%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO469^5 : 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 : n008.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 08:48:00 AM UTC 2026
% Result : Theorem 0.22s 0.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 13
% Syntax : Number of formulae : 142 ( 79 unt; 0 typ; 3 def)
% Number of atoms : 985 ( 198 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 1150 ( 123 ~; 180 |; 13 &; 749 @)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 57 usr; 9 con; 0-4 aty)
% ( 70 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 240 ( 0 sgn 73 !; 0 ?; 240 :)
% 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_s4: $i > $i > $o ).
thf(func_def_33,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s4: ( $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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
vNOT: $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
sK3: $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,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
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(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
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,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ q ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ q ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f38,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(f39,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,[],[f38]) ).
thf(f47,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f48,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f47]) ).
thf(f52,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f53,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f52]) ).
thf(f59,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f60,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f64,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f65,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f75,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f76,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f79,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f80,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f84,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f86,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f87,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f96,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ q ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f97,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ q ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ q ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[f97]) ).
thf(f106,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f107,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f53]) ).
thf(f113,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f48]) ).
thf(f115,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f116,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f117,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,[],[f39]) ).
thf(f118,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f122,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ q ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f127,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f132,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f138,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,[],[f116,f106,f115]) ).
thf(f147,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f107,f117]) ).
thf(f148,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f113,f132]) ).
thf(f149,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ q ) ) ) ) ) ),
inference(definition_unfolding,[],[f122,f127,f138,f118,f138,f118,f118,f138,f118,f118]) ).
thf(f150,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( q @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( q @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f159,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f161,plain,
( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( $false
= ( ( q @ sK2 )
| ~ ( rel_s4 @ sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $false
= ( q @ sK2 ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( $true
= ( rel_s4 @ sK1 @ sK2 ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f167,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( ( p @ X1 )
| ~ ( rel_s4 @ sK1 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK1 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( $true
= ( rel_s4 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f172,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f173,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( $true
= ( ( q @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true )
| ( $true
= ( ( q @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( ( q @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) )
= $true )
| ( ( q @ X1 )
= $true )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( q @ X1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ ( sK3 @ X1 ) )
= $false )
| ( ( q @ X1 )
= $true )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( q @ X1 )
= $true )
| ( $false
= ( ( p @ ( sK3 @ X1 ) )
| ~ ( rel_s4 @ X1 @ ( sK3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( ( q @ X1 )
= $true )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK3 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( q @ X1 )
= $true )
| ( $false
= ( p @ ( sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK3 @ X1 ) ) )
| ( ( q @ X1 )
= $true )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f184,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y0 )
& ( rel_s4 @ Y1 @ Y2 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f185,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y0 )
& ( rel_s4 @ Y1 @ Y2 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ X1 )
& ( rel_s4 @ Y0 @ Y1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ X1 )
& ( rel_s4 @ Y0 @ Y1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X1 )
& ( rel_s4 @ X2 @ Y0 ) )
=> ( rel_s4 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X1 )
& ( rel_s4 @ X2 @ Y0 ) )
=> ( rel_s4 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s4 @ X3 @ X1 )
& ( rel_s4 @ X2 @ X3 ) )
=> ( rel_s4 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X2 @ X1 )
= $true )
| ( $false
= ( ( rel_s4 @ X3 @ X1 )
& ( rel_s4 @ X2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( ( rel_s4 @ X2 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f194,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f269,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK0 ) )
| ( $true
= ( rel_s4 @ X0 @ sK1 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f192,f171]) ).
thf(f271,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X1 @ X0 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $false = $true )
| ( $true
= ( p @ X0 ) ) ),
inference(constrained_superposition,[],[f192,f170]) ).
thf(f280,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f165,f192]) ).
thf(f286,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f289,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f293,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $false
= ( rel_s4 @ X1 @ X0 ) )
| ( $true
= ( p @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f271]) ).
thf(f304,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X0 @ X1 ) )
| ( $false = $true )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f286,f192]) ).
thf(f310,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f304]) ).
thf(f318,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $false
= ( p @ ( sK3 @ sK2 ) ) )
| ( $false = $true )
| ( $true
= ( q @ sK2 ) ) ),
inference(constrained_superposition,[],[f289,f182]) ).
thf(f324,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( rel_s4 @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f192,f289]) ).
thf(f326,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( $true
= ( rel_s4 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f324]) ).
thf(f328,plain,
( ( $true
= ( q @ sK2 ) )
| ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $false
= ( p @ ( sK3 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[],[f318]) ).
thf(f333,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $false
= ( p @ ( sK3 @ sK2 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f328,f164]) ).
thf(f334,plain,
( ( $false
= ( p @ ( sK3 @ sK2 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f333]) ).
thf(f337,plain,
( ( $false = $true )
| ( $false
= ( p @ ( sK3 @ sK2 ) ) ) ),
inference(forward_demodulation,[],[f334,f171]) ).
thf(f338,plain,
( $false
= ( p @ ( sK3 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f337]) ).
thf(f402,plain,
! [X0: $i] :
( ( $false = $true )
| ( $false
= ( rel_s4 @ X0 @ sK0 ) )
| ( $true
= ( rel_s4 @ X0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f165,f310]) ).
thf(f413,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f402]) ).
thf(f548,plain,
! [X0: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( $false = $true )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( ( rel_s4 @ sK1 @ X0 )
= $false )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(constrained_superposition,[],[f293,f326]) ).
thf(f576,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( p @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( ( rel_s4 @ sK1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f548]) ).
thf(f583,definition,
( spl4_7
<=> ! [X0: $i] :
( ( ( rel_s4 @ sK1 @ X0 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f584,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( ( rel_s4 @ sK1 @ X0 )
= $false ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f583]) ).
thf(f586,definition,
( spl4_8
<=> ! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f587,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( p @ X1 )
= $true ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f586]) ).
thf(f589,plain,
( spl4_7
| spl4_8 ),
inference(avatar_split_clause,[],[f576,f586,f583]) ).
thf(f596,definition,
( spl4_10
<=> ( $false
= ( rel_s4 @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
thf(f598,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f596]) ).
thf(f618,plain,
( ( ( rel_s4 @ sK1 @ sK1 )
= $false )
| ( $false != $false )
| ~ spl4_7 ),
inference(equality_factoring,[],[f584]) ).
thf(f640,plain,
( ( ( rel_s4 @ sK1 @ sK1 )
= $false )
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f618]) ).
thf(f648,plain,
( ( $false = $true )
| ~ spl4_7 ),
inference(forward_demodulation,[],[f640,f195]) ).
thf(f649,plain,
( $false
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f648]) ).
thf(f650,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[],[f649]) ).
thf(f663,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( q @ sK2 ) )
| ( ( p @ ( sK3 @ sK2 ) )
= $true )
| ( $false = $true )
| ~ spl4_8 ),
inference(constrained_superposition,[],[f183,f587]) ).
thf(f672,plain,
( ( ( p @ ( sK3 @ sK2 ) )
= $true )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( q @ sK2 ) )
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f663]) ).
thf(f685,plain,
( ( $false = $true )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( q @ sK2 ) )
| ~ spl4_8 ),
inference(forward_demodulation,[],[f672,f338]) ).
thf(f686,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( q @ sK2 ) )
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f685]) ).
thf(f689,plain,
( ( $false = $true )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ~ spl4_8 ),
inference(forward_demodulation,[],[f686,f164]) ).
thf(f690,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f689]) ).
thf(f693,plain,
( spl4_10
| ~ spl4_8 ),
inference(avatar_split_clause,[],[f690,f586,f596]) ).
thf(f698,plain,
( ( $false = $true )
| ( ( rel_s4 @ sK0 @ sK0 )
= $false )
| ~ spl4_10 ),
inference(constrained_superposition,[],[f413,f598]) ).
thf(f704,plain,
( ( ( rel_s4 @ sK0 @ sK0 )
= $false )
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f698]) ).
thf(f715,plain,
( ( $false = $true )
| ~ spl4_10 ),
inference(forward_demodulation,[],[f704,f195]) ).
thf(f716,plain,
( $false
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f715]) ).
thf(f717,plain,
~ spl4_10,
inference(avatar_contradiction_clause,[],[f716]) ).
cnf(s10,plain,
( spl4_7
| spl4_8 ),
inference(sat_conversion,[],[f589]) ).
cnf(s16,plain,
~ spl4_7,
inference(sat_conversion,[],[f650]) ).
cnf(s17,plain,
( ~ spl4_8
| spl4_10 ),
inference(sat_conversion,[],[f693]) ).
cnf(s22,plain,
~ spl4_10,
inference(sat_conversion,[],[f717]) ).
cnf(s23,plain,
~ spl4_8,
inference(rat,[],[s17,s22]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s10,s23,s16]) ).
thf(f718,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO469^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n008.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 17:03:54 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.07/0.26 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
% 0.22/0.33 % (3440591)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.33 % (3440599)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=3062563898: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)
% 0.22/0.33 % (3440597)lrs+10_16_si=on:nwc=1.5:random_seed=4292397741:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.33 % (3440596)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2319087423:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.33 % (3440598)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2165857719:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.33 % (3440600)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2334467367:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.33 % (3440598)Instruction limit reached!
% 0.22/0.33 % (3440598)------------------------------
% 0.22/0.33 % (3440598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (3440598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (3440598)CaDiCaL version: 2.1.3
% 0.22/0.33 % (3440598)Termination reason: Instruction limit
% 0.22/0.33 % (3440598)Termination phase: Property scanning
% 0.22/0.33 % (3440598)Time elapsed: 0.002 s
% 0.22/0.33 % (3440598)Peak memory usage: 10 MB
% 0.22/0.33 % (3440598)Instructions burned: 4 (million)
% 0.22/0.33 % (3440597)Instruction limit reached!
% 0.22/0.33 % (3440597)------------------------------
% 0.22/0.33 % (3440597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (3440597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (3440597)CaDiCaL version: 2.1.3
% 0.22/0.33 % (3440597)Termination reason: Instruction limit
% 0.22/0.33 % (3440597)Termination phase: Saturation
% 0.22/0.33 % (3440597)Time elapsed: 0.010 s
% 0.22/0.33 % (3440597)Peak memory usage: 12 MB
% 0.22/0.33 % (3440597)Instructions burned: 19 (million)
% 0.22/0.33 % (3440602)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.33 % (3440602)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
% 0.22/0.33 % (3440601)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1612631231:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.33 % (3440600)Instruction limit reached!
% 0.22/0.33 % (3440600)------------------------------
% 0.22/0.33 % (3440600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (3440600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (3440600)CaDiCaL version: 2.1.3
% 0.22/0.33 % (3440600)Termination reason: Instruction limit
% 0.22/0.33 % (3440600)Termination phase: Saturation
% 0.22/0.33 % (3440600)Time elapsed: 0.014 s
% 0.22/0.33 % (3440600)Peak memory usage: 12 MB
% 0.22/0.33 % (3440600)Instructions burned: 25 (million)
% 0.22/0.33 % (3440602)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=1927364995:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.33 % (3440596) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3440591-3440596"...
% 0.22/0.33 % (3440608)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2089647170:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.33 % (3440608)Instruction limit reached!
% 0.22/0.33 % (3440608)------------------------------
% 0.22/0.33 % (3440608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (3440608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (3440608)CaDiCaL version: 2.1.3
% 0.22/0.33 % (3440608)Termination reason: Instruction limit
% 0.22/0.33 % (3440608)Termination phase: shuffling
% 0.22/0.33 % (3440608)Time elapsed: 0.002 s
% 0.22/0.33 % (3440608)Peak memory usage: 10 MB
% 0.22/0.33 % (3440608)Instructions burned: 2 (million)
% 0.22/0.33 % (3440596)...printing done.
% 0.22/0.33 % (3440596)Refutation found. Thanks to Tanya!
% 0.22/0.33 % SZS status Theorem for theBenchmark
% 0.22/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.33 % (3440596)------------------------------
% 0.22/0.33 % (3440596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (3440596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (3440596)CaDiCaL version: 2.1.3
% 0.22/0.33 % (3440596)Termination reason: Refutation
% 0.22/0.33 % (3440596)Time elapsed: 0.025 s
% 0.22/0.33 % (3440596)Peak memory usage: 13 MB
% 0.22/0.33 % (3440596)Instructions burned: 46 (million)
% 0.22/0.33 % (3440591)Success in time 0.064 s
% 0.22/0.33 % Vampire exiting
%------------------------------------------------------------------------------