f270,plain,
! [X2: reg,X1: reg] :
( ( ^ [Y0: reg] :
( ~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ X1 )
=> ( c @ Y1 @ Y0 ) ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) )
@ X2 )
= $false ),
inference(pi_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: reg,X1: reg] :
( ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
! [X2: reg,X1: reg] :
( ( ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) )
= $false )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: reg,X1: reg] :
( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) )
= $false )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) )
= $false )
| ( ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false )
| ( ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) ) ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false ) ),
inference(pi_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) ) )
= $true )
| ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f277,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) ) )
| ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false )
| ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f275]) ).
thf(f278,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false )
| ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) )
@ X4 )
= $true )
| ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f278]) ).
thf(f280,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( ( c @ X4 @ X2 )
=> ( c @ X4 @ X1 ) )
= $true )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) ) )
= $false )
| ( ( c @ X4 @ X1 )
= $true )
| ( ( c @ X4 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( c @ X4 @ X1 )
= $true )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ X1 ) ) ) )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) )
= $false )
| ( ( c @ X4 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ X1 ) )
@ ( sK7 @ X3 @ X1 ) )
= $false )
| ( ( c @ X4 @ X2 )
= $false )
| ( ( c @ X4 @ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( c @ X4 @ X2 )
= $false )
| ( ( c @ X4 @ X1 )
= $true )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ X1 ) )
@ ( sK7 @ X3 @ X1 ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) )
@ ( sK8 @ X3 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( c @ X4 @ X1 )
= $true )
| ( ( ( c @ ( sK7 @ X3 @ X1 ) @ X3 )
=> ( c @ ( sK7 @ X3 @ X1 ) @ X1 ) )
= $false )
| ( $false
= ( ( c @ ( sK8 @ X3 ) @ X3 )
=> ( c @ ( sK8 @ X3 ) @ france ) ) )
| ( ( c @ X4 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f286,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( c @ X4 @ X2 )
= $false )
| ( $false
= ( ( c @ ( sK8 @ X3 ) @ X3 )
=> ( c @ ( sK8 @ X3 ) @ france ) ) )
| ( ( c @ ( sK7 @ X3 @ X1 ) @ X1 )
= $false )
| ( ( c @ X4 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( c @ X4 @ X1 )
= $true )
| ( $false
= ( ( c @ ( sK8 @ X3 ) @ X3 )
=> ( c @ ( sK8 @ X3 ) @ france ) ) )
| ( ( c @ X4 @ X2 )
= $false )
| ( ( c @ ( sK7 @ X3 @ X1 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f285]) ).
thf(f288,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( c @ ( sK7 @ X3 @ X1 ) @ X3 )
= $true )
| ( ( c @ X4 @ X1 )
= $true )
| ( ( c @ X4 @ X2 )
= $false )
| ( ( c @ ( sK8 @ X3 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( c @ ( sK7 @ X3 @ X1 ) @ X3 )
= $true )
| ( ( c @ X4 @ X2 )
= $false )
| ( $true
= ( c @ ( sK8 @ X3 ) @ X3 ) )
| ( ( c @ X4 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f287]) ).
thf(f290,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( c @ ( sK7 @ X3 @ X1 ) @ X1 )
= $false )
| ( ( c @ X4 @ X1 )
= $true )
| ( ( c @ X4 @ X2 )
= $false )
| ( ( c @ ( sK8 @ X3 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f286]) ).
thf(f291,plain,
! [X2: reg,X3: reg,X1: reg,X4: reg] :
( ( ( c @ ( sK7 @ X3 @ X1 ) @ X1 )
= $false )
| ( ( c @ X4 @ X2 )
= $false )
| ( $true
= ( c @ ( sK8 @ X3 ) @ X3 ) )
| ( ( c @ X4 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f286]) ).
thf(f359,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f360,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f360]) ).
thf(f362,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X2: $i,X1: $i] :
( ( ~ ( a @ X1 @ X2 )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f362]) ).
thf(f364,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f367,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f365]) ).
thf(f369,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f367]) ).
thf(f370,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f370]) ).
thf(f372,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ france )
= $true )
| ( $false
= ( c @ X3 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f371]) ).
thf(f414,definition,
( spl20_1
<=> ! [X2: $i,X1: $i] :
( ( fool @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
thf(f415,plain,
( ! [X2: $i,X1: $i] :
( ( fool @ X1 @ X2 )
= $false )
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f414]) ).
thf(f426,definition,
( spl20_4
<=> ! [X3: reg] :
( ( $false
= ( c @ ( sK3 @ X3 ) @ france ) )
| ( ( c @ ( sK4 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
thf(f427,plain,
( ! [X3: reg] :
( ( $false
= ( c @ ( sK3 @ X3 ) @ france ) )
| ( ( c @ ( sK4 @ X3 ) @ X3 )
= $true ) )
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f426]) ).
thf(f428,plain,
( spl20_1
| spl20_4 ),
inference(avatar_split_clause,[],[f256,f426,f414]) ).
thf(f434,definition,
( spl20_6
<=> ! [X3: reg] :
( ( ( c @ ( sK4 @ X3 ) @ spain )
= $false )
| ( $false
= ( c @ ( sK3 @ X3 ) @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
thf(f435,plain,
( ! [X3: reg] :
( ( $false
= ( c @ ( sK3 @ X3 ) @ france ) )
| ( ( c @ ( sK4 @ X3 ) @ spain )
= $false ) )
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f434]) ).
thf(f436,plain,
( spl20_1
| spl20_6 ),
inference(avatar_split_clause,[],[f258,f434,f414]) ).
thf(f441,definition,
( spl20_8
<=> ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
thf(f442,plain,
( ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false )
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f441]) ).
thf(f497,definition,
( spl20_21
<=> ! [X3: reg] :
( ( ( c @ X3 @ france )
= $true )
| ( $false
= ( c @ X3 @ paris ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_21])],[avatar_definition]) ).
thf(f498,plain,
( ! [X3: reg] :
( ( $false
= ( c @ X3 @ paris ) )
| ( ( c @ X3 @ france )
= $true ) )
| ~ spl20_21 ),
inference(avatar_component_clause,[],[f497]) ).
thf(f499,plain,
( spl20_8
| spl20_21 ),
inference(avatar_split_clause,[],[f372,f497,f441]) ).
thf(f557,plain,
! [X0: $i] :
( ( ( fool @ X0 @ X0 )
= $true )
| ( ( fool @ X0 @ X0 )
= $true )
| ( $true = $false ) ),
inference(superposition,[],[f234,f236]) ).
thf(f558,plain,
! [X0: $i] :
( ( ( fool @ X0 @ X0 )
= $true )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[],[f557]) ).
thf(f559,plain,
! [X0: $i] :
( ( fool @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f650,plain,
( ( $true = $false )
| ~ spl20_8 ),
inference(superposition,[],[f267,f442]) ).
thf(f654,plain,
( $false
| ~ spl20_8 ),
inference(trivial_inequality_removal,[],[f650]) ).
thf(f655,plain,
~ spl20_8,
inference(avatar_contradiction_clause,[],[f654]) ).
thf(f733,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( $true = $false )
| ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ ( sK7 @ paris @ X0 ) @ france )
= $true )
| ( $true
= ( c @ ( sK8 @ paris ) @ paris ) )
| ( ( c @ X1 @ X2 )
= $false ) )
| ~ spl20_21 ),
inference(superposition,[],[f498,f289]) ).
thf(f743,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( ( c @ ( sK7 @ paris @ X0 ) @ france )
= $true )
| ( $true = $false )
| ( $false
= ( c @ ( sK8 @ paris ) @ france ) )
| ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ X1 @ X2 )
= $false ) )
| ~ spl20_21 ),
inference(superposition,[],[f288,f498]) ).
thf(f755,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( ( c @ ( sK7 @ paris @ X0 ) @ france )
= $true )
| ( $true
= ( c @ ( sK8 @ paris ) @ paris ) )
| ( ( c @ X1 @ X2 )
= $false )
| ( ( c @ X1 @ X0 )
= $true ) )
| ~ spl20_21 ),
inference(trivial_inequality_removal,[],[f733]) ).
thf(f762,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( ( c @ ( sK7 @ paris @ X0 ) @ france )
= $true )
| ( $false
= ( c @ ( sK8 @ paris ) @ france ) )
| ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ X1 @ X2 )
= $false ) )
| ~ spl20_21 ),
inference(trivial_inequality_removal,[],[f743]) ).
thf(f771,definition,
( spl20_30
<=> ( $false
= ( c @ ( sK8 @ paris ) @ france ) ) ),
introduced(definition,[new_symbols(definition,[spl20_30])],[avatar_definition]) ).
thf(f773,plain,
( ( $false
= ( c @ ( sK8 @ paris ) @ france ) )
| ~ spl20_30 ),
inference(avatar_component_clause,[],[f771]) ).
thf(f776,definition,
( spl20_31
<=> ( $true
= ( c @ ( sK8 @ paris ) @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl20_31])],[avatar_definition]) ).
thf(f778,plain,
( ( $true
= ( c @ ( sK8 @ paris ) @ paris ) )
| ~ spl20_31 ),
inference(avatar_component_clause,[],[f776]) ).
thf(f784,definition,
( spl20_32
<=> ! [X2: reg,X0: reg,X1: reg] :
( ( ( c @ X1 @ X2 )
= $false )
| ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ ( sK7 @ paris @ X0 ) @ france )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl20_32])],[avatar_definition]) ).
thf(f785,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( ( c @ ( sK7 @ paris @ X0 ) @ france )
= $true )
| ( ( c @ X1 @ X2 )
= $false )
| ( ( c @ X1 @ X0 )
= $true ) )
| ~ spl20_32 ),
inference(avatar_component_clause,[],[f784]) ).
thf(f787,plain,
( spl20_31
| spl20_32
| ~ spl20_21 ),
inference(avatar_split_clause,[],[f755,f497,f784,f776]) ).
thf(f792,plain,
( spl20_30
| spl20_32
| ~ spl20_21 ),
inference(avatar_split_clause,[],[f762,f497,f784,f771]) ).
thf(f808,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK8 @ paris ) @ france ) )
| ~ spl20_21
| ~ spl20_31 ),
inference(superposition,[],[f498,f778]) ).
thf(f812,plain,
( ( $true
= ( c @ ( sK8 @ paris ) @ france ) )
| ~ spl20_21
| ~ spl20_31 ),
inference(trivial_inequality_removal,[],[f808]) ).
thf(f816,plain,
( ( $true = $false )
| ~ spl20_21
| ~ spl20_30
| ~ spl20_31 ),
inference(forward_demodulation,[],[f812,f773]) ).
thf(f817,plain,
( $false
| ~ spl20_21
| ~ spl20_30
| ~ spl20_31 ),
inference(trivial_inequality_removal,[],[f816]) ).
thf(f818,plain,
( ~ spl20_21
| ~ spl20_30
| ~ spl20_31 ),
inference(avatar_contradiction_clause,[],[f817]) ).
thf(f1050,plain,
( ! [X2: reg,X3: reg,X0: reg,X1: reg] :
( ( $false
= ( c @ ( sK8 @ paris ) @ france ) )
| ( ( c @ X0 @ X1 )
= $false )
| ( $true
= ( c @ X2 @ france ) )
| ( ( c @ X2 @ X3 )
= $false )
| ( ( c @ X0 @ france )
= $true )
| ( $true = $false ) )
| ~ spl20_32 ),
inference(superposition,[],[f290,f785]) ).
thf(f1074,plain,
( ! [X2: reg,X3: reg,X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
= $false )
| ( $false
= ( c @ ( sK8 @ paris ) @ france ) )
| ( ( c @ X2 @ X3 )
= $false )
| ( ( c @ X0 @ france )
= $true )
| ( $true
= ( c @ X2 @ france ) ) )
| ~ spl20_32 ),
inference(trivial_inequality_removal,[],[f1050]) ).
thf(f1104,definition,
( spl20_37
<=> ! [X0: reg,X1: reg] :
( ( ( c @ X0 @ france )
= $true )
| ( ( c @ X0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl20_37])],[avatar_definition]) ).
thf(f1105,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ X0 @ france )
= $true )
| ( ( c @ X0 @ X1 )
= $false ) )
| ~ spl20_37 ),
inference(avatar_component_clause,[],[f1104]) ).
thf(f1125,plain,
( ! [X2: reg,X3: reg,X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
= $false )
| ( ( c @ X0 @ france )
= $true )
| ( $true
= ( c @ X2 @ france ) )
| ( ( c @ X2 @ X3 )
= $false )
| ( $true
= ( c @ ( sK8 @ paris ) @ paris ) )
| ( $true = $false ) )
| ~ spl20_32 ),
inference(superposition,[],[f785,f291]) ).
thf(f1139,plain,
( ! [X2: reg,X3: reg,X0: reg,X1: reg] :
( ( $true
= ( c @ X2 @ france ) )
| ( $true
= ( c @ ( sK8 @ paris ) @ paris ) )
| ( ( c @ X0 @ france )
= $true )
| ( ( c @ X2 @ X3 )
= $false )
| ( ( c @ X0 @ X1 )
= $false ) )
| ~ spl20_32 ),
inference(trivial_inequality_removal,[],[f1125]) ).
thf(f1338,plain,
( spl20_37
| spl20_37
| spl20_31
| ~ spl20_32 ),
inference(avatar_split_clause,[],[f1139,f784,f776,f1104,f1104]) ).
thf(f1343,plain,
( spl20_30
| spl20_37
| spl20_37
| ~ spl20_32 ),
inference(avatar_split_clause,[],[f1074,f784,f1104,f1104,f771]) ).
thf(f1750,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ ( sK4 @ X0 ) @ X0 )
= $true )
| ( ( c @ ( sK3 @ X0 ) @ X1 )
= $false )
| ( $true = $false ) )
| ~ spl20_4
| ~ spl20_37 ),
inference(superposition,[],[f1105,f427]) ).
thf(f1752,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ ( sK4 @ X0 ) @ X0 )
= $true )
| ( ( c @ ( sK3 @ X0 ) @ X1 )
= $false ) )
| ~ spl20_4
| ~ spl20_37 ),
inference(trivial_inequality_removal,[],[f1750]) ).
thf(f1783,definition,
( spl20_73
<=> ! [X0: reg] :
( $false
= ( c @ ( sK3 @ spain ) @ X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_73])],[avatar_definition]) ).
thf(f1784,plain,
( ! [X0: reg] :
( $false
= ( c @ ( sK3 @ spain ) @ X0 ) )
| ~ spl20_73 ),
inference(avatar_component_clause,[],[f1783]) ).
thf(f1807,plain,
( ( $true = $false )
| ~ spl20_1 ),
inference(superposition,[],[f559,f415]) ).
thf(f1823,plain,
( $false
| ~ spl20_1 ),
inference(trivial_inequality_removal,[],[f1807]) ).
thf(f1824,plain,
~ spl20_1,
inference(avatar_contradiction_clause,[],[f1823]) ).
thf(f1865,plain,
( ! [X0: reg,X1: reg] :
( ( $true = $false )
| ( $false
= ( c @ ( sK4 @ X0 ) @ spain ) )
| ( ( c @ ( sK3 @ X0 ) @ X1 )
= $false ) )
| ~ spl20_6
| ~ spl20_37 ),
inference(superposition,[],[f1105,f435]) ).
thf(f1867,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ ( sK4 @ X0 ) @ spain ) )
| ( ( c @ ( sK3 @ X0 ) @ X1 )
= $false ) )
| ~ spl20_6
| ~ spl20_37 ),
inference(trivial_inequality_removal,[],[f1865]) ).
thf(f1881,plain,
( ! [X0: reg,X1: reg] :
( ( $true = $false )
| ( ( c @ ( sK3 @ spain ) @ X1 )
= $false )
| ( $false
= ( c @ ( sK3 @ spain ) @ X0 ) ) )
| ~ spl20_4
| ~ spl20_6
| ~ spl20_37 ),
inference(superposition,[],[f1867,f1752]) ).
thf(f1892,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ ( sK3 @ spain ) @ X0 ) )
| ( ( c @ ( sK3 @ spain ) @ X1 )
= $false ) )
| ~ spl20_4
| ~ spl20_6
| ~ spl20_37 ),
inference(trivial_inequality_removal,[],[f1881]) ).
thf(f1897,plain,
( spl20_73
| spl20_73
| ~ spl20_4
| ~ spl20_6
| ~ spl20_37 ),
inference(avatar_split_clause,[],[f1892,f1104,f434,f426,f1783,f1783]) ).
thf(f1906,plain,
( ( $true = $false )
| ~ spl20_73 ),
inference(superposition,[],[f154,f1784]) ).
thf(f1924,plain,
( $false
| ~ spl20_73 ),
inference(trivial_inequality_removal,[],[f1906]) ).
thf(f1925,plain,
~ spl20_73,
inference(avatar_contradiction_clause,[],[f1924]) ).
cnf(s3,plain,
( spl20_1
| spl20_4 ),
inference(sat_conversion,[],[f428]) ).
cnf(s5,plain,
( spl20_1
| spl20_6 ),
inference(sat_conversion,[],[f436]) ).
cnf(s19,plain,
( spl20_8
| spl20_21 ),
inference(sat_conversion,[],[f499]) ).
cnf(s27,plain,
~ spl20_8,
inference(sat_conversion,[],[f655]) ).
cnf(s34,plain,
( ~ spl20_21
| spl20_31
| spl20_32 ),
inference(sat_conversion,[],[f787]) ).
cnf(s39,plain,
( ~ spl20_21
| spl20_30
| spl20_32 ),
inference(sat_conversion,[],[f792]) ).
cnf(s41,plain,
( ~ spl20_21
| ~ spl20_30
| ~ spl20_31 ),
inference(sat_conversion,[],[f818]) ).
cnf(s71,plain,
( spl20_37
| ~ spl20_32
| spl20_31
| spl20_37 ),
inference(sat_conversion,[],[f1338]) ).
cnf(s72,plain,
( spl20_31
| ~ spl20_32
| spl20_37 ),
inference(rat,[],[s71]) ).
cnf(s77,plain,
( spl20_37
| ~ spl20_32
| spl20_30
| spl20_37 ),
inference(sat_conversion,[],[f1343]) ).
cnf(s78,plain,
( spl20_30
| ~ spl20_32
| spl20_37 ),
inference(rat,[],[s77]) ).
cnf(s134,plain,
~ spl20_1,
inference(sat_conversion,[],[f1824]) ).
cnf(s145,plain,
( spl20_73
| ~ spl20_6
| ~ spl20_37
| ~ spl20_4
| spl20_73 ),
inference(sat_conversion,[],[f1897]) ).
cnf(s146,plain,
( ~ spl20_4
| ~ spl20_6
| ~ spl20_37
| spl20_73 ),
inference(rat,[],[s145]) ).
cnf(s150,plain,
~ spl20_73,
inference(sat_conversion,[],[f1925]) ).
cnf(s151,plain,
( ~ spl20_4
| ~ spl20_6
| ~ spl20_37 ),
inference(rat,[],[s146,s150]) ).
cnf(s163,plain,
spl20_21,
inference(rat,[],[s19,s27]) ).
cnf(s177,plain,
spl20_6,
inference(rat,[],[s5,s134]) ).
cnf(s179,plain,
spl20_4,
inference(rat,[],[s3,s134]) ).
cnf(s180,plain,
~ spl20_37,
inference(rat,[],[s151,s177,s179]) ).
cnf(s185,plain,
spl20_30,
inference(rat,[],[s39,s78,s163,s180]) ).
cnf(s186,plain,
~ spl20_31,
inference(rat,[],[s41,s163,s185]) ).
cnf(s188,plain,
~ spl20_32,
inference(rat,[],[s72,s180,s186]) ).
cnf(s189,plain,
$false,
inference(rat,[],[s34,s163,s188,s186]) ).
thf(f1929,plain,
$false,
inference(avatar_sat_refutation,[],[s189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEG014^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 18:34:15 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.20/0.35 % (3043157)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (3043174)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1898515473:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (3043175)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (3043175)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.35 % (3043171)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1481108673:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (3043168)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3436050181:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (3043172)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=3993885577:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.35 % (3043169)lrs+10_16_si=on:nwc=1.5:random_seed=265879043:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (3043173)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3978141172:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (3043175)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=3995061336:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (3043171)Instruction limit reached!
% 0.20/0.35 % (3043171)------------------------------
% 0.20/0.35 % (3043171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3043171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3043171)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3043171)Termination reason: Instruction limit
% 0.20/0.35 % (3043171)Termination phase: Property scanning
% 0.20/0.35 % (3043171)Time elapsed: 0.002 s
% 0.20/0.35 % (3043171)Peak memory usage: 10 MB
% 0.20/0.35 % (3043171)Instructions burned: 4 (million)
% 0.20/0.35 % (3043169)Instruction limit reached!
% 0.20/0.35 % (3043169)------------------------------
% 0.20/0.35 % (3043169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3043169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3043169)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3043169)Termination reason: Instruction limit
% 0.20/0.35 % (3043169)Termination phase: Saturation
% 0.20/0.35 % (3043169)Time elapsed: 0.009 s
% 0.20/0.35 % (3043169)Peak memory usage: 11 MB
% 0.20/0.35 % (3043169)Instructions burned: 19 (million)
% 0.20/0.35 % (3043174)Instruction limit reached!
% 0.20/0.35 % (3043174)------------------------------
% 0.20/0.35 % (3043174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3043174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3043174)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3043174)Termination reason: Instruction limit
% 0.20/0.35 % (3043174)Termination phase: Saturation
% 0.20/0.35 % (3043174)Time elapsed: 0.020 s
% 0.20/0.35 % (3043174)Peak memory usage: 12 MB
% 0.20/0.35 % (3043174)Instructions burned: 75 (million)
% 0.20/0.35 % (3043173)Instruction limit reached!
% 0.20/0.35 % (3043173)------------------------------
% 0.20/0.35 % (3043173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3043173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3043173)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3043173)Termination reason: Instruction limit
% 0.20/0.35 % (3043173)Termination phase: Saturation
% 0.20/0.35 % (3043173)Time elapsed: 0.014 s
% 0.20/0.35 % (3043173)Peak memory usage: 11 MB
% 0.20/0.35 % (3043173)Instructions burned: 25 (million)
% 0.20/0.35 % (3043191)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2849639800:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (3043196)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.84/0.38 % (3043191)Instruction limit reached!
% 0.84/0.38 % (3043191)------------------------------
% 0.84/0.38 % (3043191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.38 % (3043191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.38 % (3043191)CaDiCaL version: 2.1.3
% 0.84/0.38 % (3043191)Termination reason: Instruction limit
% 0.84/0.38 % (3043191)Termination phase: Property scanning
% 0.84/0.38 % (3043191)Time elapsed: 0.002 s
% 0.84/0.38 % (3043191)Peak memory usage: 10 MB
% 0.84/0.38 % (3043191)Instructions burned: 4 (million)
% 0.84/0.38 % (3043196)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2465867551:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.84/0.38 % (3043196)Instruction limit reached!
% 0.84/0.38 % (3043196)------------------------------
% 0.84/0.38 % (3043196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.38 % (3043196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.38 % (3043196)CaDiCaL version: 2.1.3
% 0.84/0.38 % (3043196)Termination reason: Instruction limit
% 0.84/0.38 % (3043196)Termination phase: Clausification
% 0.84/0.38 % (3043196)Time elapsed: 0.002 s
% 0.84/0.38 % (3043196)Peak memory usage: 10 MB
% 0.84/0.38 % (3043196)Instructions burned: 8 (million)
% 0.84/0.38 % (3043193)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=94270793:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.84/0.38 % (3043193)Instruction limit reached!
% 0.84/0.38 % (3043193)------------------------------
% 0.84/0.38 % (3043193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.38 % (3043193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.38 % (3043193)CaDiCaL version: 2.1.3
% 0.84/0.38 % (3043193)Termination reason: Instruction limit
% 0.84/0.38 % (3043193)Termination phase: Property scanning
% 0.84/0.38 % (3043193)Time elapsed: 0.003 s
% 0.84/0.38 % (3043193)Peak memory usage: 10 MB
% 0.84/0.38 % (3043193)Instructions burned: 6 (million)
% 0.84/0.38 % (3043198)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2292674432:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.84/0.38 % (3043202)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=4216871338:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.84/0.38 % (3043200)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
% 0.84/0.38 % (3043200)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.84/0.38 % (3043168)Instruction limit reached!
% 0.84/0.38 % (3043168)------------------------------
% 0.84/0.38 % (3043168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.38 % (3043168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.38 % (3043168)CaDiCaL version: 2.1.3
% 0.84/0.38 % (3043168)Termination reason: Instruction limit
% 0.84/0.38 % (3043168)Termination phase: Saturation
% 0.84/0.38 % (3043168)Time elapsed: 0.040 s
% 0.84/0.38 % (3043168)Peak memory usage: 12 MB
% 0.84/0.38 % (3043168)Instructions burned: 88 (million)
% 0.84/0.38 % (3043198)Instruction limit reached!
% 0.84/0.38 % (3043198)------------------------------
% 0.84/0.38 % (3043198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.38 % (3043198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.38 % (3043198)CaDiCaL version: 2.1.3
% 0.84/0.38 % (3043198)Termination reason: Instruction limit
% 0.84/0.38 % (3043198)Termination phase: Property scanning
% 0.84/0.38 % (3043198)Time elapsed: 0.006 s
% 0.84/0.38 % (3043198)Peak memory usage: 10 MB
% 0.84/0.38 % (3043198)Instructions burned: 14 (million)
% 0.84/0.38 % (3043200)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1240472482:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.84/0.38 % (3043204)lrs+10_1_si=on:cs=on:random_seed=1714456300:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.84/0.41 % (3043207)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.84/0.41 % (3043204)Instruction limit reached!
% 0.84/0.41 % (3043204)------------------------------
% 0.84/0.41 % (3043204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.41 % (3043204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.41 % (3043204)CaDiCaL version: 2.1.3
% 0.84/0.41 % (3043204)Termination reason: Instruction limit
% 0.84/0.41 % (3043204)Termination phase: Property scanning
% 0.84/0.41 % (3043204)Time elapsed: 0.004 s
% 0.84/0.41 % (3043204)Peak memory usage: 10 MB
% 0.84/0.41 % (3043204)Instructions burned: 8 (million)
% 0.84/0.41 % (3043200)Instruction limit reached!
% 0.84/0.41 % (3043200)------------------------------
% 0.84/0.41 % (3043200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.41 % (3043200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.41 % (3043200)CaDiCaL version: 2.1.3
% 0.84/0.41 % (3043200)Termination reason: Instruction limit
% 0.84/0.41 % (3043200)Termination phase: Saturation
% 0.84/0.41 % (3043200)Time elapsed: 0.014 s
% 0.84/0.41 % (3043200)Peak memory usage: 11 MB
% 0.84/0.41 % (3043200)Instructions burned: 30 (million)
% 0.84/0.41 % (3043208)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1787817382:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.84/0.41 % (3043207)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=222983494:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.84/0.41 % (3043207)Instruction limit reached!
% 0.84/0.41 % (3043207)------------------------------
% 0.84/0.41 % (3043207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.41 % (3043207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.41 % (3043207)CaDiCaL version: 2.1.3
% 0.84/0.41 % (3043207)Termination reason: Instruction limit
% 0.84/0.41 % (3043207)Termination phase: Property scanning
% 0.84/0.41 % (3043207)Time elapsed: 0.002 s
% 0.84/0.41 % (3043207)Peak memory usage: 9 MB
% 0.84/0.41 % (3043207)Instructions burned: 5 (million)
% 0.84/0.41 % (3043202)Instruction limit reached!
% 0.84/0.41 % (3043202)------------------------------
% 0.84/0.41 % (3043202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.41 % (3043202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.41 % (3043202)CaDiCaL version: 2.1.3
% 0.84/0.41 % (3043202)Termination reason: Instruction limit
% 0.84/0.41 % (3043202)Termination phase: Saturation
% 0.84/0.41 % (3043202)Time elapsed: 0.025 s
% 0.84/0.41 % (3043202)Peak memory usage: 13 MB
% 0.84/0.41 % (3043202)Instructions burned: 88 (million)
% 0.84/0.41 % (3043208)Refutation not found, incomplete strategy
% 0.84/0.41 % (3043208)------------------------------
% 0.84/0.41 % (3043208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.41 % (3043208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.41 % (3043208)CaDiCaL version: 2.1.3
% 0.84/0.41 % (3043208)Termination reason: Refutation not found, incomplete strategy
% 0.84/0.41 % (3043208)Time elapsed: 0.006 s
% 0.84/0.41 % (3043208)Peak memory usage: 12 MB
% 0.84/0.41 % (3043208)Instructions burned: 11 (million)
% 0.84/0.41 % (3043208)------------------------------
% 0.84/0.41 % (3043208)------------------------------
% 0.84/0.41 % (3043215)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3727498550:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.84/0.41 % (3043212)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4232615129:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.84/0.41 % (3043211)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=990236266:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.84/0.41 % (3043215)Instruction limit reached!
% 0.84/0.41 % (3043215)------------------------------
% 0.84/0.41 % (3043215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.41 % (3043215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.41 % (3043215)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043215)Termination reason: Instruction limit
% 0.84/0.43 % (3043215)Termination phase: Saturation
% 0.84/0.43 % (3043215)Time elapsed: 0.004 s
% 0.84/0.43 % (3043215)Peak memory usage: 11 MB
% 0.84/0.43 % (3043215)Instructions burned: 16 (million)
% 0.84/0.43 % (3043216)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2438951432:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.84/0.43 % (3043175)Instruction limit reached!
% 0.84/0.43 % (3043175)------------------------------
% 0.84/0.43 % (3043175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043175)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043175)Termination reason: Instruction limit
% 0.84/0.43 % (3043175)Termination phase: Saturation
% 0.84/0.43 % (3043175)Time elapsed: 0.082 s
% 0.84/0.43 % (3043175)Peak memory usage: 13 MB
% 0.84/0.43 % (3043175)Instructions burned: 158 (million)
% 0.84/0.43 % (3043211)Refutation not found, incomplete strategy
% 0.84/0.43 % (3043211)------------------------------
% 0.84/0.43 % (3043211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043211)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043211)Termination reason: Refutation not found, incomplete strategy
% 0.84/0.43 % (3043211)Time elapsed: 0.006 s
% 0.84/0.43 % (3043211)Peak memory usage: 12 MB
% 0.84/0.43 % (3043211)Instructions burned: 10 (million)
% 0.84/0.43 % (3043211)------------------------------
% 0.84/0.43 % (3043211)------------------------------
% 0.84/0.43 % (3043217)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2459453792:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.84/0.43 % (3043221)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=191073201:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.84/0.43 % (3043221)Instruction limit reached!
% 0.84/0.43 % (3043221)------------------------------
% 0.84/0.43 % (3043221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043221)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043221)Termination reason: Instruction limit
% 0.84/0.43 % (3043221)Termination phase: Property scanning
% 0.84/0.43 % (3043221)Time elapsed: 0.001 s
% 0.84/0.43 % (3043221)Peak memory usage: 10 MB
% 0.84/0.43 % (3043221)Instructions burned: 4 (million)
% 0.84/0.43 % (3043212)Instruction limit reached!
% 0.84/0.43 % (3043212)------------------------------
% 0.84/0.43 % (3043212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043212)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043212)Termination reason: Instruction limit
% 0.84/0.43 % (3043212)Termination phase: Saturation
% 0.84/0.43 % (3043212)Time elapsed: 0.015 s
% 0.84/0.43 % (3043212)Peak memory usage: 12 MB
% 0.84/0.43 % (3043212)Instructions burned: 25 (million)
% 0.84/0.43 % (3043217)Instruction limit reached!
% 0.84/0.43 % (3043217)------------------------------
% 0.84/0.43 % (3043217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043217)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043217)Termination reason: Instruction limit
% 0.84/0.43 % (3043217)Termination phase: Saturation
% 0.84/0.43 % (3043217)Time elapsed: 0.006 s
% 0.84/0.43 % (3043217)Peak memory usage: 12 MB
% 0.84/0.43 % (3043217)Instructions burned: 14 (million)
% 0.84/0.43 % (3043227)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=929800538:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.84/0.43 % (3043223)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1445731408:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.84/0.43 % (3043224)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=414436934:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.84/0.43 % (3043228)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 0.84/0.43 % (3043228)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.84/0.43 % (3043229)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.84/0.43 % (3043228)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=2264153146:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.84/0.43 % (3043229)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=588054480:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.84/0.43 % (3043223)Instruction limit reached!
% 0.84/0.43 % (3043223)------------------------------
% 0.84/0.43 % (3043223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043223)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043223)Termination reason: Instruction limit
% 0.84/0.43 % (3043223)Termination phase: Saturation
% 0.84/0.43 % (3043223)Time elapsed: 0.013 s
% 0.84/0.43 % (3043223)Peak memory usage: 12 MB
% 0.84/0.43 % (3043223)Instructions burned: 26 (million)
% 0.84/0.43 % (3043224)Instruction limit reached!
% 0.84/0.43 % (3043224)------------------------------
% 0.84/0.43 % (3043224)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043224)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043224)Termination reason: Instruction limit
% 0.84/0.43 % (3043224)Termination phase: Saturation
% 0.84/0.43 % (3043224)Time elapsed: 0.011 s
% 0.84/0.43 % (3043224)Peak memory usage: 11 MB
% 0.84/0.43 % (3043224)Instructions burned: 24 (million)
% 0.84/0.43 % (3043229)Instruction limit reached!
% 0.84/0.43 % (3043229)------------------------------
% 0.84/0.43 % (3043229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043229)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043229)Termination reason: Instruction limit
% 0.84/0.43 % (3043229)Termination phase: Property scanning
% 0.84/0.43 % (3043229)Time elapsed: 0.004 s
% 0.84/0.43 % (3043229)Peak memory usage: 10 MB
% 0.84/0.43 % (3043229)Instructions burned: 8 (million)
% 0.84/0.43 % (3043228)Instruction limit reached!
% 0.84/0.43 % (3043228)------------------------------
% 0.84/0.43 % (3043228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043228)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043228)Termination reason: Instruction limit
% 0.84/0.43 % (3043228)Termination phase: Saturation
% 0.84/0.43 % (3043228)Time elapsed: 0.007 s
% 0.84/0.43 % (3043228)Peak memory usage: 11 MB
% 0.84/0.43 % (3043228)Instructions burned: 16 (million)
% 0.84/0.43 % (3043227)Instruction limit reached!
% 0.84/0.43 % (3043227)------------------------------
% 0.84/0.43 % (3043227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043227)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043227)Termination reason: Instruction limit
% 0.84/0.43 % (3043227)Termination phase: Saturation
% 0.84/0.43 % (3043227)Time elapsed: 0.019 s
% 0.84/0.43 % (3043227)Peak memory usage: 12 MB
% 0.84/0.43 % (3043227)Instructions burned: 63 (million)
% 0.84/0.43 % (3043239)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3291132907:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 0.84/0.43 % (3043235)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3050638710:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.84/0.43 % (3043236)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2955639098:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.84/0.43 % (3043237)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3723869338:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.84/0.43 % (3043238)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3216522816:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 0.84/0.43 % (3043236)Instruction limit reached!
% 0.84/0.43 % (3043236)------------------------------
% 0.84/0.43 % (3043236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043236)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043236)Termination reason: Instruction limit
% 0.84/0.43 % (3043236)Termination phase: Function definition elimination
% 0.84/0.43 % (3043236)Time elapsed: 0.004 s
% 0.84/0.43 % (3043236)Peak memory usage: 10 MB
% 0.84/0.43 % (3043236)Instructions burned: 9 (million)
% 0.84/0.43 % (3043237)Instruction limit reached!
% 0.84/0.43 % (3043237)------------------------------
% 0.84/0.43 % (3043237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043237)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043237)Termination reason: Instruction limit
% 0.84/0.43 % (3043237)Termination phase: Saturation
% 0.84/0.43 % (3043237)Time elapsed: 0.011 s
% 0.84/0.43 % (3043237)Peak memory usage: 11 MB
% 0.84/0.43 % (3043237)Instructions burned: 25 (million)
% 0.84/0.43 % (3043216) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3043157-3043216"...
% 0.84/0.43 % (3043238)Instruction limit reached!
% 0.84/0.43 % (3043238)------------------------------
% 0.84/0.43 % (3043238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043238)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043238)Termination reason: Instruction limit
% 0.84/0.43 % (3043238)Termination phase: Saturation
% 0.84/0.43 % (3043238)Time elapsed: 0.011 s
% 0.84/0.43 % (3043238)Peak memory usage: 12 MB
% 0.84/0.43 % (3043238)Instructions burned: 21 (million)
% 0.84/0.43 % (3043235)Instruction limit reached!
% 0.84/0.43 % (3043235)------------------------------
% 0.84/0.43 % (3043235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.43 % (3043235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.43 % (3043235)CaDiCaL version: 2.1.3
% 0.84/0.43 % (3043235)Termination reason: Instruction limit
% 0.84/0.43 % (3043235)Termination phase: Saturation
% 0.84/0.43 % (3043235)Time elapsed: 0.017 s
% 0.84/0.43 % (3043235)Peak memory usage: 12 MB
% 0.84/0.43 % (3043235)Instructions burned: 31 (million)
% 0.84/0.43 % (3043245)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3817695275:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 0.84/0.43 % (3043216)...printing done.
% 0.84/0.43 % (3043216)Refutation found. Thanks to Tanya!
% 0.84/0.43 % SZS status Theorem for theBenchmark
% 0.84/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.84/0.44 % (3043216)------------------------------
% 0.84/0.44 % (3043216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.44 % (3043216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.44 % (3043216)CaDiCaL version: 2.1.3
% 0.84/0.44 % (3043216)Termination reason: Refutation
% 0.84/0.44 % (3043216)Time elapsed: 0.074 s
% 0.84/0.44 % (3043216)Peak memory usage: 14 MB
% 0.84/0.44 % (3043216)Instructions burned: 144 (million)
% 0.84/0.44 % (3043157)Success in time 0.184 s
% 0.84/0.44 % Vampire exiting
%------------------------------------------------------------------------------