%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO399^1 : 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 : n018.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 08:47:36 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 16
% Syntax : Number of formulae : 166 ( 47 unt; 0 typ; 7 def)
% Number of atoms : 1390 ( 238 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 1911 ( 560 ~; 392 |; 0 &; 893 @)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 115 ( 115 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 13 con; 0-4 aty)
% ( 59 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 272 ( 0 sgn 38 !; 0 ?; 272 :)
% 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,
r: $i > $o ).
thf(func_def_38,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_48,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
vNOT: $o > $o ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(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,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/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/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,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_k @ X1 @ X2 ) ) )
= mbox_k ),
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 @ ( mnot @ ( mdia_k @ ( mand @ q @ r ) ) ) @ ( mbox_k @ ( mimplies @ q @ ( mnot @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f35,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mnot @ ( mdia_k @ ( mand @ q @ r ) ) ) @ ( mbox_k @ ( mimplies @ q @ ( mnot @ r ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f44,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f45,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f49,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f58,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f65,plain,
~ ( mvalid @ ( mequiv @ ( mnot @ ( mdia_k @ ( mand @ q @ r ) ) ) @ ( mbox_k @ ( mimplies @ q @ ( mnot @ r ) ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f66,plain,
( ( mvalid @ ( mequiv @ ( mnot @ ( mdia_k @ ( mand @ q @ r ) ) ) @ ( mbox_k @ ( mimplies @ q @ ( mnot @ r ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f65]) ).
thf(f74,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f79,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_k @ X1 @ X2 ) ) )
= mbox_k ),
inference(rectify,[],[f32]) ).
thf(f80,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f85,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f86,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f88,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f89,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f88]) ).
thf(f92,plain,
( ( mvalid @ ( mequiv @ ( mnot @ ( mdia_k @ ( mand @ q @ r ) ) ) @ ( mbox_k @ ( mimplies @ q @ ( mnot @ r ) ) ) ) )
!= $true ),
inference(flattening,[],[f66]) ).
thf(f93,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f97,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f103,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f104,plain,
( ( mvalid @ ( mequiv @ ( mnot @ ( mdia_k @ ( mand @ q @ r ) ) ) @ ( mbox_k @ ( mimplies @ q @ ( mnot @ r ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f108,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f114,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f118,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f120,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f124,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f89]) ).
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,[],[f93,f124,f108,f124,f124]) ).
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,[],[f97,f108,f124]) ).
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,[],[f114,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] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f103,f124,f120,f124]) ).
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] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [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 ) ) )
@ q
@ r ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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 )
@ q
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ r ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f104,f118,f132,f124,f138,f129,f120,f130,f124]) ).
thf(f140,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( ~ ( q @ Y1 )
| ~ ( r @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 )
| ~ ( r @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 )
| ~ ( r @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( ~ ( q @ Y1 )
| ~ ( r @ Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( ~ ( q @ Y1 )
| ~ ( r @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 )
| ~ ( r @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 )
| ~ ( r @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( ~ ( q @ Y1 )
| ~ ( r @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $false
= ( ~ ( ~ ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( ( ~ ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( ( ~ ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $false
= ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) )
= $true )
| ( $false
= ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
= $true )
| ( $false
= ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( $false
= ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_k @ sK0 @ X2 )
| ~ ~ ( ~ ( q @ X2 )
| ~ ( r @ X2 ) ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( q @ X1 )
| ~ ( r @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ~ ~ ( ~ ( q @ X2 )
| ~ ( r @ X2 ) ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( q @ X1 )
| ~ ( r @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ~ ( ~ ( q @ X2 )
| ~ ( r @ X2 ) ) )
= $true )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( q @ X1 )
| ~ ( r @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( q @ X1 )
| ~ ( r @ X1 ) )
= $true )
| ( $false
= ( ~ ( ~ ( q @ X2 )
| ~ ( r @ X2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( ~ ( ~ ( q @ X2 )
| ~ ( r @ X2 ) ) ) )
| ( ( ~ ( q @ X1 )
| ~ ( r @ X1 ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( q @ X2 )
| ~ ( r @ X2 ) )
= $true )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( q @ X1 )
| ~ ( r @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( q @ X2 ) )
= $true )
| ( ( ~ ( q @ X1 )
| ~ ( r @ X1 ) )
= $true )
| ( ( ~ ( r @ X2 ) )
= $true )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( r @ X2 ) )
= $true )
| ( ( ~ ( q @ X2 ) )
= $true )
| ( ( ~ ( q @ X1 )
| ~ ( r @ X1 ) )
= $true )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( rel_k @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( r @ X2 )
= $false )
| ( ( ~ ( q @ X1 )
| ~ ( r @ X1 ) )
= $true )
| ( ( ~ ( q @ X2 ) )
= $true )
| ( ( rel_k @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( r @ X1 ) )
= $true )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( ~ ( q @ X1 ) )
= $true )
| ( ( r @ X2 )
= $false )
| ( ( ~ ( q @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X1: $i] :
( ( ( r @ X1 )
= $false )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( ~ ( q @ X1 ) )
= $true )
| ( ( r @ X2 )
= $false )
| ( ( ~ ( q @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( r @ X2 )
= $false )
| ( ( r @ X1 )
= $false )
| ( $false
= ( q @ X1 ) )
| ( ( ~ ( q @ X2 ) )
= $true )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X1: $i] :
( ( ( r @ X2 )
= $false )
| ( $false
= ( q @ X2 ) )
| ( ( rel_k @ sK0 @ X1 )
= $false )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( r @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f207,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f208,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f227,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f228,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) )
@ sK3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f227]) ).
thf(f229,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) )
@ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( ~ ( q @ Y0 )
| ~ ( r @ Y0 ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ~ ( r @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( ( ~ ( rel_k @ sK0 @ sK4 )
| ~ ~ ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ~ ( r @ sK3 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,plain,
( ( ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ~ ( r @ sK3 ) )
= $false )
| ( ( ~ ~ ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( $false
= ( ~ ( rel_k @ sK0 @ sK4 ) ) )
| ( ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ~ ( r @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f234,plain,
( ( ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ~ ( r @ sK3 ) )
= $false )
| ( ( rel_k @ sK0 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( $false
= ( ~ ( q @ sK3 )
| ~ ( r @ sK3 ) ) )
| ( ( rel_k @ sK0 @ sK4 )
= $true ) ),
inference(or_proxy_clausification,[],[f234]) ).
thf(f236,plain,
( ( ( rel_k @ sK0 @ sK4 )
= $true )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f234]) ).
thf(f237,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( rel_k @ sK0 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f238,plain,
( ( $false
= ( ~ ( r @ sK3 ) ) )
| ( ( rel_k @ sK0 @ sK4 )
= $true ) ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f239,plain,
( ( ( rel_k @ sK0 @ sK4 )
= $true )
| ( $false
= ( ~ ( q @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f240,plain,
( ( ( rel_k @ sK0 @ sK4 )
= $true )
| ( ( q @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
( ( ( r @ sK3 )
= $true )
| ( ( rel_k @ sK0 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f238]) ).
thf(f242,plain,
( ( ( ~ ~ ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) )
= $false )
| ( $false
= ( ~ ( q @ sK3 )
| ~ ( r @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f243,plain,
( ( $false
= ( ~ ( rel_k @ sK0 @ sK3 ) ) )
| ( ( ~ ~ ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f244,plain,
( ( ( ~ ~ ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) )
= $false )
| ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f245,plain,
( ( ( ~ ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) )
= $true )
| ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( $false
= ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
( ( $false
= ( ~ ( r @ sK4 ) ) )
| ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f248,plain,
( ( $false
= ( ~ ( q @ sK4 ) ) )
| ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f249,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( q @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f248]) ).
thf(f250,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( r @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f251,plain,
( ( ( ~ ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) )
= $true )
| ( $false
= ( ~ ( q @ sK3 )
| ~ ( r @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f252,plain,
( ( $false
= ( ~ ( q @ sK3 )
| ~ ( r @ sK3 ) ) )
| ( $false
= ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) ) ),
inference(not_proxy_clausification,[],[f251]) ).
thf(f253,plain,
( ( $false
= ( ~ ( r @ sK3 ) ) )
| ( $false
= ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f254,plain,
( ( $false
= ( ~ ( q @ sK3 ) ) )
| ( $false
= ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f255,plain,
( ( ( q @ sK3 )
= $true )
| ( $false
= ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) ) ),
inference(not_proxy_clausification,[],[f254]) ).
thf(f256,plain,
( ( ( q @ sK3 )
= $true )
| ( $false
= ( ~ ( r @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f255]) ).
thf(f257,plain,
( ( ( q @ sK3 )
= $true )
| ( $false
= ( ~ ( q @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f255]) ).
thf(f258,plain,
( ( ( q @ sK4 )
= $true )
| ( ( q @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f257]) ).
thf(f259,plain,
( ( ( r @ sK4 )
= $true )
| ( ( q @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f256]) ).
thf(f260,plain,
( ( ( r @ sK3 )
= $true )
| ( $false
= ( ~ ( q @ sK4 )
| ~ ( r @ sK4 ) ) ) ),
inference(not_proxy_clausification,[],[f253]) ).
thf(f261,plain,
( ( ( r @ sK3 )
= $true )
| ( $false
= ( ~ ( r @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( ( $false
= ( ~ ( q @ sK4 ) ) )
| ( ( r @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f263,plain,
( ( ( r @ sK3 )
= $true )
| ( ( q @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f262]) ).
thf(f264,plain,
( ( ( r @ sK4 )
= $true )
| ( ( r @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f266,definition,
( spl5_1
<=> ! [X2: $i] :
( ( ( r @ X2 )
= $false )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( q @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f267,plain,
( ! [X2: $i] :
( ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( q @ X2 ) )
| ( ( r @ X2 )
= $false ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f268,plain,
( spl5_1
| spl5_1 ),
inference(avatar_split_clause,[],[f169,f266,f266]) ).
thf(f300,definition,
( spl5_8
<=> ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f302,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f304,definition,
( spl5_9
<=> ( ( rel_k @ sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f306,plain,
( ( ( rel_k @ sK0 @ sK4 )
= $true )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f304]) ).
thf(f307,plain,
( spl5_8
| spl5_9 ),
inference(avatar_split_clause,[],[f237,f304,f300]) ).
thf(f309,definition,
( spl5_10
<=> ( ( q @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
thf(f311,plain,
( ( ( q @ sK3 )
= $true )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f309]) ).
thf(f312,plain,
( spl5_9
| spl5_10 ),
inference(avatar_split_clause,[],[f240,f309,f304]) ).
thf(f314,definition,
( spl5_11
<=> ( ( r @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
thf(f316,plain,
( ( ( r @ sK3 )
= $true )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f314]) ).
thf(f317,plain,
( spl5_9
| spl5_11 ),
inference(avatar_split_clause,[],[f241,f314,f304]) ).
thf(f319,definition,
( spl5_12
<=> ( ( q @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
thf(f321,plain,
( ( ( q @ sK4 )
= $true )
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f319]) ).
thf(f322,plain,
( spl5_12
| spl5_8 ),
inference(avatar_split_clause,[],[f249,f300,f319]) ).
thf(f324,definition,
( spl5_13
<=> ( ( r @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_13])],[avatar_definition]) ).
thf(f326,plain,
( ( ( r @ sK4 )
= $true )
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f324]) ).
thf(f327,plain,
( spl5_8
| spl5_13 ),
inference(avatar_split_clause,[],[f250,f324,f300]) ).
thf(f328,plain,
( spl5_12
| spl5_10 ),
inference(avatar_split_clause,[],[f258,f309,f319]) ).
thf(f329,plain,
( spl5_13
| spl5_10 ),
inference(avatar_split_clause,[],[f259,f309,f324]) ).
thf(f330,plain,
( spl5_12
| spl5_11 ),
inference(avatar_split_clause,[],[f263,f314,f319]) ).
thf(f331,plain,
( spl5_13
| spl5_11 ),
inference(avatar_split_clause,[],[f264,f314,f324]) ).
thf(f332,plain,
( ( ( r @ sK3 )
= $false )
| ( $false
= ( q @ sK3 ) )
| ( $false = $true )
| ~ spl5_1
| ~ spl5_8 ),
inference(constrained_superposition,[],[f302,f267]) ).
thf(f335,plain,
( ( ( r @ sK3 )
= $false )
| ( $false
= ( q @ sK3 ) )
| ~ spl5_1
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f332]) ).
thf(f338,plain,
( ( $false
= ( q @ sK3 ) )
| ( $false = $true )
| ~ spl5_1
| ~ spl5_8
| ~ spl5_11 ),
inference(forward_demodulation,[],[f335,f316]) ).
thf(f339,plain,
( ( $false
= ( q @ sK3 ) )
| ~ spl5_1
| ~ spl5_8
| ~ spl5_11 ),
inference(trivial_inequality_removal,[],[f338]) ).
thf(f343,plain,
( ( $false = $true )
| ~ spl5_1
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11 ),
inference(forward_demodulation,[],[f339,f311]) ).
thf(f344,plain,
( $false
| ~ spl5_1
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11 ),
inference(trivial_inequality_removal,[],[f343]) ).
thf(f345,plain,
( ~ spl5_1
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f344]) ).
thf(f347,plain,
( ( $false = $true )
| ( ( q @ sK4 )
= $false )
| ( $false
= ( r @ sK4 ) )
| ~ spl5_1
| ~ spl5_9 ),
inference(constrained_superposition,[],[f306,f267]) ).
thf(f350,plain,
( ( $false
= ( r @ sK4 ) )
| ( ( q @ sK4 )
= $false )
| ~ spl5_1
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f353,plain,
( ( ( q @ sK4 )
= $false )
| ( $false = $true )
| ~ spl5_1
| ~ spl5_9
| ~ spl5_13 ),
inference(forward_demodulation,[],[f350,f326]) ).
thf(f354,plain,
( ( ( q @ sK4 )
= $false )
| ~ spl5_1
| ~ spl5_9
| ~ spl5_13 ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f358,plain,
( ( $false = $true )
| ~ spl5_1
| ~ spl5_9
| ~ spl5_12
| ~ spl5_13 ),
inference(forward_demodulation,[],[f354,f321]) ).
thf(f359,plain,
( $false
| ~ spl5_1
| ~ spl5_9
| ~ spl5_12
| ~ spl5_13 ),
inference(trivial_inequality_removal,[],[f358]) ).
thf(f360,plain,
( ~ spl5_1
| ~ spl5_9
| ~ spl5_12
| ~ spl5_13 ),
inference(avatar_contradiction_clause,[],[f359]) ).
cnf(s1,plain,
( spl5_1
| spl5_1 ),
inference(sat_conversion,[],[f268]) ).
cnf(s2,plain,
spl5_1,
inference(rat,[],[s1]) ).
cnf(s9,plain,
( spl5_8
| spl5_9 ),
inference(sat_conversion,[],[f307]) ).
cnf(s10,plain,
( spl5_9
| spl5_10 ),
inference(sat_conversion,[],[f312]) ).
cnf(s11,plain,
( spl5_9
| spl5_11 ),
inference(sat_conversion,[],[f317]) ).
cnf(s12,plain,
( spl5_8
| spl5_12 ),
inference(sat_conversion,[],[f322]) ).
cnf(s13,plain,
( spl5_8
| spl5_13 ),
inference(sat_conversion,[],[f327]) ).
cnf(s14,plain,
( spl5_10
| spl5_12 ),
inference(sat_conversion,[],[f328]) ).
cnf(s15,plain,
( spl5_10
| spl5_13 ),
inference(sat_conversion,[],[f329]) ).
cnf(s16,plain,
( spl5_11
| spl5_12 ),
inference(sat_conversion,[],[f330]) ).
cnf(s17,plain,
( spl5_11
| spl5_13 ),
inference(sat_conversion,[],[f331]) ).
cnf(s19,plain,
( ~ spl5_1
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11 ),
inference(sat_conversion,[],[f345]) ).
cnf(s21,plain,
( ~ spl5_1
| ~ spl5_9
| ~ spl5_12
| ~ spl5_13 ),
inference(sat_conversion,[],[f360]) ).
cnf(s22,plain,
spl5_8,
inference(rat,[],[s21,s9,s12,s13,s2]) ).
cnf(s23,plain,
( spl5_10
| ~ spl5_9 ),
inference(rat,[],[s21,s14,s15,s2]) ).
cnf(s24,plain,
~ spl5_9,
inference(rat,[],[s21,s16,s17,s19,s23,s2,s22]) ).
cnf(s25,plain,
spl5_11,
inference(rat,[],[s11,s24]) ).
cnf(s26,plain,
spl5_10,
inference(rat,[],[s10,s24]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s19,s22,s2,s25,s26]) ).
thf(f361,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO399^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:52:57 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (339684)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (339692)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=4195841680: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)
% 0.20/0.28 % (339695)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (339695)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
% 0.20/0.28 % (339691)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2293045719:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (339689)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2523934780:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (339690)lrs+10_16_si=on:nwc=1.5:random_seed=3370326332:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (339694)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3865639388:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (339693)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2079286446:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (339695)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=4247303809:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (339691)Instruction limit reached!
% 0.20/0.28 % (339691)------------------------------
% 0.20/0.28 % (339691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (339691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (339691)CaDiCaL version: 2.1.3
% 0.20/0.28 % (339691)Termination reason: Instruction limit
% 0.20/0.28 % (339691)Termination phase: Preprocessing 3
% 0.20/0.28 % (339691)Time elapsed: 0.002 s
% 0.20/0.28 % (339691)Peak memory usage: 10 MB
% 0.20/0.28 % (339691)Instructions burned: 4 (million)
% 0.20/0.28 % (339690) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-339684-339690"...
% 0.20/0.28 % (339689) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-339684-339689"...
% 0.20/0.28 % (339694) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-339684-339694"...
% 0.20/0.28 % (339695) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-339684-339695"...
% 0.20/0.28 % (339689)...printing done.
% 0.20/0.28 % (339690)...printing done.
% 0.20/0.28 % (339693)Instruction limit reached!
% 0.20/0.28 % (339693)------------------------------
% 0.20/0.28 % (339693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (339693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (339693)CaDiCaL version: 2.1.3
% 0.20/0.28 % (339693)Termination reason: Instruction limit
% 0.20/0.28 % (339693)Termination phase: Saturation
% 0.20/0.28 % (339693)Time elapsed: 0.014 s
% 0.20/0.28 % (339693)Peak memory usage: 11 MB
% 0.20/0.28 % (339693)Instructions burned: 25 (million)
% 0.20/0.28 % (339694)...printing done.
% 0.20/0.28 % (339689)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (339689)------------------------------
% 0.20/0.28 % (339689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (339689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (339689)CaDiCaL version: 2.1.3
% 0.20/0.28 % (339689)Termination reason: Refutation
% 0.20/0.28 % (339689)Time elapsed: 0.013 s
% 0.20/0.28 % (339689)Peak memory usage: 13 MB
% 0.20/0.28 % (339689)Instructions burned: 25 (million)
% 0.20/0.28 % (339684)Success in time 0.038 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------