%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO462^6 : 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 : n002.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 08:47:55 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 14
% Syntax : Number of formulae : 144 ( 47 unt; 0 typ; 6 def)
% Number of atoms : 1069 ( 177 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 1432 ( 300 ~; 305 |; 0 &; 759 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 12 con; 0-4 aty)
% ( 62 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 269 ( 0 sgn 35 !; 0 ?; 269 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
vIMP: $o > $o > $o ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [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,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f37,conjecture,
mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f43,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f44,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f43]) ).
thf(f46,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f47,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f68,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f75,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f80,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f81,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f84,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f85,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f84]) ).
thf(f96,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f97,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) )
!= $true ),
inference(flattening,[],[f44]) ).
thf(f118,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f122,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f123,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f125,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f127,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f131,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f134,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f138,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f141,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f134,f138,f122,f138,f138]) ).
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,[],[f127,f122,f138]) ).
thf(f144,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f125,f141,f142,f142]) ).
thf(f153,plain,
( ( ^ [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_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ q ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f131,f123,f142,f118,f144,f144,f118,f118]) ).
thf(f164,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f165,plain,
( ( ^ [Y0: $i] :
( ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f176,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ sK1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ sK1 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( ( ( p @ sK1 )
| ~ ( rel_s5 @ sK0 @ sK1 ) )
= $false )
| ( $false
= ( ( q @ sK2 )
| ~ ( rel_s5 @ sK0 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK1 ) )
= $false )
| ( $false
= ( ( q @ sK2 )
| ~ ( rel_s5 @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( ( p @ sK1 )
= $false )
| ( $false
= ( ( q @ sK2 )
| ~ ( rel_s5 @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK2 ) )
= $false )
| ( ( p @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( ( q @ sK2 )
= $false )
| ( ( p @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f184,plain,
( ( ( p @ sK1 )
= $false )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ( q @ sK2 )
| ~ ( rel_s5 @ sK0 @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f186,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( ( ~ ( rel_s5 @ sK0 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( ( q @ sK2 )
= $false )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f188,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f199,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f200,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f212,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f213,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( q @ X2 )
| ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK0 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s5 @ sK0 @ X2 )
= $false )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s5 @ sK0 @ X2 )
= $false )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f221,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) )
| ~ ( rel_s5 @ sK0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X1: $i] :
( ( ( ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) )
= $true )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X1: $i] :
( ( ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) )
= $false )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $false
= ( ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $false
= ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f228,plain,
! [X1: $i] :
( ( $true
= ( ( p @ X1 )
| ~ ( q @ X1 ) ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 ) ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) )
| ( ( q @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X1: $i] :
( ( ( ( q @ X1 )
| ~ ( p @ X1 ) )
= $true )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f232,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f244,definition,
( spl5_1
<=> ( ( q @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f246,plain,
( ( ( q @ sK2 )
= $false )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f244]) ).
thf(f248,definition,
( spl5_2
<=> ( ( p @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f250,plain,
( ( ( p @ sK1 )
= $false )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f251,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f183,f248,f244]) ).
thf(f253,definition,
( spl5_3
<=> ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f255,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f256,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f184,f248,f253]) ).
thf(f258,definition,
( spl5_4
<=> ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f260,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f258]) ).
thf(f261,plain,
( spl5_4
| spl5_1 ),
inference(avatar_split_clause,[],[f187,f244,f258]) ).
thf(f262,plain,
( spl5_3
| spl5_4 ),
inference(avatar_split_clause,[],[f188,f258,f253]) ).
thf(f268,definition,
( spl5_6
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f269,plain,
( ! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f268]) ).
thf(f281,definition,
( spl5_9
<=> ! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f282,plain,
( ! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f289,plain,
( spl5_6
| spl5_9 ),
inference(avatar_split_clause,[],[f219,f281,f268]) ).
thf(f290,plain,
( ( ( q @ sK1 )
= $false )
| ( ( p @ sK1 )
= $true )
| ( $true = $false )
| ~ spl5_4 ),
inference(constrained_superposition,[],[f260,f230]) ).
thf(f292,plain,
( ( ( q @ sK1 )
= $false )
| ( ( p @ sK1 )
= $true )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f290]) ).
thf(f294,plain,
( ( ( q @ sK1 )
= $false )
| ( $true = $false )
| ~ spl5_2
| ~ spl5_4 ),
inference(forward_demodulation,[],[f292,f250]) ).
thf(f295,plain,
( ( ( q @ sK1 )
= $false )
| ~ spl5_2
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f294]) ).
thf(f299,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true = $false )
| ~ spl5_4
| ~ spl5_6 ),
inference(constrained_superposition,[],[f260,f269]) ).
thf(f301,plain,
( ( $true
= ( q @ sK1 ) )
| ~ spl5_4
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f299]) ).
thf(f305,plain,
( ( $true = $false )
| ~ spl5_2
| ~ spl5_4
| ~ spl5_6 ),
inference(forward_demodulation,[],[f301,f295]) ).
thf(f306,plain,
( $false
| ~ spl5_2
| ~ spl5_4
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f305]) ).
thf(f307,plain,
( ~ spl5_2
| ~ spl5_4
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f306]) ).
thf(f314,plain,
( ( ( p @ sK1 )
= $true )
| ( $true = $false )
| ~ spl5_4
| ~ spl5_9 ),
inference(constrained_superposition,[],[f260,f282]) ).
thf(f317,plain,
( ( ( p @ sK1 )
= $true )
| ~ spl5_4
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f314]) ).
thf(f323,plain,
( ( $true = $false )
| ~ spl5_2
| ~ spl5_4
| ~ spl5_9 ),
inference(forward_demodulation,[],[f317,f250]) ).
thf(f324,plain,
( $false
| ~ spl5_2
| ~ spl5_4
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f323]) ).
thf(f325,plain,
( ~ spl5_2
| ~ spl5_4
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[],[f324]) ).
thf(f338,plain,
( ( $true = $false )
| ( ( p @ sK2 )
= $true )
| ~ spl5_3
| ~ spl5_9 ),
inference(constrained_superposition,[],[f255,f282]) ).
thf(f342,plain,
( ( ( p @ sK2 )
= $true )
| ~ spl5_3
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f338]) ).
thf(f347,plain,
( ( ( p @ sK2 )
= $false )
| ( $true = $false )
| ( $true
= ( q @ sK2 ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f233,f255]) ).
thf(f357,plain,
( ( $true
= ( q @ sK2 ) )
| ( ( p @ sK2 )
= $false )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f366,plain,
( ( $true = $false )
| ( ( p @ sK2 )
= $false )
| ~ spl5_1
| ~ spl5_3 ),
inference(forward_demodulation,[],[f357,f246]) ).
thf(f367,plain,
( ( ( p @ sK2 )
= $false )
| ~ spl5_1
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f366]) ).
thf(f377,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_3
| ~ spl5_9 ),
inference(forward_demodulation,[],[f367,f342]) ).
thf(f378,plain,
( $false
| ~ spl5_1
| ~ spl5_3
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f377]) ).
thf(f379,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[],[f378]) ).
thf(f395,plain,
( ( $true
= ( q @ sK2 ) )
| ( $true = $false )
| ~ spl5_3
| ~ spl5_6 ),
inference(constrained_superposition,[],[f269,f255]) ).
thf(f407,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl5_3
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f395]) ).
thf(f422,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_3
| ~ spl5_6 ),
inference(forward_demodulation,[],[f407,f246]) ).
thf(f423,plain,
( $false
| ~ spl5_1
| ~ spl5_3
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f422]) ).
thf(f424,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f423]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f251]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f256]) ).
cnf(s3,plain,
( spl5_1
| spl5_4 ),
inference(sat_conversion,[],[f261]) ).
cnf(s4,plain,
( spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f262]) ).
cnf(s9,plain,
( spl5_6
| spl5_9 ),
inference(sat_conversion,[],[f289]) ).
cnf(s11,plain,
( ~ spl5_2
| ~ spl5_4
| ~ spl5_6 ),
inference(sat_conversion,[],[f307]) ).
cnf(s13,plain,
( ~ spl5_2
| ~ spl5_4
| ~ spl5_9 ),
inference(sat_conversion,[],[f325]) ).
cnf(s21,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_9 ),
inference(sat_conversion,[],[f379]) ).
cnf(s26,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_6 ),
inference(sat_conversion,[],[f424]) ).
cnf(s28,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(rat,[],[s9,s11,s13]) ).
cnf(s29,plain,
spl5_1,
inference(rat,[],[s28,s1,s3]) ).
cnf(s30,plain,
~ spl5_3,
inference(rat,[],[s9,s21,s26,s29]) ).
cnf(s31,plain,
spl5_4,
inference(rat,[],[s4,s30]) ).
cnf(s32,plain,
spl5_2,
inference(rat,[],[s2,s30]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s28,s31,s32]) ).
thf(f428,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO462^6 : 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 : n002.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 17:01:38 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
% 0.21/0.27 % (1564217)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (1564228)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=789132856:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (1564235)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (1564235)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
% 0.21/0.27 % (1564228) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1564217-1564228"...
% 0.21/0.27 % (1564230)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=115407799:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (1564229)lrs+10_16_si=on:nwc=1.5:random_seed=3786568123:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (1564233)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2071903332:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (1564232)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=1467572737: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)
% 0.21/0.27 % (1564234)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2968899276:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.27 % (1564228)...printing done.
% 0.21/0.27 % (1564235)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=3306661416:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.27 % (1564228)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (1564228)------------------------------
% 0.21/0.27 % (1564228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1564228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1564228)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1564228)Termination reason: Refutation
% 0.21/0.27 % (1564228)Time elapsed: 0.008 s
% 0.21/0.27 % (1564228)Peak memory usage: 13 MB
% 0.21/0.27 % (1564228)Instructions burned: 27 (million)
% 0.21/0.27 % (1564217)Success in time 0.024 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------