%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO409^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:47:37 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 18
% Syntax : Number of formulae : 200 ( 48 unt; 0 typ; 9 def)
% Number of atoms : 1943 ( 318 equ; 0 cnn)
% Maximal formula atoms : 11 ( 9 avg)
% Number of connectives : 2454 ( 569 ~; 549 |; 0 &;1221 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 112 ( 112 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 63 usr; 16 con; 0-4 aty)
% ( 106 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 328 ( 0 sgn 46 !; 0 ?; 328 :)
% 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_k: $i > $i > $o ).
thf(func_def_33,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_k: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_k @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^1.ax',mbox_k) ).
thf(f33,axiom,
( mdia_k
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^1.ax',mdia_k) ).
thf(f34,conjecture,
mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_k @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f35,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_k @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f36,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f40,plain,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_k @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f41,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f58,plain,
~ ( mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_k @ q ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f59,plain,
( ( mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_k @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f58]) ).
thf(f60,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f65,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f66,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f71,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f72,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f74,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f77,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f87,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f92,plain,
( ( mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_k @ q ) ) ) )
!= $true ),
inference(flattening,[],[f59]) ).
thf(f94,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f97,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f98,plain,
( ( mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_k @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f107,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f110,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f115,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f120,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f122,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f129,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f97,f120,f102,f120,f120]) ).
thf(f130,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f115,f102,f120]) ).
thf(f132,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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f107,f129,f130,f130]) ).
thf(f138,plain,
( mdia_k
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_k @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f110,f120,f122,f120]) ).
thf(f139,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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_k @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_k @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_k @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f98,f94,f132,f138,f102,f102,f138,f138]) ).
thf(f140,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( ( ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f150,plain,
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( ( ~ ( q @ sK3 )
| ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( ( p @ sK1 )
| ( q @ sK1 ) )
| ~ ( rel_k @ sK0 @ sK1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( ( ( ~ ( ( p @ sK1 )
| ( q @ sK1 ) )
| ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( ( ~ ( ( p @ sK1 )
| ( q @ sK1 ) )
| ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( q @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( ~ ( ( p @ sK1 )
| ( q @ sK1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( ( ~ ( ( p @ sK1 )
| ( q @ sK1 ) ) )
= $false )
| ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( ( ~ ( ( p @ sK1 )
| ( q @ sK1 ) ) )
= $false )
| ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( ~ ( p @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( ( ( ~ ( p @ sK2 ) )
= $false )
| ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( ( p @ sK1 )
| ( q @ sK1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( ( ( p @ sK1 )
| ( q @ sK1 ) )
= $true )
| ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( p @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( ( p @ sK1 )
= $true )
| ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( q @ sK1 )
= $true )
| ( ( p @ sK2 )
= $true ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( q @ sK3 )
= $true )
| ( ( q @ sK1 )
= $true )
| ( ( p @ sK2 )
= $true )
| ( ( p @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( ( ( p @ sK1 )
| ( q @ sK1 ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( q @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f172,plain,
( ( ( p @ sK1 )
= $true )
| ( ( q @ sK1 )
= $true )
| ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( ( q @ sK3 )
= $true )
| ( ( q @ sK1 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( p @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( ( p @ sK1 )
= $true )
| ( ( rel_k @ sK0 @ sK2 )
= $true )
| ( ( q @ sK1 )
= $true )
| ( ( q @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f176,plain,
( ( ( ~ ( p @ sK2 ) )
= $false )
| ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f177,plain,
( ( ( ~ ( q @ sK3 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( p @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( ( q @ sK3 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( p @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( ( q @ sK3 )
= $true )
| ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( p @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( ( q @ sK3 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f181,plain,
( ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( rel_k @ sK0 @ sK2 )
= $true )
| ( ( q @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( ( rel_k @ sK0 @ sK2 )
= $true )
| ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( q @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f184,plain,
( ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( ( ~ ( ( p @ sK1 )
| ( q @ sK1 ) ) )
= $false )
| ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f185,plain,
( ( ( ~ ( ( p @ sK1 )
| ( q @ sK1 ) ) )
= $false )
| ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( ( ( p @ sK1 )
| ( q @ sK1 ) )
= $true )
| ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( ( q @ sK1 )
= $true )
| ( ( p @ sK1 )
= $true )
| ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( ( p @ sK1 )
= $true )
| ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( q @ sK1 )
= $true ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( p @ sK1 )
= $true )
| ( ( ~ ( p @ sK2 ) )
= $false )
| ( ( q @ sK1 )
= $true ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f190,plain,
( ( ( q @ sK1 )
= $true )
| ( ( p @ sK1 )
= $true )
| ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( p @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( ( rel_k @ sK0 @ sK2 )
= $true )
| ( ( q @ sK1 )
= $true )
| ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( p @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f192,plain,
( ( ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f193,plain,
( ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( ~ ( p @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
( ( ( ~ ( p @ sK2 ) )
= $false )
| ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( rel_k @ sK0 @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( p @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( rel_k @ sK0 @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f198,plain,
( ( ( rel_k @ sK0 @ sK2 )
= $true )
| ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( rel_k @ sK0 @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f219,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f220,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f221,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f255,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f256,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( ( p @ X2 )
| ( q @ X2 ) )
| ~ ( rel_k @ sK0 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( p @ X1 ) )
= $true )
| ( ( ~ ( ( p @ X2 )
| ( q @ X2 ) )
| ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( ( p @ X2 )
| ( q @ X2 ) )
| ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( p @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $false )
| ( ( ~ ( ( p @ X2 )
| ( q @ X2 ) )
| ~ ( rel_k @ sK0 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( p @ X1 )
= $false )
| ( ( ~ ( ( p @ X2 )
| ( q @ X2 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ( p @ X2 )
| ( q @ X2 ) ) )
= $true )
| ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( rel_k @ sK0 @ X2 )
= $false )
| ( ( p @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X2 )
= $false )
| ( ( ( p @ X2 )
| ( q @ X2 ) )
= $false )
| ( ( p @ X1 )
= $false )
| ( ( rel_k @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f264]) ).
thf(f267,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X2 )
= $false )
| ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X2 )
= $false )
| ( ( p @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f265]) ).
thf(f268,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f269,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f268]) ).
thf(f300,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f301,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f301]) ).
thf(f303,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ( p @ X1 )
| ( q @ X1 ) )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( q @ X2 )
| ~ ( rel_k @ sK0 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f302]) ).
thf(f304,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ( p @ X1 )
| ( q @ X1 ) ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( q @ X2 )
| ~ ( rel_k @ sK0 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X2: $i,X1: $i] :
( ( ( ( p @ X1 )
| ( q @ X1 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( q @ X2 )
| ~ ( rel_k @ sK0 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: $i,X1: $i] :
( ( ( q @ X1 )
= $false )
| ( ( ~ ( q @ X2 )
| ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f305]) ).
thf(f312,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ~ ( q @ X2 ) )
= $true )
| ( ( q @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f306]) ).
thf(f313,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( q @ X1 )
= $false )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ~ ( q @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( ~ ( q @ X2 ) )
= $true )
| ( ( q @ X1 )
= $false )
| ( ( rel_k @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: $i,X1: $i] :
( ( ( q @ X2 )
= $false )
| ( ( rel_k @ sK0 @ X2 )
= $false )
| ( ( q @ X1 )
= $false )
| ( ( rel_k @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f314]) ).
thf(f317,definition,
( spl9_1
<=> ( ( q @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f318,plain,
( ( ( q @ sK1 )
= $true )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f317]) ).
thf(f320,definition,
( spl9_2
<=> ( ( p @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f321,plain,
( ( ( p @ sK2 )
= $true )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f320]) ).
thf(f323,definition,
( spl9_3
<=> ( ( p @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f324,plain,
( ( ( p @ sK1 )
= $true )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f323]) ).
thf(f326,definition,
( spl9_4
<=> ( ( q @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f327,plain,
( ( ( q @ sK3 )
= $true )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f326]) ).
thf(f328,plain,
( spl9_1
| spl9_2
| spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f170,f326,f323,f320,f317]) ).
thf(f330,definition,
( spl9_5
<=> ( ( rel_k @ sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
thf(f331,plain,
( ( ( rel_k @ sK0 @ sK2 )
= $true )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f330]) ).
thf(f332,plain,
( spl9_4
| spl9_5
| spl9_3
| spl9_1 ),
inference(avatar_split_clause,[],[f174,f317,f323,f330,f326]) ).
thf(f334,definition,
( spl9_6
<=> ( ( rel_k @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f335,plain,
( ( ( rel_k @ sK0 @ sK1 )
= $true )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f334]) ).
thf(f336,plain,
( spl9_6
| spl9_4
| spl9_2 ),
inference(avatar_split_clause,[],[f179,f320,f326,f334]) ).
thf(f337,plain,
( spl9_6
| spl9_4
| spl9_5 ),
inference(avatar_split_clause,[],[f182,f330,f326,f334]) ).
thf(f339,definition,
( spl9_7
<=> ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
thf(f340,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f339]) ).
thf(f341,plain,
( spl9_3
| spl9_7
| spl9_2
| spl9_1 ),
inference(avatar_split_clause,[],[f190,f317,f320,f339,f323]) ).
thf(f342,plain,
( spl9_1
| spl9_3
| spl9_7
| spl9_5 ),
inference(avatar_split_clause,[],[f191,f330,f339,f323,f317]) ).
thf(f343,plain,
( spl9_6
| spl9_7
| spl9_2 ),
inference(avatar_split_clause,[],[f196,f320,f339,f334]) ).
thf(f344,plain,
( spl9_6
| spl9_7
| spl9_5 ),
inference(avatar_split_clause,[],[f198,f330,f339,f334]) ).
thf(f346,definition,
( spl9_8
<=> ! [X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
thf(f347,plain,
( ! [X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $false ) )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f346]) ).
thf(f356,definition,
( spl9_11
<=> ! [X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( q @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
thf(f357,plain,
( ! [X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( q @ X1 )
= $false ) )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f356]) ).
thf(f380,plain,
( spl9_8
| spl9_8 ),
inference(avatar_split_clause,[],[f267,f346,f346]) ).
thf(f399,plain,
( spl9_11
| spl9_11 ),
inference(avatar_split_clause,[],[f315,f356,f356]) ).
thf(f400,plain,
( ( ( p @ sK2 )
= $false )
| ( $true = $false )
| ~ spl9_5
| ~ spl9_8 ),
inference(constrained_superposition,[],[f331,f347]) ).
thf(f402,plain,
( ( ( p @ sK2 )
= $false )
| ~ spl9_5
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f400]) ).
thf(f404,plain,
( ( $true = $false )
| ~ spl9_2
| ~ spl9_5
| ~ spl9_8 ),
inference(backward_demodulation,[],[f321,f402]) ).
thf(f405,plain,
( $false
| ~ spl9_2
| ~ spl9_5
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f404]) ).
thf(f406,plain,
( ~ spl9_2
| ~ spl9_5
| ~ spl9_8 ),
inference(avatar_contradiction_clause,[],[f405]) ).
thf(f407,plain,
( ( ( q @ sK3 )
= $false )
| ( $true = $false )
| ~ spl9_7
| ~ spl9_11 ),
inference(constrained_superposition,[],[f340,f357]) ).
thf(f412,plain,
( ( ( q @ sK3 )
= $false )
| ~ spl9_7
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f407]) ).
thf(f415,plain,
( ( $true = $false )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_11 ),
inference(backward_demodulation,[],[f327,f412]) ).
thf(f416,plain,
( $false
| ~ spl9_4
| ~ spl9_7
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f415]) ).
thf(f417,plain,
( ~ spl9_4
| ~ spl9_7
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f416]) ).
thf(f418,plain,
( ( $true = $false )
| ( ( q @ sK1 )
= $false )
| ~ spl9_6
| ~ spl9_11 ),
inference(constrained_superposition,[],[f335,f357]) ).
thf(f419,plain,
( ( $true = $false )
| ( ( p @ sK1 )
= $false )
| ~ spl9_6
| ~ spl9_8 ),
inference(constrained_superposition,[],[f335,f347]) ).
thf(f422,plain,
( ( ( q @ sK1 )
= $false )
| ~ spl9_6
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f418]) ).
thf(f423,plain,
( ( ( p @ sK1 )
= $false )
| ~ spl9_6
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f419]) ).
thf(f426,plain,
( ( $true = $false )
| ~ spl9_3
| ~ spl9_6
| ~ spl9_8 ),
inference(backward_demodulation,[],[f324,f423]) ).
thf(f427,plain,
( $false
| ~ spl9_3
| ~ spl9_6
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f426]) ).
thf(f428,plain,
( ~ spl9_3
| ~ spl9_6
| ~ spl9_8 ),
inference(avatar_contradiction_clause,[],[f427]) ).
thf(f429,plain,
( ( $true = $false )
| ~ spl9_1
| ~ spl9_6
| ~ spl9_11 ),
inference(forward_demodulation,[],[f318,f422]) ).
thf(f430,plain,
( $false
| ~ spl9_1
| ~ spl9_6
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f429]) ).
thf(f431,plain,
( ~ spl9_1
| ~ spl9_6
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f430]) ).
cnf(s1,plain,
( spl9_1
| spl9_2
| spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f328]) ).
cnf(s2,plain,
( spl9_1
| spl9_3
| spl9_4
| spl9_5 ),
inference(sat_conversion,[],[f332]) ).
cnf(s3,plain,
( spl9_2
| spl9_4
| spl9_6 ),
inference(sat_conversion,[],[f336]) ).
cnf(s4,plain,
( spl9_4
| spl9_5
| spl9_6 ),
inference(sat_conversion,[],[f337]) ).
cnf(s5,plain,
( spl9_1
| spl9_2
| spl9_3
| spl9_7 ),
inference(sat_conversion,[],[f341]) ).
cnf(s6,plain,
( spl9_1
| spl9_3
| spl9_5
| spl9_7 ),
inference(sat_conversion,[],[f342]) ).
cnf(s7,plain,
( spl9_2
| spl9_6
| spl9_7 ),
inference(sat_conversion,[],[f343]) ).
cnf(s8,plain,
( spl9_5
| spl9_6
| spl9_7 ),
inference(sat_conversion,[],[f344]) ).
cnf(s17,plain,
( spl9_8
| spl9_8 ),
inference(sat_conversion,[],[f380]) ).
cnf(s18,plain,
spl9_8,
inference(rat,[],[s17]) ).
cnf(s25,plain,
( spl9_11
| spl9_11 ),
inference(sat_conversion,[],[f399]) ).
cnf(s26,plain,
spl9_11,
inference(rat,[],[s25]) ).
cnf(s27,plain,
( ~ spl9_2
| ~ spl9_5
| ~ spl9_8 ),
inference(sat_conversion,[],[f406]) ).
cnf(s28,plain,
( ~ spl9_4
| ~ spl9_7
| ~ spl9_11 ),
inference(sat_conversion,[],[f417]) ).
cnf(s29,plain,
( ~ spl9_3
| ~ spl9_6
| ~ spl9_8 ),
inference(sat_conversion,[],[f428]) ).
cnf(s30,plain,
( ~ spl9_1
| ~ spl9_6
| ~ spl9_11 ),
inference(sat_conversion,[],[f431]) ).
cnf(s31,plain,
( spl9_3
| spl9_2
| spl9_1 ),
inference(rat,[],[s28,s1,s5,s26]) ).
cnf(s32,plain,
( spl9_6
| spl9_2 ),
inference(rat,[],[s28,s3,s7,s26]) ).
cnf(s33,plain,
( spl9_2
| spl9_1 ),
inference(rat,[],[s32,s29,s31,s18]) ).
cnf(s34,plain,
( spl9_6
| spl9_5 ),
inference(rat,[],[s28,s4,s8,s26]) ).
cnf(s35,plain,
( spl9_3
| spl9_5
| spl9_1 ),
inference(rat,[],[s28,s2,s6,s26]) ).
cnf(s36,plain,
spl9_1,
inference(rat,[],[s35,s29,s34,s27,s33,s18]) ).
cnf(s37,plain,
~ spl9_6,
inference(rat,[],[s30,s26,s36]) ).
cnf(s38,plain,
spl9_2,
inference(rat,[],[s32,s37]) ).
cnf(s39,plain,
spl9_5,
inference(rat,[],[s34,s37]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s27,s18,s39,s38]) ).
thf(f432,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO409^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n003.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:52:45 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.29 % (2750576)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (2750586)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=899999457:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (2750587)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (2750587)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
% 0.22/0.29 % (2750586) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2750576-2750586"...
% 0.22/0.29 % (2750581)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2891713865:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (2750582)lrs+10_16_si=on:nwc=1.5:random_seed=790610223:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (2750583)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1454303438:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (2750584)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=2546346028: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)
% 0.22/0.29 % (2750585)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=977616680:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (2750587)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=1677215050:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (2750586)...printing done.
% 0.22/0.29 % (2750583)Instruction limit reached!
% 0.22/0.29 % (2750583)------------------------------
% 0.22/0.29 % (2750583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2750583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2750583)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2750583)Termination reason: Instruction limit
% 0.22/0.29 % (2750583)Termination phase: shuffling
% 0.22/0.29 % (2750583)Time elapsed: 0.002 s
% 0.22/0.29 % (2750583)Peak memory usage: 10 MB
% 0.22/0.29 % (2750583)Instructions burned: 4 (million)
% 0.22/0.29 % (2750586)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (2750586)------------------------------
% 0.22/0.29 % (2750586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2750586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2750586)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2750586)Termination reason: Refutation
% 0.22/0.29 % (2750586)Time elapsed: 0.008 s
% 0.22/0.29 % (2750586)Peak memory usage: 13 MB
% 0.22/0.29 % (2750586)Instructions burned: 30 (million)
% 0.22/0.29 % (2750576)Success in time 0.027 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------