%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO458^5 : 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 08:47:51 AM UTC 2026
% Result : Theorem 0.26s 0.29s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 92 ( 62 unt; 0 typ; 3 def)
% Number of atoms : 528 ( 86 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 747 ( 154 ~; 113 |; 0 &; 448 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 8 con; 0-4 aty)
% ( 29 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 192 ( 0 sgn 12 !; 0 ?; 192 :)
% 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,
vNOT: $o > $o ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_44,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,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/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(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
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(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
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(f36,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mequiv @ p @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mequiv @ p @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f38,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f39,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f49,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f50,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f54,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f55,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f61,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f72,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f73,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f85,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f90,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f93,plain,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mequiv @ p @ q ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f94,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mequiv @ p @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f93]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mequiv @ p @ q ) ) ) )
!= $true ),
inference(flattening,[],[f94]) ).
thf(f100,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f101,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f113,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f114,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f122,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f129,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mequiv @ p @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f131,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f137,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,[],[f114,f122,f102,f122,f122]) ).
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,[],[f100,f102,f122]) ).
thf(f140,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,[],[f131,f137,f138,f138]) ).
thf(f149,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 > $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 ) ) )
@ ( ^ [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 ) )
@ ( ^ [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 > $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 ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f129,f101,f138,f137,f113,f113,f113,f140]) ).
thf(f159,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f160,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( $false
= ( ~ ( ~ ( ( p @ sK1 )
| ~ ( q @ sK1 ) )
| ~ ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) )
| ~ ( rel_s4 @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
( ( ~ ( rel_s4 @ sK0 @ sK1 ) )
= $false ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( ~ ( ~ ( ( p @ sK1 )
| ~ ( q @ sK1 ) )
| ~ ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( $true
= ( ~ ( ( p @ sK1 )
| ~ ( q @ sK1 ) )
| ~ ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( ( ~ ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) )
= $true )
| ( ( ~ ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( ~ ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) )
= $true )
| ( $false
= ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( $false
= ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( $false
= ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) )
| ( $false
= ( p @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f175,plain,
( ( $false
= ( p @ sK1 ) )
| ( ( q @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f182,plain,
( $true
= ( rel_s4 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f183,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f184,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( ( q @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( ( q @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( ( q @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f193,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( ( p @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f201,definition,
( spl2_1
<=> ( ( q @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f203,plain,
( ( ( q @ sK1 )
= $false )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f201]) ).
thf(f205,definition,
( spl2_2
<=> ( $false
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f207,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f208,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f175,f205,f201]) ).
thf(f210,definition,
( spl2_3
<=> ( ( p @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f211,plain,
( ( ( p @ sK1 )
!= $true )
| spl2_3 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f212,plain,
( ( ( p @ sK1 )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f218,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_demodulation,[],[f212,f207]) ).
thf(f219,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f218]) ).
thf(f220,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f219]) ).
thf(f222,plain,
( ( $false = $true )
| ( ( q @ sK1 )
= $true ) ),
inference(constrained_superposition,[],[f191,f182]) ).
thf(f225,plain,
( ( q @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f222]) ).
thf(f229,plain,
( ( $false = $true )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f225,f203]) ).
thf(f230,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f229]) ).
thf(f231,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f230]) ).
thf(f235,plain,
( ( $false = $true )
| ( ( p @ sK1 )
= $true ) ),
inference(constrained_superposition,[],[f182,f196]) ).
thf(f237,plain,
( ( p @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f235]) ).
thf(f240,plain,
( $false
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f237,f211]) ).
thf(f241,plain,
spl2_3,
inference(avatar_contradiction_clause,[],[f240]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f208]) ).
cnf(s3,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f220]) ).
cnf(s5,plain,
~ spl2_1,
inference(sat_conversion,[],[f231]) ).
cnf(s7,plain,
spl2_3,
inference(sat_conversion,[],[f241]) ).
cnf(s8,plain,
~ spl2_2,
inference(rat,[],[s3,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8,s5]) ).
thf(f242,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO458^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:58:39 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.26/0.29 % (3427909)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.29 % (3427922)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=539190977:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.29 % (3427924)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.29 % (3427924)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
% 0.26/0.29 % (3427918)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3833458213:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.29 % (3427920)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=32995798:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.29 % (3427919)lrs+10_16_si=on:nwc=1.5:random_seed=3087826673:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.29 % (3427921)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=3462552730: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)
% 0.26/0.29 % (3427922)Instruction limit reached!
% 0.26/0.29 % (3427922)------------------------------
% 0.26/0.29 % (3427922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.29 % (3427922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.29 % (3427922)CaDiCaL version: 2.1.3
% 0.26/0.29 % (3427922)Termination reason: Instruction limit
% 0.26/0.29 % (3427922)Termination phase: Saturation
% 0.26/0.29 % (3427922)Time elapsed: 0.008 s
% 0.26/0.29 % (3427922)Peak memory usage: 11 MB
% 0.26/0.29 % (3427922)Instructions burned: 25 (million)
% 0.26/0.29 % (3427924)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=2035791306:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.26/0.29 % (3427923)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=323954210:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.26/0.29 % (3427920)Instruction limit reached!
% 0.26/0.29 % (3427920)------------------------------
% 0.26/0.29 % (3427920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.29 % (3427920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.29 % (3427920)CaDiCaL version: 2.1.3
% 0.26/0.29 % (3427920)Termination reason: Instruction limit
% 0.26/0.29 % (3427920)Termination phase: Property scanning
% 0.26/0.29 % (3427920)Time elapsed: 0.002 s
% 0.26/0.29 % (3427920)Peak memory usage: 10 MB
% 0.26/0.29 % (3427920)Instructions burned: 4 (million)
% 0.26/0.29 % (3427918) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3427909-3427918"...
% 0.26/0.29 % (3427919) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3427909-3427919"...
% 0.26/0.29 % (3427924) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3427909-3427924"...
% 0.26/0.29 % (3427923) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3427909-3427923"...
% 0.26/0.29 % (3427932)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=800899754:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.26/0.29 % (3427918)...printing done.
% 0.26/0.29 % (3427919)...printing done.
% 0.26/0.29 % (3427932)Instruction limit reached!
% 0.26/0.29 % (3427932)------------------------------
% 0.26/0.29 % (3427932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.29 % (3427932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.29 % (3427932)CaDiCaL version: 2.1.3
% 0.26/0.29 % (3427932)Termination reason: Instruction limit
% 0.26/0.29 % (3427932)Termination phase: Property scanning
% 0.26/0.29 % (3427932)Time elapsed: 0.002 s
% 0.26/0.29 % (3427932)Peak memory usage: 10 MB
% 0.26/0.29 % (3427932)Instructions burned: 7 (million)
% 0.26/0.29 % (3427918)Refutation found. Thanks to Tanya!
% 0.26/0.29 % SZS status Theorem for theBenchmark
% 0.26/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.29 % (3427918)------------------------------
% 0.26/0.29 % (3427918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.29 % (3427918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.29 % (3427918)CaDiCaL version: 2.1.3
% 0.26/0.29 % (3427918)Termination reason: Refutation
% 0.26/0.29 % (3427918)Time elapsed: 0.010 s
% 0.26/0.29 % (3427918)Peak memory usage: 13 MB
% 0.26/0.29 % (3427918)Instructions burned: 18 (million)
% 0.26/0.29 % (3427909)Success in time 0.045 s
% 0.26/0.29 % Vampire exiting
%------------------------------------------------------------------------------