%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO442^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:42 AM UTC 2026
% Result : Theorem 0.83s 0.48s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 33
% Syntax : Number of formulae : 334 ( 88 unt; 0 typ; 18 def)
% Number of atoms : 3347 ( 626 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 4854 ( 866 ~; 937 |; 13 &;2686 @)
% ( 18 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 138 ( 138 >; 0 *; 0 +; 0 <<)
% Number of symbols : 87 ( 83 usr; 26 con; 0-4 aty)
% ( 312 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 806 ( 0 sgn 283 !; 0 ?; 806 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
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,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
sK4: $i > $i ).
thf(func_def_57,type,
sK6: $i > $i ).
thf(func_def_58,type,
sK7: $i > $i ).
thf(func_def_59,type,
sK8: $i > $i ).
thf(func_def_60,type,
sK9: $i > $i ).
thf(func_def_61,type,
sK10: $i > $i ).
thf(func_def_62,type,
sK11: $i > $i ).
thf(func_def_63,type,
sK12: $i > $i ).
thf(func_def_64,type,
sK13: $i > $i ).
thf(func_def_67,type,
sK16: $i > $i ).
thf(func_def_68,type,
sK17: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f34,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mequiv @ ( mbox_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ ( mbox_s5 @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ ( mbox_s5 @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f40,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f42,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f49,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f50,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f52,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f56,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f57,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f60,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f61,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f60]) ).
thf(f62,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f63,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f69,plain,
mreflexive @ rel_s5,
inference(rectify,[],[f34]) ).
thf(f70,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f72,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f74,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f77,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f84,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f85,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f84]) ).
thf(f87,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f97,plain,
~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ ( mbox_s5 @ p ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f98,plain,
( ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ ( mbox_s5 @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f101,plain,
( ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ ( mbox_s5 @ p ) ) ) )
!= $true ),
inference(flattening,[],[f98]) ).
thf(f102,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f103,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f105,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f107,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f108,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f109,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f50]) ).
thf(f111,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f61]) ).
thf(f114,plain,
( ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ ( mbox_s5 @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f115,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f116,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f117,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f118,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f119,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f120,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f121,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f124,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f116,f121,f105,f121]) ).
thf(f125,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f117,f121,f107,f121,f121]) ).
thf(f126,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f102,f107,f121]) ).
thf(f127,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f108,f125,f126,f126]) ).
thf(f131,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f109,f119]) ).
thf(f132,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f111,f118]) ).
thf(f133,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f114,f103,f127,f105,f124,f124,f105,f105,f105]) ).
thf(f134,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f115,f120]) ).
thf(f135,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y1 @ Y2 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f136,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y1 @ Y2 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X2 @ Y0 ) )
=> ( rel_s5 @ X2 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X2 @ Y0 ) )
=> ( rel_s5 @ X2 @ X1 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X2 @ X3 ) )
=> ( rel_s5 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X2 @ X3 ) ) )
| ( $true
= ( rel_s5 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X3 @ X1 )
= $false )
| ( ( rel_s5 @ X2 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f145,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f151,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
= $false )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 )
= $false )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f161,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ sK2 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK2 ) )
= $false )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f171,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( ( ~ ( rel_s5 @ sK2 @ sK3 )
| ( p @ sK3 ) )
= $false )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( ( p @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( $true
= ( rel_s5 @ sK2 @ sK3 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f177,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK0 @ sK2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ X1 @ X2 ) )
= $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) )
@ ( sK4 @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK4 @ X2 ) )
| ( p @ ( sK4 @ X2 ) ) ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ ( sK4 @ X2 ) )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK4 @ X2 ) ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK4 @ X2 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( ( ~ ( rel_s5 @ sK2 @ sK5 )
| ( p @ sK5 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK2 @ sK5 )
| ( p @ sK5 ) )
= $false )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( ( p @ sK5 )
= $false )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK2 @ sK5 ) )
= $false )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f201,plain,
! [X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $true
= ( rel_s5 @ sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X2 )
= $true )
| ( $true
= ( rel_s5 @ sK2 @ sK5 ) ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ~ ( rel_s5 @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ X1 @ X2 ) )
= $true )
| ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) )
@ ( sK6 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK6 @ X2 ) )
| ( p @ ( sK6 @ X2 ) ) ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ( ( p @ ( sK6 @ X2 ) )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK6 @ X2 ) ) ) )
| ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f214,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $true
= ( rel_s5 @ X2 @ ( sK6 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( ( p @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f216,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ sK5 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( ( p @ sK5 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( ( p @ sK5 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ X1 @ X2 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( p @ sK5 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( p @ sK5 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( p @ sK5 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) )
@ ( sK7 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ sK5 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK7 @ X2 ) )
| ( p @ ( sK7 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( p @ ( sK7 @ X2 ) )
= $false )
| ( ( p @ sK5 )
= $false ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK7 @ X2 ) ) ) )
| ( ( p @ sK5 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f227,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK7 @ X2 ) ) )
| ( ( p @ sK5 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f305,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f306,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X1: $i] :
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) ) ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f333,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) ) ),
inference(not_proxy_clausification,[],[f308]) ).
thf(f334,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( ( ~ ( rel_s5 @ sK0 @ X2 ) )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
= $false )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ~ ( rel_s5 @ sK0 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ ( sK16 @ X2 ) )
= $false )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ~ ( rel_s5 @ sK0 @ X2 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f337]) ).
thf(f339,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( ~ ( rel_s5 @ sK0 @ X2 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ ( sK16 @ X2 ) )
= $false )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f338]) ).
thf(f340,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( ( ~ ( rel_s5 @ sK0 @ X2 ) )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ ( sK16 @ X2 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f339]) ).
thf(f341,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ ( sK16 @ X2 ) )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ ( sK16 @ X2 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) ) ),
inference(not_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( ~ ( rel_s5 @ X1 @ X3 )
| ( p @ X3 ) )
= $true )
| ( ( ~ ( rel_s5 @ X2 @ ( sK16 @ X2 ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK16 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X3 ) ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( ~ ( rel_s5 @ X2 @ ( sK16 @ X2 ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK16 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $true
= ( p @ X3 ) ) ),
inference(or_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ X2 @ ( sK16 @ X2 ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK16 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X3 ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK16 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( p @ X3 ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( ( ~ ( rel_s5 @ X2 @ ( sK16 @ X2 ) ) )
= $false )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f345]) ).
thf(f348,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $true
= ( rel_s5 @ X2 @ ( sK16 @ X2 ) ) )
| ( $true
= ( p @ X3 ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f347]) ).
thf(f349,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK16 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( $true
= ( p @ X3 ) ) ),
inference(not_proxy_clausification,[],[f346]) ).
thf(f350,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK16 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( $true
= ( p @ X3 ) ) ),
inference(not_proxy_clausification,[],[f349]) ).
thf(f351,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p @ X3 ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK16 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK17 @ X2 ) )
= $false )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ ( sK16 @ X2 ) @ ( sK17 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK17 @ X2 ) @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f351]) ).
thf(f353,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK17 @ X2 ) @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X3 )
= $false ) ),
inference(or_proxy_clausification,[],[f352]) ).
thf(f354,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $false
= ( ~ ( rel_s5 @ ( sK16 @ X2 ) @ ( sK17 @ X2 ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( $true
= ( p @ X3 ) ) ),
inference(or_proxy_clausification,[],[f352]) ).
thf(f355,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ ( sK16 @ X2 ) @ ( sK17 @ X2 ) )
= $true )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X3 ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f354]) ).
thf(f356,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK17 @ X2 ) @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( ( rel_s5 @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f353]) ).
thf(f357,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ ( sK17 @ X2 ) @ Y0 )
| ( p @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( $true
= ( ~ ( rel_s5 @ ( sK17 @ X2 ) @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( p @ X3 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f357]) ).
thf(f359,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X4 ) )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s5 @ ( sK17 @ X2 ) @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f358]) ).
thf(f360,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( ( rel_s5 @ ( sK17 @ X2 ) @ X4 )
= $false )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f359]) ).
thf(f361,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f362,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X1: $i] :
( ( rel_s5 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f362]) ).
thf(f365,definition,
( spl18_1
<=> ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
thf(f367,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f365]) ).
thf(f369,definition,
( spl18_2
<=> ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
thf(f371,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f369]) ).
thf(f372,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f169,f369,f365]) ).
thf(f374,definition,
( spl18_3
<=> ( $true
= ( rel_s5 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
thf(f376,plain,
( ( $true
= ( rel_s5 @ sK2 @ sK3 ) )
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f374]) ).
thf(f377,plain,
( spl18_1
| spl18_3 ),
inference(avatar_split_clause,[],[f175,f374,f365]) ).
thf(f379,definition,
( spl18_4
<=> ( ( p @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
thf(f381,plain,
( ( ( p @ sK3 )
= $false )
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f379]) ).
thf(f382,plain,
( spl18_1
| spl18_4 ),
inference(avatar_split_clause,[],[f173,f379,f365]) ).
thf(f384,definition,
( spl18_5
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK4 @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
thf(f385,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK4 @ X2 ) ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) )
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f384]) ).
thf(f386,plain,
( spl18_5
| spl18_2 ),
inference(avatar_split_clause,[],[f195,f369,f384]) ).
thf(f388,definition,
( spl18_6
<=> ! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( p @ ( sK4 @ X2 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
thf(f389,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( p @ ( sK4 @ X2 ) )
= $false ) )
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f388]) ).
thf(f390,plain,
( spl18_6
| spl18_2 ),
inference(avatar_split_clause,[],[f193,f369,f388]) ).
thf(f392,definition,
( spl18_7
<=> ! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X2 @ ( sK6 @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
thf(f393,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK6 @ X2 ) ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) )
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f392]) ).
thf(f395,definition,
( spl18_8
<=> ( $true
= ( rel_s5 @ sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
thf(f397,plain,
( ( $true
= ( rel_s5 @ sK2 @ sK5 ) )
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f395]) ).
thf(f398,plain,
( spl18_7
| spl18_8 ),
inference(avatar_split_clause,[],[f214,f395,f392]) ).
thf(f400,definition,
( spl18_9
<=> ! [X2: $i,X1: $i] :
( ( ( p @ ( sK6 @ X2 ) )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_9])],[avatar_definition]) ).
thf(f401,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( p @ ( sK6 @ X2 ) )
= $false ) )
| ~ spl18_9 ),
inference(avatar_component_clause,[],[f400]) ).
thf(f402,plain,
( spl18_8
| spl18_9 ),
inference(avatar_split_clause,[],[f212,f400,f395]) ).
thf(f404,definition,
( spl18_10
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK7 @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_10])],[avatar_definition]) ).
thf(f405,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK7 @ X2 ) ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) )
| ~ spl18_10 ),
inference(avatar_component_clause,[],[f404]) ).
thf(f407,definition,
( spl18_11
<=> ( ( p @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl18_11])],[avatar_definition]) ).
thf(f409,plain,
( ( ( p @ sK5 )
= $false )
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f407]) ).
thf(f410,plain,
( spl18_10
| spl18_11 ),
inference(avatar_split_clause,[],[f227,f407,f404]) ).
thf(f412,definition,
( spl18_12
<=> ! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ ( sK7 @ X2 ) )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_12])],[avatar_definition]) ).
thf(f413,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ ( sK7 @ X2 ) )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) )
| ~ spl18_12 ),
inference(avatar_component_clause,[],[f412]) ).
thf(f414,plain,
( spl18_12
| spl18_11 ),
inference(avatar_split_clause,[],[f225,f407,f412]) ).
thf(f458,definition,
( spl18_24
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( p @ X2 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_24])],[avatar_definition]) ).
thf(f459,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X2 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) )
| ~ spl18_24 ),
inference(avatar_component_clause,[],[f458]) ).
thf(f476,definition,
( spl18_28
<=> ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $true
= ( rel_s5 @ X2 @ ( sK16 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_28])],[avatar_definition]) ).
thf(f477,plain,
( ! [X2: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK16 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) )
| ~ spl18_28 ),
inference(avatar_component_clause,[],[f476]) ).
thf(f478,plain,
( spl18_28
| spl18_24 ),
inference(avatar_split_clause,[],[f348,f458,f476]) ).
thf(f480,definition,
( spl18_29
<=> ! [X2: $i] :
( ( ( rel_s5 @ ( sK16 @ X2 ) @ ( sK17 @ X2 ) )
= $true )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_29])],[avatar_definition]) ).
thf(f481,plain,
( ! [X2: $i] :
( ( ( rel_s5 @ ( sK16 @ X2 ) @ ( sK17 @ X2 ) )
= $true )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) )
| ~ spl18_29 ),
inference(avatar_component_clause,[],[f480]) ).
thf(f482,plain,
( spl18_24
| spl18_29 ),
inference(avatar_split_clause,[],[f355,f480,f458]) ).
thf(f484,definition,
( spl18_30
<=> ! [X4: $i,X2: $i] :
( ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( ( rel_s5 @ ( sK17 @ X2 ) @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_30])],[avatar_definition]) ).
thf(f485,plain,
( ! [X2: $i,X4: $i] :
( ( ( rel_s5 @ ( sK17 @ X2 ) @ X4 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $true
= ( p @ X4 ) ) )
| ~ spl18_30 ),
inference(avatar_component_clause,[],[f484]) ).
thf(f486,plain,
( spl18_24
| spl18_30 ),
inference(avatar_split_clause,[],[f360,f484,f458]) ).
thf(f597,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ ( sK17 @ X0 ) @ ( sK16 @ X0 ) ) )
| ( $true = $false ) )
| ~ spl18_29 ),
inference(superposition,[],[f149,f481]) ).
thf(f607,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ ( sK16 @ X0 ) @ X0 )
= $true )
| ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl18_28 ),
inference(superposition,[],[f477,f149]) ).
thf(f626,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ ( sK16 @ X0 ) @ X0 )
= $true )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl18_28 ),
inference(trivial_inequality_removal,[],[f607]) ).
thf(f629,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ ( sK17 @ X0 ) @ ( sK16 @ X0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl18_29 ),
inference(trivial_inequality_removal,[],[f597]) ).
thf(f641,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ ( sK17 @ X0 ) @ X2 ) )
| ( $true = $false )
| ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl18_30 ),
inference(superposition,[],[f143,f485]) ).
thf(f669,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ ( sK17 @ X0 ) @ X2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl18_30 ),
inference(trivial_inequality_removal,[],[f641]) ).
thf(f872,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( ( rel_s5 @ ( sK16 @ X0 ) @ X1 )
= $false )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl18_29
| ~ spl18_30 ),
inference(superposition,[],[f629,f669]) ).
thf(f876,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true = $false )
| ( ( rel_s5 @ ( sK16 @ X0 ) @ X1 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl18_29
| ~ spl18_30 ),
inference(duplicate_literal_removal,[],[f872]) ).
thf(f877,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel_s5 @ ( sK16 @ X0 ) @ X1 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl18_29
| ~ spl18_30 ),
inference(trivial_inequality_removal,[],[f876]) ).
thf(f1586,plain,
( ! [X0: $i] :
( ( $true
= ( p @ X0 ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl18_28
| ~ spl18_29
| ~ spl18_30 ),
inference(superposition,[],[f626,f877]) ).
thf(f1599,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl18_28
| ~ spl18_29
| ~ spl18_30 ),
inference(duplicate_literal_removal,[],[f1586]) ).
thf(f1600,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl18_28
| ~ spl18_29
| ~ spl18_30 ),
inference(trivial_inequality_removal,[],[f1599]) ).
thf(f2016,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true = $false )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X0 ) ) )
| ~ spl18_28
| ~ spl18_29
| ~ spl18_30 ),
inference(superposition,[],[f1600,f143]) ).
thf(f2035,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl18_28
| ~ spl18_29
| ~ spl18_30 ),
inference(trivial_inequality_removal,[],[f2016]) ).
thf(f2048,plain,
( spl18_24
| ~ spl18_28
| ~ spl18_29
| ~ spl18_30 ),
inference(avatar_split_clause,[],[f2035,f484,f480,f476,f458]) ).
thf(f2056,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK2 @ X0 )
= $false )
| ( $true = $false )
| ( $true
= ( p @ X0 ) ) )
| ~ spl18_2
| ~ spl18_24 ),
inference(superposition,[],[f459,f371]) ).
thf(f2067,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK2 @ X0 )
= $false )
| ( $true
= ( p @ X0 ) ) )
| ~ spl18_2
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f2056]) ).
thf(f2306,plain,
( ( ( p @ sK3 )
= $true )
| ( $true = $false )
| ~ spl18_2
| ~ spl18_3
| ~ spl18_24 ),
inference(superposition,[],[f2067,f376]) ).
thf(f2307,plain,
( ( $true
= ( p @ sK5 ) )
| ( $true = $false )
| ~ spl18_2
| ~ spl18_8
| ~ spl18_24 ),
inference(superposition,[],[f2067,f397]) ).
thf(f2320,plain,
( ( $true
= ( p @ sK5 ) )
| ~ spl18_2
| ~ spl18_8
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f2307]) ).
thf(f2330,plain,
( ( ( p @ sK3 )
= $true )
| ~ spl18_2
| ~ spl18_3
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f2306]) ).
thf(f2337,plain,
( ( $true = $false )
| ~ spl18_2
| ~ spl18_8
| ~ spl18_11
| ~ spl18_24 ),
inference(forward_demodulation,[],[f2320,f409]) ).
thf(f2338,plain,
( $false
| ~ spl18_2
| ~ spl18_8
| ~ spl18_11
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f2337]) ).
thf(f2339,plain,
( ~ spl18_2
| ~ spl18_8
| ~ spl18_11
| ~ spl18_24 ),
inference(avatar_contradiction_clause,[],[f2338]) ).
thf(f2347,plain,
( ( $true = $false )
| ~ spl18_2
| ~ spl18_3
| ~ spl18_4
| ~ spl18_24 ),
inference(forward_demodulation,[],[f2330,f381]) ).
thf(f2348,plain,
( $false
| ~ spl18_2
| ~ spl18_3
| ~ spl18_4
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f2347]) ).
thf(f2349,plain,
( ~ spl18_2
| ~ spl18_3
| ~ spl18_4
| ~ spl18_24 ),
inference(avatar_contradiction_clause,[],[f2348]) ).
thf(f2359,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $true
= ( p @ X0 ) ) )
| ~ spl18_1
| ~ spl18_24 ),
inference(superposition,[],[f459,f367]) ).
thf(f2370,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $true
= ( p @ X0 ) ) )
| ~ spl18_1
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f2359]) ).
thf(f2535,plain,
( ( $false != $false )
| ( $false
= ( rel_s5 @ sK1 @ sK1 ) )
| ( ( p @ ( sK7 @ sK1 ) )
= $false )
| ~ spl18_12 ),
inference(equality_factoring,[],[f413]) ).
thf(f2536,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK1 ) )
| ( ( p @ ( sK7 @ sK1 ) )
= $false )
| ~ spl18_12 ),
inference(trivial_inequality_removal,[],[f2535]) ).
thf(f2548,plain,
( ( $true = $false )
| ( ( p @ ( sK7 @ sK1 ) )
= $false )
| ~ spl18_12 ),
inference(forward_demodulation,[],[f2536,f363]) ).
thf(f2549,plain,
( ( ( p @ ( sK7 @ sK1 ) )
= $false )
| ~ spl18_12 ),
inference(trivial_inequality_removal,[],[f2548]) ).
thf(f2621,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $true
= ( p @ ( sK7 @ sK1 ) ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl18_1
| ~ spl18_10
| ~ spl18_24 ),
inference(superposition,[],[f2370,f405]) ).
thf(f2636,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( p @ ( sK7 @ sK1 ) ) ) )
| ~ spl18_1
| ~ spl18_10
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f2621]) ).
thf(f2679,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true = $false ) )
| ~ spl18_1
| ~ spl18_10
| ~ spl18_12
| ~ spl18_24 ),
inference(forward_demodulation,[],[f2636,f2549]) ).
thf(f2680,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( ( rel_s5 @ sK1 @ X0 )
= $false ) )
| ~ spl18_1
| ~ spl18_10
| ~ spl18_12
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f2679]) ).
thf(f2702,definition,
( spl18_52
<=> ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( ( rel_s5 @ sK1 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_52])],[avatar_definition]) ).
thf(f2703,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( ( rel_s5 @ sK1 @ X0 )
= $false ) )
| ~ spl18_52 ),
inference(avatar_component_clause,[],[f2702]) ).
thf(f2747,plain,
( spl18_52
| ~ spl18_1
| ~ spl18_10
| ~ spl18_12
| ~ spl18_24 ),
inference(avatar_split_clause,[],[f2680,f458,f412,f404,f365,f2702]) ).
thf(f2981,plain,
( ( $false != $false )
| ( $false
= ( rel_s5 @ sK1 @ sK1 ) )
| ( ( p @ ( sK4 @ sK1 ) )
= $false )
| ~ spl18_6 ),
inference(equality_factoring,[],[f389]) ).
thf(f2985,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK1 ) )
| ( ( p @ ( sK4 @ sK1 ) )
= $false )
| ~ spl18_6 ),
inference(trivial_inequality_removal,[],[f2981]) ).
thf(f2996,plain,
( ( ( p @ ( sK4 @ sK1 ) )
= $false )
| ( $true = $false )
| ~ spl18_6 ),
inference(forward_demodulation,[],[f2985,f363]) ).
thf(f2997,plain,
( ( ( p @ ( sK4 @ sK1 ) )
= $false )
| ~ spl18_6 ),
inference(trivial_inequality_removal,[],[f2996]) ).
thf(f3027,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $true
= ( p @ ( sK4 @ sK1 ) ) )
| ( $true = $false ) )
| ~ spl18_1
| ~ spl18_5
| ~ spl18_24 ),
inference(superposition,[],[f2370,f385]) ).
thf(f3079,definition,
( spl18_73
<=> ( $true
= ( p @ ( sK4 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_73])],[avatar_definition]) ).
thf(f3081,plain,
( ( $true
= ( p @ ( sK4 @ sK1 ) ) )
| ~ spl18_73 ),
inference(avatar_component_clause,[],[f3079]) ).
thf(f3988,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK1 ) )
| ( $false != $false )
| ~ spl18_52 ),
inference(equality_factoring,[],[f2703]) ).
thf(f3994,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK1 ) )
| ~ spl18_52 ),
inference(trivial_inequality_removal,[],[f3988]) ).
thf(f4008,plain,
( ( $true = $false )
| ~ spl18_52 ),
inference(forward_demodulation,[],[f3994,f363]) ).
thf(f4009,plain,
( $false
| ~ spl18_52 ),
inference(trivial_inequality_removal,[],[f4008]) ).
thf(f4010,plain,
~ spl18_52,
inference(avatar_contradiction_clause,[],[f4009]) ).
thf(f4316,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK1 ) )
| ( $false
= ( p @ ( sK6 @ sK1 ) ) )
| ( $false != $false )
| ~ spl18_9 ),
inference(equality_factoring,[],[f401]) ).
thf(f4317,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK1 ) )
| ( $false
= ( p @ ( sK6 @ sK1 ) ) )
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f4316]) ).
thf(f4329,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK6 @ sK1 ) ) )
| ~ spl18_9 ),
inference(forward_demodulation,[],[f4317,f363]) ).
thf(f4330,plain,
( ( $false
= ( p @ ( sK6 @ sK1 ) ) )
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f4329]) ).
thf(f4371,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true = $false )
| ( $true
= ( p @ ( sK6 @ sK1 ) ) ) )
| ~ spl18_1
| ~ spl18_7
| ~ spl18_24 ),
inference(superposition,[],[f393,f2370]) ).
thf(f4402,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( p @ ( sK6 @ sK1 ) ) ) )
| ~ spl18_1
| ~ spl18_7
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f4371]) ).
thf(f4438,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl18_1
| ~ spl18_7
| ~ spl18_9
| ~ spl18_24 ),
inference(forward_demodulation,[],[f4402,f4330]) ).
thf(f4439,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl18_1
| ~ spl18_7
| ~ spl18_9
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f4438]) ).
thf(f4476,plain,
( spl18_52
| ~ spl18_1
| ~ spl18_7
| ~ spl18_9
| ~ spl18_24 ),
inference(avatar_split_clause,[],[f4439,f458,f400,f392,f365,f2702]) ).
thf(f4504,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK1 @ X0 )
= $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( p @ ( sK4 @ sK1 ) ) ) )
| ~ spl18_1
| ~ spl18_5
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f3027]) ).
thf(f4549,plain,
( spl18_73
| spl18_52
| ~ spl18_1
| ~ spl18_5
| ~ spl18_24 ),
inference(avatar_split_clause,[],[f4504,f458,f384,f365,f2702,f3079]) ).
thf(f4571,plain,
( ( $true = $false )
| ~ spl18_6
| ~ spl18_73 ),
inference(forward_demodulation,[],[f3081,f2997]) ).
thf(f4572,plain,
( $false
| ~ spl18_6
| ~ spl18_73 ),
inference(trivial_inequality_removal,[],[f4571]) ).
thf(f4573,plain,
( ~ spl18_6
| ~ spl18_73 ),
inference(avatar_contradiction_clause,[],[f4572]) ).
cnf(s1,plain,
( spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f372]) ).
cnf(s2,plain,
( spl18_1
| spl18_3 ),
inference(sat_conversion,[],[f377]) ).
cnf(s3,plain,
( spl18_1
| spl18_4 ),
inference(sat_conversion,[],[f382]) ).
cnf(s4,plain,
( spl18_2
| spl18_5 ),
inference(sat_conversion,[],[f386]) ).
cnf(s5,plain,
( spl18_2
| spl18_6 ),
inference(sat_conversion,[],[f390]) ).
cnf(s6,plain,
( spl18_7
| spl18_8 ),
inference(sat_conversion,[],[f398]) ).
cnf(s7,plain,
( spl18_8
| spl18_9 ),
inference(sat_conversion,[],[f402]) ).
cnf(s8,plain,
( spl18_10
| spl18_11 ),
inference(sat_conversion,[],[f410]) ).
cnf(s9,plain,
( spl18_11
| spl18_12 ),
inference(sat_conversion,[],[f414]) ).
cnf(s22,plain,
( spl18_24
| spl18_28 ),
inference(sat_conversion,[],[f478]) ).
cnf(s23,plain,
( spl18_24
| spl18_29 ),
inference(sat_conversion,[],[f482]) ).
cnf(s24,plain,
( spl18_24
| spl18_30 ),
inference(sat_conversion,[],[f486]) ).
cnf(s34,plain,
( spl18_24
| ~ spl18_28
| ~ spl18_29
| ~ spl18_30 ),
inference(sat_conversion,[],[f2048]) ).
cnf(s76,plain,
( ~ spl18_2
| ~ spl18_8
| ~ spl18_11
| ~ spl18_24 ),
inference(sat_conversion,[],[f2339]) ).
cnf(s78,plain,
( ~ spl18_2
| ~ spl18_3
| ~ spl18_4
| ~ spl18_24 ),
inference(sat_conversion,[],[f2349]) ).
cnf(s103,plain,
( ~ spl18_1
| ~ spl18_10
| ~ spl18_12
| ~ spl18_24
| spl18_52 ),
inference(sat_conversion,[],[f2747]) ).
cnf(s303,plain,
~ spl18_52,
inference(sat_conversion,[],[f4010]) ).
cnf(s322,plain,
( ~ spl18_1
| ~ spl18_7
| ~ spl18_9
| ~ spl18_24
| spl18_52 ),
inference(sat_conversion,[],[f4476]) ).
cnf(s343,plain,
( ~ spl18_1
| ~ spl18_5
| ~ spl18_24
| spl18_52
| spl18_73 ),
inference(sat_conversion,[],[f4549]) ).
cnf(s350,plain,
( ~ spl18_6
| ~ spl18_73 ),
inference(sat_conversion,[],[f4573]) ).
cnf(s397,plain,
( ~ spl18_1
| ~ spl18_10
| ~ spl18_12
| ~ spl18_24 ),
inference(rat,[],[s103,s303]) ).
cnf(s402,plain,
spl18_24,
inference(rat,[],[s34,s22,s23,s24]) ).
cnf(s403,plain,
spl18_1,
inference(rat,[],[s78,s1,s2,s3,s402]) ).
cnf(s404,plain,
spl18_11,
inference(rat,[],[s397,s8,s9,s403,s402]) ).
cnf(s405,plain,
spl18_8,
inference(rat,[],[s322,s6,s7,s403,s402,s303]) ).
cnf(s406,plain,
~ spl18_2,
inference(rat,[],[s76,s402,s404,s405]) ).
cnf(s408,plain,
spl18_6,
inference(rat,[],[s5,s406]) ).
cnf(s409,plain,
spl18_5,
inference(rat,[],[s4,s406]) ).
cnf(s410,plain,
~ spl18_73,
inference(rat,[],[s350,s408]) ).
cnf(s411,plain,
$false,
inference(rat,[],[s343,s403,s303,s402,s410,s409]) ).
thf(f4574,plain,
$false,
inference(avatar_sat_refutation,[],[s411]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO442^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n015.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 16:55:18 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.37 % (3793673)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.37 % (3793679)lrs+10_16_si=on:nwc=1.5:random_seed=348172735:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.37 % (3793684)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.37 % (3793684)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
% 0.20/0.37 % (3793679)Instruction limit reached!
% 0.20/0.37 % (3793679)------------------------------
% 0.20/0.37 % (3793679)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.37 % (3793679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.37 % (3793679)CaDiCaL version: 2.1.3
% 0.20/0.37 % (3793679)Termination reason: Instruction limit
% 0.20/0.37 % (3793679)Termination phase: Saturation
% 0.20/0.37 % (3793679)Time elapsed: 0.005 s
% 0.20/0.37 % (3793679)Peak memory usage: 12 MB
% 0.20/0.37 % (3793679)Instructions burned: 20 (million)
% 0.20/0.37 % (3793678)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3265340424:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.37 % (3793680)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=840277872:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.37 % (3793681)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=2797028240: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)
% 0.20/0.37 % (3793684)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=1933799009:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.37 % (3793682)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2160676709:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.37 % (3793680)Instruction limit reached!
% 0.20/0.37 % (3793680)------------------------------
% 0.20/0.37 % (3793680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.37 % (3793680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.37 % (3793680)CaDiCaL version: 2.1.3
% 0.20/0.37 % (3793680)Termination reason: Instruction limit
% 0.20/0.37 % (3793680)Termination phase: shuffling
% 0.20/0.37 % (3793680)Time elapsed: 0.002 s
% 0.20/0.37 % (3793680)Peak memory usage: 10 MB
% 0.20/0.37 % (3793680)Instructions burned: 4 (million)
% 0.20/0.37 % (3793686)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2974821419:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (3793686)Instruction limit reached!
% 0.20/0.37 % (3793686)------------------------------
% 0.20/0.37 % (3793686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.37 % (3793686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.37 % (3793686)CaDiCaL version: 2.1.3
% 0.20/0.37 % (3793686)Termination reason: Instruction limit
% 0.20/0.37 % (3793686)Termination phase: Property scanning
% 0.20/0.37 % (3793686)Time elapsed: 0.001 s
% 0.20/0.37 % (3793686)Peak memory usage: 10 MB
% 0.20/0.37 % (3793686)Instructions burned: 4 (million)
% 0.20/0.37 % (3793683)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1677127422:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.37 % (3793694)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.37 % (3793694)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=317600764:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.37 % (3793692)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=399953436:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.37 % (3793682)Instruction limit reached!
% 0.20/0.37 % (3793682)------------------------------
% 0.20/0.37 % (3793682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.42 % (3793682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.42 % (3793682)CaDiCaL version: 2.1.3
% 0.83/0.42 % (3793682)Termination reason: Instruction limit
% 0.83/0.42 % (3793682)Termination phase: Saturation
% 0.83/0.42 % (3793682)Time elapsed: 0.020 s
% 0.83/0.42 % (3793682)Peak memory usage: 11 MB
% 0.83/0.42 % (3793682)Instructions burned: 25 (million)
% 0.83/0.42 % (3793694)Instruction limit reached!
% 0.83/0.42 % (3793694)------------------------------
% 0.83/0.42 % (3793694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.42 % (3793694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.42 % (3793694)CaDiCaL version: 2.1.3
% 0.83/0.42 % (3793694)Termination reason: Instruction limit
% 0.83/0.42 % (3793694)Termination phase: Saturation
% 0.83/0.42 % (3793694)Time elapsed: 0.002 s
% 0.83/0.42 % (3793694)Peak memory usage: 11 MB
% 0.83/0.42 % (3793694)Instructions burned: 9 (million)
% 0.83/0.42 % (3793692)Instruction limit reached!
% 0.83/0.42 % (3793692)------------------------------
% 0.83/0.42 % (3793692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.42 % (3793692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.42 % (3793692)CaDiCaL version: 2.1.3
% 0.83/0.42 % (3793692)Termination reason: Instruction limit
% 0.83/0.42 % (3793692)Termination phase: Property scanning
% 0.83/0.42 % (3793692)Time elapsed: 0.002 s
% 0.83/0.42 % (3793692)Peak memory usage: 10 MB
% 0.83/0.42 % (3793692)Instructions burned: 5 (million)
% 0.83/0.42 % (3793699)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
% 0.83/0.42 % (3793699)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.83/0.42 % (3793699)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=304490814:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.83/0.42 % (3793698)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=323746536:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.83/0.42 % (3793699)Instruction limit reached!
% 0.83/0.42 % (3793699)------------------------------
% 0.83/0.42 % (3793699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.42 % (3793699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.42 % (3793699)CaDiCaL version: 2.1.3
% 0.83/0.42 % (3793699)Termination reason: Instruction limit
% 0.83/0.42 % (3793699)Termination phase: Saturation
% 0.83/0.42 % (3793699)Time elapsed: 0.007 s
% 0.83/0.42 % (3793699)Peak memory usage: 11 MB
% 0.83/0.42 % (3793699)Instructions burned: 31 (million)
% 0.83/0.42 % (3793678)Instruction limit reached!
% 0.83/0.42 % (3793678)------------------------------
% 0.83/0.42 % (3793678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.42 % (3793678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.42 % (3793678)CaDiCaL version: 2.1.3
% 0.83/0.42 % (3793678)Termination reason: Instruction limit
% 0.83/0.42 % (3793678)Termination phase: Saturation
% 0.83/0.42 % (3793678)Time elapsed: 0.044 s
% 0.83/0.42 % (3793678)Peak memory usage: 12 MB
% 0.83/0.42 % (3793678)Instructions burned: 88 (million)
% 0.83/0.42 % (3793698)Instruction limit reached!
% 0.83/0.42 % (3793698)------------------------------
% 0.83/0.42 % (3793698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.42 % (3793698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.42 % (3793698)CaDiCaL version: 2.1.3
% 0.83/0.42 % (3793698)Termination reason: Instruction limit
% 0.83/0.42 % (3793698)Termination phase: Saturation
% 0.83/0.42 % (3793698)Time elapsed: 0.006 s
% 0.83/0.42 % (3793698)Peak memory usage: 12 MB
% 0.83/0.42 % (3793698)Instructions burned: 13 (million)
% 0.83/0.42 % (3793703)lrs+10_1_si=on:cs=on:random_seed=1490509954:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.83/0.42 % (3793704)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.83/0.42 % (3793703)Instruction limit reached!
% 0.83/0.42 % (3793703)------------------------------
% 0.83/0.42 % (3793703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.47 % (3793703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.47 % (3793703)CaDiCaL version: 2.1.3
% 0.83/0.47 % (3793703)Termination reason: Instruction limit
% 0.83/0.47 % (3793703)Termination phase: Saturation
% 0.83/0.47 % (3793703)Time elapsed: 0.004 s
% 0.83/0.47 % (3793703)Peak memory usage: 11 MB
% 0.83/0.47 % (3793703)Instructions burned: 11 (million)
% 0.83/0.47 % (3793704)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=3824807995:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.83/0.47 % (3793700)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=3481276060:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.83/0.47 % (3793704)Instruction limit reached!
% 0.83/0.47 % (3793704)------------------------------
% 0.83/0.47 % (3793704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.47 % (3793704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.47 % (3793704)CaDiCaL version: 2.1.3
% 0.83/0.47 % (3793704)Termination reason: Instruction limit
% 0.83/0.47 % (3793704)Termination phase: Property scanning
% 0.83/0.47 % (3793704)Time elapsed: 0.002 s
% 0.83/0.47 % (3793704)Peak memory usage: 10 MB
% 0.83/0.47 % (3793704)Instructions burned: 4 (million)
% 0.83/0.47 % (3793705)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2721470161:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.83/0.47 % (3793705)Refutation not found, incomplete strategy
% 0.83/0.47 % (3793705)------------------------------
% 0.83/0.47 % (3793705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.47 % (3793705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.47 % (3793705)CaDiCaL version: 2.1.3
% 0.83/0.47 % (3793705)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.47 % (3793705)Time elapsed: 0.004 s
% 0.83/0.47 % (3793705)Peak memory usage: 12 MB
% 0.83/0.47 % (3793705)Instructions burned: 7 (million)
% 0.83/0.47 % (3793705)------------------------------
% 0.83/0.47 % (3793705)------------------------------
% 0.83/0.47 % (3793707)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2430461372:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.83/0.47 % (3793683)Instruction limit reached!
% 0.83/0.47 % (3793683)------------------------------
% 0.83/0.47 % (3793683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.47 % (3793683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.47 % (3793683)CaDiCaL version: 2.1.3
% 0.83/0.47 % (3793683)Termination reason: Instruction limit
% 0.83/0.47 % (3793683)Termination phase: Saturation
% 0.83/0.47 % (3793683)Time elapsed: 0.064 s
% 0.83/0.47 % (3793683)Peak memory usage: 12 MB
% 0.83/0.47 % (3793683)Instructions burned: 75 (million)
% 0.83/0.47 % (3793707)Refutation not found, incomplete strategy
% 0.83/0.47 % (3793707)------------------------------
% 0.83/0.47 % (3793707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.47 % (3793707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.47 % (3793707)CaDiCaL version: 2.1.3
% 0.83/0.47 % (3793707)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.47 % (3793707)Time elapsed: 0.004 s
% 0.83/0.47 % (3793707)Peak memory usage: 12 MB
% 0.83/0.47 % (3793707)Instructions burned: 8 (million)
% 0.83/0.47 % (3793707)------------------------------
% 0.83/0.47 % (3793707)------------------------------
% 0.83/0.47 % (3793712)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3792081141:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.83/0.47 % (3793710)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2748903128:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.83/0.47 % (3793712)Instruction limit reached!
% 0.83/0.47 % (3793712)------------------------------
% 0.83/0.47 % (3793712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.47 % (3793712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793712)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793712)Termination reason: Instruction limit
% 0.83/0.48 % (3793712)Termination phase: Saturation
% 0.83/0.48 % (3793712)Time elapsed: 0.007 s
% 0.83/0.48 % (3793712)Peak memory usage: 11 MB
% 0.83/0.48 % (3793712)Instructions burned: 15 (million)
% 0.83/0.48 % (3793714)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3657733241:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.83/0.48 % (3793684)Instruction limit reached!
% 0.83/0.48 % (3793684)------------------------------
% 0.83/0.48 % (3793684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793684)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793684)Termination reason: Instruction limit
% 0.83/0.48 % (3793684)Termination phase: Saturation
% 0.83/0.48 % (3793684)Time elapsed: 0.110 s
% 0.83/0.48 % (3793684)Peak memory usage: 13 MB
% 0.83/0.48 % (3793684)Instructions burned: 159 (million)
% 0.83/0.48 % (3793710)Instruction limit reached!
% 0.83/0.48 % (3793710)------------------------------
% 0.83/0.48 % (3793710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793710)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793710)Termination reason: Instruction limit
% 0.83/0.48 % (3793710)Termination phase: Saturation
% 0.83/0.48 % (3793710)Time elapsed: 0.018 s
% 0.83/0.48 % (3793710)Peak memory usage: 12 MB
% 0.83/0.48 % (3793710)Instructions burned: 27 (million)
% 0.83/0.48 % (3793715)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=884959607:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.83/0.48 % (3793718)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2416925354: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)
% 0.83/0.48 % (3793715)Instruction limit reached!
% 0.83/0.48 % (3793715)------------------------------
% 0.83/0.48 % (3793715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793715)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793715)Termination reason: Instruction limit
% 0.83/0.48 % (3793715)Termination phase: Saturation
% 0.83/0.48 % (3793715)Time elapsed: 0.013 s
% 0.83/0.48 % (3793715)Peak memory usage: 11 MB
% 0.83/0.48 % (3793715)Instructions burned: 15 (million)
% 0.83/0.48 % (3793718)Instruction limit reached!
% 0.83/0.48 % (3793718)------------------------------
% 0.83/0.48 % (3793718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793718)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793718)Termination reason: Instruction limit
% 0.83/0.48 % (3793718)Termination phase: Property scanning
% 0.83/0.48 % (3793718)Time elapsed: 0.003 s
% 0.83/0.48 % (3793718)Peak memory usage: 10 MB
% 0.83/0.48 % (3793718)Instructions burned: 3 (million)
% 0.83/0.48 % (3793721)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1942927473:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.83/0.48 % (3793722)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3029203986:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.83/0.48 % (3793722)Instruction limit reached!
% 0.83/0.48 % (3793722)------------------------------
% 0.83/0.48 % (3793722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793722)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793722)Termination reason: Instruction limit
% 0.83/0.48 % (3793722)Termination phase: Saturation
% 0.83/0.48 % (3793722)Time elapsed: 0.011 s
% 0.83/0.48 % (3793722)Peak memory usage: 11 MB
% 0.83/0.48 % (3793722)Instructions burned: 24 (million)
% 0.83/0.48 % (3793721)Instruction limit reached!
% 0.83/0.48 % (3793721)------------------------------
% 0.83/0.48 % (3793721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793721)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793721)Termination reason: Instruction limit
% 0.83/0.48 % (3793721)Termination phase: Saturation
% 0.83/0.48 % (3793721)Time elapsed: 0.014 s
% 0.83/0.48 % (3793721)Peak memory usage: 12 MB
% 0.83/0.48 % (3793721)Instructions burned: 27 (million)
% 0.83/0.48 % (3793725)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3310324580:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.83/0.48 % (3793726)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
% 0.83/0.48 % (3793726)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.83/0.48 % (3793700)Instruction limit reached!
% 0.83/0.48 % (3793700)------------------------------
% 0.83/0.48 % (3793700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793700)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793700)Termination reason: Instruction limit
% 0.83/0.48 % (3793700)Termination phase: Saturation
% 0.83/0.48 % (3793700)Time elapsed: 0.083 s
% 0.83/0.48 % (3793700)Peak memory usage: 12 MB
% 0.83/0.48 % (3793700)Instructions burned: 86 (million)
% 0.83/0.48 % (3793726)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=718223960:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.83/0.48 % (3793729)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.83/0.48 % (3793729)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=1529788761:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.83/0.48 % (3793731)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=1646567937:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.83/0.48 % (3793726)Instruction limit reached!
% 0.83/0.48 % (3793726)------------------------------
% 0.83/0.48 % (3793726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793726)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793726)Termination reason: Instruction limit
% 0.83/0.48 % (3793726)Termination phase: Saturation
% 0.83/0.48 % (3793726)Time elapsed: 0.012 s
% 0.83/0.48 % (3793726)Peak memory usage: 12 MB
% 0.83/0.48 % (3793726)Instructions burned: 14 (million)
% 0.83/0.48 % (3793729)Instruction limit reached!
% 0.83/0.48 % (3793729)------------------------------
% 0.83/0.48 % (3793729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793729)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793729)Termination reason: Instruction limit
% 0.83/0.48 % (3793729)Termination phase: Property scanning
% 0.83/0.48 % (3793729)Time elapsed: 0.004 s
% 0.83/0.48 % (3793729)Peak memory usage: 10 MB
% 0.83/0.48 % (3793729)Instructions burned: 8 (million)
% 0.83/0.48 % (3793731)Instruction limit reached!
% 0.83/0.48 % (3793731)------------------------------
% 0.83/0.48 % (3793731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793731)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793731)Termination reason: Instruction limit
% 0.83/0.48 % (3793731)Termination phase: Saturation
% 0.83/0.48 % (3793731)Time elapsed: 0.034 s
% 0.83/0.48 % (3793731)Peak memory usage: 12 MB
% 0.83/0.48 % (3793731)Instructions burned: 32 (million)
% 0.83/0.48 % (3793732)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=767181909:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.83/0.48 % (3793736)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3783011424:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 0.83/0.48 % (3793714) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3793673-3793714"...
% 0.83/0.48 % (3793725)Instruction limit reached!
% 0.83/0.48 % (3793725)------------------------------
% 0.83/0.48 % (3793725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793725)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793725)Termination reason: Instruction limit
% 0.83/0.48 % (3793725)Termination phase: Saturation
% 0.83/0.48 % (3793725)Time elapsed: 0.058 s
% 0.83/0.48 % (3793725)Peak memory usage: 12 MB
% 0.83/0.48 % (3793725)Instructions burned: 61 (million)
% 0.83/0.48 % (3793732)Instruction limit reached!
% 0.83/0.48 % (3793732)------------------------------
% 0.83/0.48 % (3793732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.48 % (3793732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.48 % (3793732)CaDiCaL version: 2.1.3
% 0.83/0.48 % (3793732)Termination reason: Instruction limit
% 0.83/0.48 % (3793732)Termination phase: Saturation
% 0.83/0.48 % (3793732)Time elapsed: 0.008 s
% 0.83/0.48 % (3793732)Peak memory usage: 11 MB
% 0.83/0.48 % (3793732)Instructions burned: 8 (million)
% 0.83/0.48 % (3793714)...printing done.
% 0.83/0.48 % (3793737)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1696557213:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 0.83/0.48 % (3793714)Refutation found. Thanks to Tanya!
% 0.83/0.48 % SZS status Theorem for theBenchmark
% 0.83/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.83/0.49 % (3793714)------------------------------
% 0.83/0.49 % (3793714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.49 % (3793714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.49 % (3793714)CaDiCaL version: 2.1.3
% 0.83/0.49 % (3793714)Termination reason: Refutation
% 0.83/0.49 % (3793714)Time elapsed: 0.103 s
% 0.83/0.49 % (3793714)Peak memory usage: 14 MB
% 0.83/0.49 % (3793714)Instructions burned: 295 (million)
% 0.83/0.49 % (3793673)Success in time 0.257 s
% 0.83/0.49 % Vampire exiting
%------------------------------------------------------------------------------