%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO450^6 : 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 : n019.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 08:47:45 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 11
% Syntax : Number of formulae : 123 ( 57 unt; 0 typ; 2 def)
% Number of atoms : 967 ( 192 equ; 0 cnn)
% Maximal formula atoms : 17 ( 7 avg)
% Number of connectives : 1301 ( 235 ~; 223 |; 0 &; 777 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 6 con; 0-4 aty)
% ( 64 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 248 ( 0 sgn 56 !; 0 ?; 248 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
vAND: $o > $o > $o ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
vOR: $o > $o > $o ).
thf(func_def_54,type,
sK1: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
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(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f34,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a1) ).
thf(f37,conjecture,
mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mdia_s5 @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_s5 @ ( mimplies @ q @ ( mimplies @ ( mbox_s5 @ p ) @ ( mdia_s5 @ r ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mdia_s5 @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_s5 @ ( mimplies @ q @ ( mimplies @ ( mbox_s5 @ p ) @ ( mdia_s5 @ r ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f59,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f60,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f77,plain,
mreflexive @ rel_s5,
inference(rectify,[],[f34]) ).
thf(f78,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f77]) ).
thf(f83,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f84,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f89,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f90,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f95,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mdia_s5 @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_s5 @ ( mimplies @ q @ ( mimplies @ ( mbox_s5 @ p ) @ ( mdia_s5 @ r ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f96,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mdia_s5 @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_s5 @ ( mimplies @ q @ ( mimplies @ ( mbox_s5 @ p ) @ ( mdia_s5 @ r ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f98,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f99,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f98]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mdia_s5 @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_s5 @ ( mimplies @ q @ ( mimplies @ ( mbox_s5 @ p ) @ ( mdia_s5 @ r ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f96]) ).
thf(f103,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f99]) ).
thf(f104,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f78]) ).
thf(f114,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f116,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f117,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f120,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f121,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mdia_s5 @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_s5 @ ( mimplies @ q @ ( mimplies @ ( mbox_s5 @ p ) @ ( mdia_s5 @ r ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f132,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f134,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f142,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,[],[f114,f134,f120]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f132,f120,f117,f120]) ).
thf(f151,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f104,f116]) ).
thf(f154,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] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ 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 )
@ p
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ q
@ r ) ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ q
@ ( ^ [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] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ r ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f121,f103,f142,f117,f142,f150,f142,f150,f142,f142,f117,f150]) ).
thf(f170,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( r @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( q @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( ( r @ Y2 )
| ~ ( q @ Y2 ) ) ) )
| ~ ( p @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f171,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( r @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( q @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( ( r @ Y2 )
| ~ ( q @ Y2 ) ) ) )
| ~ ( p @ Y1 ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( r @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ( r @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( p @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ( r @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( p @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( r @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( q @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( r @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( r @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( q @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( q @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( q @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( q @ X1 ) )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f183,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( r @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f185,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( r @ Y0 ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( r @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ~ ( r @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( r @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( r @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( r @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f192,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( p @ X2 ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f197,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ( r @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( p @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f198,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ( r @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( p @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( ( r @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( ( r @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( ( r @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( p @ X1 ) )
= $true )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( ( ~ ( p @ X1 ) )
= $true )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( ( r @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( ( p @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( ( r @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( ( r @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( p @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( ( r @ Y0 )
| ~ ( q @ Y0 ) ) )
@ ( sK1 @ X1 ) )
= $false )
| ( ( p @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ X1 @ ( sK1 @ X1 ) )
| ~ ( ( r @ ( sK1 @ X1 ) )
| ~ ( q @ ( sK1 @ X1 ) ) ) )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( p @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( ( p @ X1 )
= $false )
| ( $false
= ( ~ ( ( r @ ( sK1 @ X1 ) )
| ~ ( q @ ( sK1 @ X1 ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ X1 @ ( sK1 @ X1 ) ) )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( p @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f209,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( p @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ( r @ ( sK1 @ X1 ) )
| ~ ( q @ ( sK1 @ X1 ) ) ) )
| ( ( p @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f211,plain,
! [X1: $i] :
( ( $true
= ( r @ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( q @ ( sK1 @ X1 ) ) ) )
| ( ( p @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( p @ X1 )
= $false )
| ( $true
= ( r @ ( sK1 @ X1 ) ) )
| ( ( q @ ( sK1 @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f214,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( $true
= ( rel_s5 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
( ( $true = $false )
| ( ( p @ sK0 )
= $false )
| ( $true
= ( q @ ( sK1 @ sK0 ) ) )
| ( ( rel_s5 @ sK0 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f209,f196]) ).
thf(f219,plain,
( ( ( rel_s5 @ sK0 @ sK0 )
= $false )
| ( $true
= ( q @ ( sK1 @ sK0 ) ) )
| ( ( p @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f216]) ).
thf(f222,plain,
( ( $true = $false )
| ( ( p @ sK0 )
= $false )
| ( $true
= ( q @ ( sK1 @ sK0 ) ) ) ),
inference(forward_demodulation,[],[f219,f215]) ).
thf(f223,plain,
( ( ( p @ sK0 )
= $false )
| ( $true
= ( q @ ( sK1 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[],[f222]) ).
thf(f225,definition,
( spl2_1
<=> ( $true
= ( q @ ( sK1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f227,plain,
( ( $true
= ( q @ ( sK1 @ sK0 ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f225]) ).
thf(f229,definition,
( spl2_2
<=> ( ( p @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f231,plain,
( ( ( p @ sK0 )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f233,plain,
( spl2_2
| spl2_1 ),
inference(avatar_split_clause,[],[f223,f225,f229]) ).
thf(f234,plain,
! [X0: $i] :
( ( ( r @ ( sK1 @ X0 ) )
= $false )
| ( ( rel_s5 @ sK0 @ X0 )
= $false )
| ( ( rel_s5 @ sK0 @ X0 )
= $false )
| ( $false
= ( p @ X0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f190,f209]) ).
thf(f239,plain,
! [X0: $i] :
( ( ( rel_s5 @ sK0 @ X0 )
= $false )
| ( $false
= ( p @ X0 ) )
| ( ( r @ ( sK1 @ X0 ) )
= $false )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[],[f234]) ).
thf(f240,plain,
! [X0: $i] :
( ( ( rel_s5 @ sK0 @ X0 )
= $false )
| ( ( r @ ( sK1 @ X0 ) )
= $false )
| ( $false
= ( p @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f239]) ).
thf(f254,plain,
( ( ( rel_s5 @ sK0 @ sK0 )
= $false )
| ( $false != $false )
| ( $true
= ( p @ sK0 ) ) ),
inference(equality_factoring,[],[f195]) ).
thf(f259,plain,
( ( ( rel_s5 @ sK0 @ sK0 )
= $false )
| ( $true
= ( p @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f254]) ).
thf(f264,plain,
( ( $true
= ( p @ sK0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f259,f215]) ).
thf(f265,plain,
( $true
= ( p @ sK0 ) ),
inference(trivial_inequality_removal,[],[f264]) ).
thf(f269,plain,
( ( $true = $false )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f265,f231]) ).
thf(f270,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f271,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f270]) ).
thf(f321,plain,
( ( ( q @ ( sK1 @ sK0 ) )
= $false )
| ( $true
= ( r @ ( sK1 @ sK0 ) ) )
| ( $true = $false )
| ( ( p @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f212,f215]) ).
thf(f324,plain,
( ( ( p @ sK0 )
= $false )
| ( ( r @ ( sK1 @ sK0 ) )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f240,f215]) ).
thf(f332,plain,
( ( ( r @ ( sK1 @ sK0 ) )
= $false )
| ( ( p @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f324]) ).
thf(f337,plain,
( ( ( q @ ( sK1 @ sK0 ) )
= $false )
| ( ( p @ sK0 )
= $false )
| ( $true
= ( r @ ( sK1 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f347,plain,
( ( $true = $false )
| ( ( r @ ( sK1 @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f332,f265]) ).
thf(f348,plain,
( ( r @ ( sK1 @ sK0 ) )
= $false ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f351,plain,
( ( ( p @ sK0 )
= $false )
| ( $true
= ( r @ ( sK1 @ sK0 ) ) )
| ( $true = $false )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f337,f227]) ).
thf(f352,plain,
( ( ( p @ sK0 )
= $false )
| ( $true
= ( r @ ( sK1 @ sK0 ) ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f351]) ).
thf(f362,plain,
( ( $true
= ( r @ ( sK1 @ sK0 ) ) )
| ( $true = $false )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f352,f265]) ).
thf(f363,plain,
( ( $true
= ( r @ ( sK1 @ sK0 ) ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f362]) ).
thf(f370,plain,
( ( $true = $false )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f363,f348]) ).
thf(f371,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f372,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f371]) ).
cnf(s2,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f233]) ).
cnf(s4,plain,
~ spl2_2,
inference(sat_conversion,[],[f271]) ).
cnf(s12,plain,
~ spl2_1,
inference(sat_conversion,[],[f372]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s2,s4,s12]) ).
thf(f373,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO450^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:52:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.31 % (1058473)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (1058481)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=3337603888: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)
% 0.21/0.31 % (1058484)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (1058484)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
% 0.21/0.31 % (1058478)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1029582959:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (1058479)lrs+10_16_si=on:nwc=1.5:random_seed=664555221:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (1058480)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2665117493:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (1058482)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=121591085:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (1058483)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2487990894:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (1058484)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=631208211:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (1058480)Instruction limit reached!
% 0.21/0.31 % (1058480)------------------------------
% 0.21/0.31 % (1058480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1058480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1058480)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1058480)Termination reason: Instruction limit
% 0.21/0.31 % (1058480)Termination phase: Property scanning
% 0.21/0.31 % (1058480)Time elapsed: 0.002 s
% 0.21/0.31 % (1058480)Peak memory usage: 10 MB
% 0.21/0.31 % (1058480)Instructions burned: 4 (million)
% 0.21/0.31 % (1058479)Instruction limit reached!
% 0.21/0.31 % (1058479)------------------------------
% 0.21/0.31 % (1058479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1058479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1058479)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1058479)Termination reason: Instruction limit
% 0.21/0.31 % (1058479)Termination phase: Saturation
% 0.21/0.31 % (1058479)Time elapsed: 0.009 s
% 0.21/0.31 % (1058479)Peak memory usage: 12 MB
% 0.21/0.31 % (1058479)Instructions burned: 19 (million)
% 0.21/0.31 % (1058478) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1058473-1058478"...
% 0.21/0.31 % (1058482)Instruction limit reached!
% 0.21/0.31 % (1058482)------------------------------
% 0.21/0.31 % (1058482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1058482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1058482)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1058482)Termination reason: Instruction limit
% 0.21/0.31 % (1058482)Termination phase: Saturation
% 0.21/0.31 % (1058482)Time elapsed: 0.014 s
% 0.21/0.31 % (1058482)Peak memory usage: 12 MB
% 0.21/0.31 % (1058482)Instructions burned: 25 (million)
% 0.21/0.31 % (1058478)...printing done.
% 0.21/0.31 % (1058478)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (1058478)------------------------------
% 0.21/0.31 % (1058478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1058478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1058478)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1058478)Termination reason: Refutation
% 0.21/0.31 % (1058478)Time elapsed: 0.014 s
% 0.21/0.31 % (1058478)Peak memory usage: 13 MB
% 0.21/0.31 % (1058478)Instructions burned: 27 (million)
% 0.21/0.31 % (1058473)Success in time 0.055 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------