%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO403^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:36 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 43 unt; 0 typ; 2 def)
% Number of atoms : 424 ( 76 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 500 ( 68 ~; 88 |; 0 &; 316 @)
% ( 2 <=>; 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 : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 54 usr; 7 con; 0-4 aty)
% ( 26 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 117 ( 0 sgn 21 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_k: $i > $i > $o ).
thf(func_def_33,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_k: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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,
vAND: $o > $o > $o ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_k @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_k ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^1.ax',mbox_k) ).
thf(f34,conjecture,
mvalid @ ( mimplies @ ( mor @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) @ ( mbox_k @ ( mor @ p @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f35,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mor @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) @ ( mbox_k @ ( mor @ p @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f54,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f60,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f61,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f62,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f63,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f68,plain,
~ ( mvalid @ ( mimplies @ ( mor @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) @ ( mbox_k @ ( mor @ p @ q ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f69,plain,
( ( mvalid @ ( mimplies @ ( mor @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) @ ( mbox_k @ ( mor @ p @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f68]) ).
thf(f88,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_k @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_k ),
inference(rectify,[],[f32]) ).
thf(f89,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f88]) ).
thf(f90,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f91,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( ( mvalid @ ( mimplies @ ( mor @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) @ ( mbox_k @ ( mor @ p @ q ) ) ) )
!= $true ),
inference(flattening,[],[f69]) ).
thf(f99,plain,
( ( mvalid @ ( mimplies @ ( mor @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) @ ( mbox_k @ ( mor @ p @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f101,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f115,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f117,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f119,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f126,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f130,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,[],[f117,f126,f115]) ).
thf(f139,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 > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ p
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f99,f119,f130,f126,f101,f101,f101,f126]) ).
thf(f140,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f145,plain,
( ( ^ [Y0: $i] :
( ( q @ Y0 )
| ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( ( q @ sK1 )
| ( p @ sK1 )
| ~ ( rel_k @ sK0 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
( $false
= ( ~ ( rel_k @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( $false
= ( ( q @ sK1 )
| ( p @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( ( p @ sK1 )
= $false ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( q @ sK1 )
= $false ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( $true
= ( rel_k @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f152,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f143]) ).
thf(f153,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( q @ X2 )
| ~ ( rel_k @ sK0 @ X2 ) ) )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) ) )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_k @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( p @ X1 )
= $true )
| ( ( rel_k @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f162,definition,
( spl2_1
<=> ! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_k @ sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f163,plain,
( ! [X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f162]) ).
thf(f165,definition,
( spl2_2
<=> ! [X2: $i] :
( ( ( rel_k @ sK0 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f166,plain,
( ! [X2: $i] :
( ( ( rel_k @ sK0 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f167,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f160,f165,f162]) ).
thf(f169,plain,
( ( $true = $false )
| ( ( q @ sK1 )
= $true )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f166,f151]) ).
thf(f171,plain,
( ( ( q @ sK1 )
= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f169]) ).
thf(f175,plain,
( ( $true = $false )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f171,f150]) ).
thf(f176,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f175]) ).
thf(f177,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f176]) ).
thf(f178,plain,
( ( $true
= ( p @ sK1 ) )
| ( $true = $false )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f163,f151]) ).
thf(f181,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f178]) ).
thf(f185,plain,
( ( $true = $false )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f181,f149]) ).
thf(f186,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f185]) ).
thf(f187,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f186]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f167]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f177]) ).
cnf(s5,plain,
~ spl2_1,
inference(sat_conversion,[],[f187]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f188,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO403^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n005.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 16:50:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.30 % (1913300)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (1913327)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.30 % (1913327)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.30 % (1913322)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4201740744:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.30 % (1913324)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3465023277:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (1913321)lrs+10_16_si=on:nwc=1.5:random_seed=3709918930:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.30 % (1913320)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3298466338:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (1913323)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=956781362:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.30 % (1913327)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=3757702986:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (1913326)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3512415605:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.30 % (1913322)Instruction limit reached!
% 0.20/0.30 % (1913322)------------------------------
% 0.20/0.30 % (1913322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1913322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1913322)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1913322)Termination reason: Instruction limit
% 0.20/0.30 % (1913322)Termination phase: Property scanning
% 0.20/0.30 % (1913322)Time elapsed: 0.002 s
% 0.20/0.30 % (1913322)Peak memory usage: 10 MB
% 0.20/0.30 % (1913322)Instructions burned: 4 (million)
% 0.20/0.30 % (1913321) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1913300-1913321"...
% 0.20/0.30 % (1913320) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1913300-1913320"...
% 0.20/0.30 % (1913326) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1913300-1913326"...
% 0.20/0.30 % (1913327) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1913300-1913327"...
% 0.20/0.30 % (1913321)...printing done.
% 0.20/0.30 % (1913320)...printing done.
% 0.20/0.30 % (1913326)...printing done.
% 0.20/0.30 % (1913321)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (1913321)------------------------------
% 0.20/0.30 % (1913321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1913321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1913321)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1913321)Termination reason: Refutation
% 0.20/0.30 % (1913321)Time elapsed: 0.007 s
% 0.20/0.30 % (1913321)Peak memory usage: 13 MB
% 0.20/0.30 % (1913321)Instructions burned: 13 (million)
% 0.20/0.30 % (1913300)Success in time 0.056 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------