%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CSR137^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 07:47:07 AM UTC 2026
% Result : Theorem 0.11s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 9
% Syntax : Number of formulae : 87 ( 15 unt; 0 typ; 6 def)
% Number of atoms : 516 ( 180 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 624 ( 133 ~; 134 |; 12 &; 312 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 106 ( 106 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 30 usr; 13 con; 0-4 aty)
% ( 27 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 283 ( 0 sgn 220 !; 12 ?; 283 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
num: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
domain_THFTYPE_IIiioIiioI: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_2,type,
domain_THFTYPE_IiiioI: $i > $i > $i > $o ).
thf(func_def_4,type,
holdsDuring_THFTYPE_IiooI: $i > $o > $o ).
thf(func_def_5,type,
instance_THFTYPE_IIiioIioI: ( $i > $i > $o ) > $i > $o ).
thf(func_def_6,type,
instance_THFTYPE_IIiooIioI: ( $i > $o > $o ) > $i > $o ).
thf(func_def_7,type,
instance_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_17,type,
likes_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_20,type,
parent_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_21,type,
range_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_22,type,
subclass_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_23,type,
subrelation_THFTYPE_IIioIIioIoI: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_24,type,
subrelation_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_29,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_33,type,
sK0: $i > $i ).
thf(func_def_34,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f4,axiom,
~ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_003) ).
thf(f19,axiom,
likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_018) ).
thf(f45,conjecture,
? [X1: $i > $i > $o,X0: $i > $i > $o,X2: $i] :
( ( X1 @ X2 @ lBill_THFTYPE_i )
& ( X0 @ X2 @ lAnna_THFTYPE_i )
& ~ ! [X4: $i,X3: $i] : ( X0 @ X3 @ X4 )
& ~ ! [X3: $i,X4: $i] : ( X1 @ X3 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f46,negated_conjecture,
~ ? [X1: $i > $i > $o,X0: $i > $i > $o,X2: $i] :
( ( X1 @ X2 @ lBill_THFTYPE_i )
& ( X0 @ X2 @ lAnna_THFTYPE_i )
& ~ ! [X4: $i,X3: $i] : ( X0 @ X3 @ X4 )
& ~ ! [X3: $i,X4: $i] : ( X1 @ X3 @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
thf(f49,plain,
~ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ),
inference(rectify,[],[f4]) ).
thf(f50,plain,
( ( ~ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ) )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f61,plain,
~ ? [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i] :
( ( X0 @ X2 @ lBill_THFTYPE_i )
& ( X1 @ X2 @ lAnna_THFTYPE_i )
& ~ ! [X3: $i,X4: $i] : ( X1 @ X4 @ X3 )
& ~ ! [X5: $i,X6: $i] : ( X0 @ X5 @ X6 ) ),
inference(rectify,[],[f46]) ).
thf(f62,plain,
~ ? [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i] :
( ( ( X1 @ X2 @ lAnna_THFTYPE_i )
= $true )
& ( ( X0 @ X2 @ lBill_THFTYPE_i )
= $true )
& ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) )
& ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
= $true ) ),
inference(fool_elimination,[],[f61]) ).
thf(f89,plain,
likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
inference(rectify,[],[f19]) ).
thf(f90,plain,
( ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i )
= $true ),
inference(fool_elimination,[],[f89]) ).
thf(f139,plain,
! [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i] :
( ( $true
!= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) )
| ( ( X1 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
!= $true ) ),
inference(ennf_transformation,[],[f62]) ).
thf(f168,plain,
( ( ~ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ) )
= $true ),
inference(cnf_transformation,[],[f50]) ).
thf(f171,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
!= $true )
| ( $true
!= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) )
| ( ( X1 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f179,plain,
( ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i )
= $true ),
inference(cnf_transformation,[],[f90]) ).
thf(f213,plain,
( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i )
= $false ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f215,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
| ( $true
!= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) )
| ( ( X1 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f216,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( X1 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( $true
!= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y0 @ Y1 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y0 @ Y1 ) )
@ X3 ) )
| ( ( X1 @ X2 @ lAnna_THFTYPE_i )
!= $true ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y0 @ Y1 ) )
@ X3 ) )
| ( ( X1 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X4: $i] :
( ( ( !! @ $i @ ( X1 @ X3 ) )
= $true )
| ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] : ( X0 @ Y0 @ X4 ) )
= $true )
| ( ( X1 @ X2 @ lAnna_THFTYPE_i )
!= $true ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] : ( X0 @ Y0 @ X4 ) )
= $true )
| ( ( X1 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( X1 @ X3 @ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X6: $i,X4: $i,X5: $i] :
( ( ( X1 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( $true
= ( ^ [Y0: $i] : ( X0 @ Y0 @ X4 )
@ X6 ) )
| ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( X1 @ X3 @ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X6: $i,X4: $i,X5: $i] :
( ( ( X1 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( X1 @ X3 @ X5 )
= $true )
| ( ( X0 @ X6 @ X4 )
= $true ) ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f234,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X0 @ X6 @ X4 )
= $true )
| ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( ^ [Y0: $i,Y1: $i] :
~ ( X7 @ Y0 @ Y1 )
@ X3
@ X5 )
= $true )
| ( ( ^ [Y0: $i,Y1: $i] :
~ ( X7 @ Y0 @ Y1 )
@ X2
@ lAnna_THFTYPE_i )
!= $true ) ),
inference(primitive_instantiation,[],[f222]) ).
thf(f247,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( ~ ( X7 @ X2 @ lAnna_THFTYPE_i ) )
!= $true )
| ( ( X0 @ X6 @ X4 )
= $true )
| ( ( ~ ( X7 @ X3 @ X5 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f234]) ).
thf(f248,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true )
| ( ( ~ ( X7 @ X3 @ X5 ) )
= $true )
| ( ( X0 @ X6 @ X4 )
= $true ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X0 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( X0 @ X6 @ X4 )
= $true )
| ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true ) ),
inference(not_proxy_clausification,[],[f248]) ).
thf(f254,definition,
( spl1_2
<=> ! [X5: $i,X3: $i] : ( X3 != X5 ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f255,plain,
( ! [X3: $i,X5: $i] : ( X3 != X5 )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f254]) ).
thf(f258,definition,
( spl1_3
<=> ! [X5: $i,X3: $i] : ( X3 = X5 ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f259,plain,
( ! [X3: $i,X5: $i] : ( X3 = X5 )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f258]) ).
thf(f264,plain,
( $false
| ~ spl1_2 ),
inference(flex-flex_simplification,[],[f255]) ).
thf(f265,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f264]) ).
thf(f268,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X6
@ X4 )
= $true )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X2
@ lBill_THFTYPE_i )
!= $true )
| ( ( X7 @ X3 @ X5 )
= $false ) ),
inference(primitive_instantiation,[],[f249]) ).
thf(f269,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true )
| ( $true
= ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X6
@ X4 ) )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2
@ lBill_THFTYPE_i )
!= $true ) ),
inference(primitive_instantiation,[],[f249]) ).
thf(f279,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true )
| ( $true
= ( X6 != X4 ) )
| ( ( X2 != lBill_THFTYPE_i )
!= $true ) ),
inference(beta-eta_normalization,[],[f269]) ).
thf(f280,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X6 = X4 )
= $false )
| ( ( X2 != lBill_THFTYPE_i )
!= $true )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true ) ),
inference(not_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X2 != lBill_THFTYPE_i )
!= $true )
| ( X4 != X6 )
| ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true ) ),
inference(equality_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true )
| ( X4 != X6 )
| ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X2 = lBill_THFTYPE_i )
= $true ) ),
inference(not_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( lBill_THFTYPE_i = X2 )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true )
| ( X4 != X6 )
| ( ( X7 @ X3 @ X5 )
= $false ) ),
inference(equality_proxy_clausification,[],[f282]) ).
thf(f287,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X6 = X4 )
= $true )
| ( ( X2 = lBill_THFTYPE_i )
!= $true )
| ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true ) ),
inference(beta-eta_normalization,[],[f268]) ).
thf(f288,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X2 = lBill_THFTYPE_i )
!= $true )
| ( X4 = X6 )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true ) ),
inference(equality_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i > $i > $o,X4: $i,X5: $i] :
( ( X4 = X6 )
| ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true )
| ( lBill_THFTYPE_i != X2 ) ),
inference(equality_proxy_clausification,[],[f288]) ).
thf(f312,plain,
( ! [X0: $i] :
( $true
= ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ X0 ) )
| ~ spl1_3 ),
inference(constrained_superposition,[],[f179,f259]) ).
thf(f355,definition,
( spl1_7
<=> ! [X5: $i,X4: $i > $i > $o,X6: $i,X1: $i] :
( ( ( X4 @ X1 @ lAnna_THFTYPE_i )
= $true )
| ( ( X4 @ X5 @ X6 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
thf(f356,plain,
( ! [X1: $i,X6: $i,X4: $i > $i > $o,X5: $i] :
( ( ( X4 @ X5 @ X6 )
= $false )
| ( ( X4 @ X1 @ lAnna_THFTYPE_i )
= $true ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f355]) ).
thf(f368,plain,
( ! [X0: $i,X1: $i] :
( ( likes_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ~ spl1_3 ),
inference(constrained_superposition,[],[f312,f259]) ).
thf(f388,plain,
( ( $true = $false )
| ~ spl1_3 ),
inference(backward_demodulation,[],[f213,f368]) ).
thf(f389,plain,
( $false
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f388]) ).
thf(f390,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f389]) ).
thf(f406,plain,
( ! [X1: $i,X6: $i,X5: $i] :
( ( ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X5
@ X6 )
= $false )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X1
@ lAnna_THFTYPE_i )
= $true ) )
| ~ spl1_7 ),
inference(primitive_instantiation,[],[f356]) ).
thf(f407,plain,
( ! [X1: $i,X6: $i,X5: $i] :
( ( ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X5
@ X6 )
= $false )
| ( $true
= ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X1
@ lAnna_THFTYPE_i ) ) )
| ~ spl1_7 ),
inference(primitive_instantiation,[],[f356]) ).
thf(f433,plain,
( ! [X1: $i,X6: $i,X5: $i] :
( ( ( X1 != lAnna_THFTYPE_i )
= $true )
| ( ( X5 != X6 )
= $false ) )
| ~ spl1_7 ),
inference(beta-eta_normalization,[],[f407]) ).
thf(f434,plain,
( ! [X1: $i,X6: $i,X5: $i] :
( ( ( X5 != X6 )
= $false )
| ( ( X1 = lAnna_THFTYPE_i )
= $false ) )
| ~ spl1_7 ),
inference(not_proxy_clausification,[],[f433]) ).
thf(f435,plain,
( ! [X1: $i,X6: $i,X5: $i] :
( ( ( X1 = lAnna_THFTYPE_i )
= $false )
| ( $true
= ( X5 = X6 ) ) )
| ~ spl1_7 ),
inference(not_proxy_clausification,[],[f434]) ).
thf(f436,plain,
( ! [X1: $i,X6: $i,X5: $i] :
( ( lAnna_THFTYPE_i != X1 )
| ( $true
= ( X5 = X6 ) ) )
| ~ spl1_7 ),
inference(equality_proxy_clausification,[],[f435]) ).
thf(f477,plain,
( ! [X1: $i,X6: $i,X5: $i] :
( ( ( X5 = X6 )
= $false )
| ( ( X1 = lAnna_THFTYPE_i )
= $true ) )
| ~ spl1_7 ),
inference(beta-eta_normalization,[],[f406]) ).
thf(f478,plain,
( ! [X1: $i,X6: $i,X5: $i] :
( ( X5 != X6 )
| ( ( X1 = lAnna_THFTYPE_i )
= $true ) )
| ~ spl1_7 ),
inference(equality_proxy_clausification,[],[f477]) ).
thf(f479,plain,
( ! [X1: $i,X6: $i,X5: $i] :
( ( lAnna_THFTYPE_i = X1 )
| ( X5 != X6 ) )
| ~ spl1_7 ),
inference(equality_proxy_clausification,[],[f478]) ).
thf(f500,definition,
( spl1_10
<=> ! [X1: $i] : ( lAnna_THFTYPE_i != X1 ) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
thf(f501,plain,
( ! [X1: $i] : ( lAnna_THFTYPE_i != X1 )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f500]) ).
thf(f514,definition,
( spl1_12
<=> ! [X3: $i,X7: $i > $i > $o,X5: $i,X2: $i] :
( ( lBill_THFTYPE_i = X2 )
| ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
thf(f515,plain,
( ! [X2: $i,X3: $i,X7: $i > $i > $o,X5: $i] :
( ( lBill_THFTYPE_i = X2 )
| ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true ) )
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f514]) ).
thf(f516,plain,
( spl1_2
| spl1_12 ),
inference(avatar_split_clause,[],[f283,f514,f254]) ).
thf(f518,definition,
( spl1_13
<=> ! [X3: $i,X7: $i > $i > $o,X5: $i,X2: $i] :
( ( ( X7 @ X3 @ X5 )
= $false )
| ( lBill_THFTYPE_i != X2 )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
thf(f519,plain,
( ! [X2: $i,X3: $i,X7: $i > $i > $o,X5: $i] :
( ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true )
| ( lBill_THFTYPE_i != X2 ) )
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f518]) ).
thf(f520,plain,
( spl1_13
| spl1_3 ),
inference(avatar_split_clause,[],[f289,f258,f518]) ).
thf(f521,plain,
( ! [X2: $i,X3: $i,X7: $i > $i > $o,X5: $i] :
( ( ( X7 @ X3 @ X5 )
= $false )
| ( ( X7 @ X2 @ lAnna_THFTYPE_i )
= $true ) )
| ~ spl1_12
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f519,f515]) ).
thf(f522,plain,
( spl1_7
| ~ spl1_12
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f521,f518,f514,f355]) ).
thf(f528,plain,
( ! [X1: $i,X6: $i,X5: $i] :
( ( X5 = X6 )
| ( lAnna_THFTYPE_i != X1 ) )
| ~ spl1_7 ),
inference(equality_proxy_clausification,[],[f436]) ).
thf(f533,plain,
( spl1_10
| spl1_3
| ~ spl1_7 ),
inference(avatar_split_clause,[],[f528,f355,f258,f500]) ).
thf(f537,plain,
( ! [X6: $i,X5: $i] : ( X5 != X6 )
| ~ spl1_7
| ~ spl1_10 ),
inference(forward_subsumption_resolution,[],[f479,f501]) ).
thf(f538,plain,
( $false
| ~ spl1_7
| ~ spl1_10 ),
inference(flex-flex_simplification,[],[f537]) ).
thf(f539,plain,
( ~ spl1_7
| ~ spl1_10 ),
inference(avatar_contradiction_clause,[],[f538]) ).
cnf(s3,plain,
~ spl1_2,
inference(sat_conversion,[],[f265]) ).
cnf(s9,plain,
~ spl1_3,
inference(sat_conversion,[],[f390]) ).
cnf(s14,plain,
( spl1_2
| spl1_12 ),
inference(sat_conversion,[],[f516]) ).
cnf(s15,plain,
( spl1_3
| spl1_13 ),
inference(sat_conversion,[],[f520]) ).
cnf(s16,plain,
( spl1_7
| ~ spl1_12
| ~ spl1_13 ),
inference(sat_conversion,[],[f522]) ).
cnf(s20,plain,
( spl1_3
| ~ spl1_7
| spl1_10 ),
inference(sat_conversion,[],[f533]) ).
cnf(s23,plain,
( ~ spl1_7
| ~ spl1_10 ),
inference(sat_conversion,[],[f539]) ).
cnf(s24,plain,
spl1_13,
inference(rat,[],[s15,s9]) ).
cnf(s25,plain,
spl1_12,
inference(rat,[],[s14,s3]) ).
cnf(s26,plain,
spl1_7,
inference(rat,[],[s16,s24,s25]) ).
cnf(s27,plain,
~ spl1_10,
inference(rat,[],[s23,s26]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s20,s9,s27,s26]) ).
thf(f540,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CSR137^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n013.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 17:55:36 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.23 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
% 0.11/0.27 % (2443352)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.11/0.27 % (2443372)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4254066958:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.11/0.27 % (2443373)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.11/0.27 % (2443373)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
% 0.11/0.27 % (2443367)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2865996986:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.11/0.27 % (2443368)lrs+10_16_si=on:nwc=1.5:random_seed=1154907158:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.11/0.27 % (2443369)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3517700449:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.11/0.27 % (2443370)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=1470105685: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)
% 0.11/0.27 % (2443371)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3226578528:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.11/0.27 % (2443373)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=643644925:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.11/0.27 % (2443369)Instruction limit reached!
% 0.11/0.27 % (2443369)------------------------------
% 0.11/0.27 % (2443369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.27 % (2443369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.27 % (2443369)CaDiCaL version: 2.1.3
% 0.11/0.27 % (2443369)Termination reason: Instruction limit
% 0.11/0.27 % (2443369)Termination phase: Preprocessing 3
% 0.11/0.27 % (2443369)Time elapsed: 0.002 s
% 0.11/0.27 % (2443369)Peak memory usage: 10 MB
% 0.11/0.27 % (2443369)Instructions burned: 3 (million)
% 0.11/0.27 % (2443372) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2443352-2443372"...
% 0.11/0.27 % (2443372)...printing done.
% 0.11/0.27 % (2443372)Refutation found. Thanks to Tanya!
% 0.11/0.27 % SZS status Theorem for theBenchmark
% 0.11/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (2443372)------------------------------
% 0.21/0.28 % (2443372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2443372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2443372)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2443372)Termination reason: Refutation
% 0.21/0.28 % (2443372)Time elapsed: 0.011 s
% 0.21/0.28 % (2443372)Peak memory usage: 13 MB
% 0.21/0.28 % (2443372)Instructions burned: 32 (million)
% 0.21/0.28 % (2443352)Success in time 0.039 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------