%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO224^5 : 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 : n026.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 08:47:14 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 125 ( 12 unt; 0 typ; 11 def)
% Number of atoms : 1144 ( 260 equ; 0 cnn)
% Maximal formula atoms : 18 ( 9 avg)
% Number of connectives : 896 ( 206 ~; 263 |; 70 &; 331 @)
% ( 12 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 17 con; 0-4 aty)
% Number of variables : 76 ( 4 sgn 60 !; 12 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cLIKE: $i > $i > $o ).
thf(func_def_2,type,
cWRH: $i > $o ).
thf(func_def_3,type,
cW: $i > $o ).
thf(func_def_4,type,
cUNIQUE: $i > $o ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,conjecture,
( ( ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS )
& ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] :
( ( ( cW @ X1 )
& ( cWRH @ X1 ) )
=> ( X0 = X1 ) ) ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( X2 @ cJ )
= ( ? [X0: $i] :
( ( cW @ X0 )
& ( cLIKE @ cJ @ X0 )
& ( cUNIQUE @ X0 )
& ( cWRH @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cLING1) ).
thf(f2,negated_conjecture,
~ ( ( ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS )
& ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] :
( ( ( cW @ X1 )
& ( cWRH @ X1 ) )
=> ( X0 = X1 ) ) ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( X2 @ cJ )
= ( ? [X0: $i] :
( ( cW @ X0 )
& ( cLIKE @ cJ @ X0 )
& ( cUNIQUE @ X0 )
& ( cWRH @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS )
& ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] :
( ( ( cW @ X1 )
& ( cWRH @ X1 ) )
=> ( X0 = X1 ) ) ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( X2 @ cJ )
= ( ? [X3: $i] :
( ( cW @ X3 )
& ( cLIKE @ cJ @ X3 )
& ( cUNIQUE @ X3 )
& ( cWRH @ X3 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( ( cWRH @ X1 )
= $true )
& ( ( cW @ X1 )
= $true ) )
=> ( X0 = X1 ) ) )
& ( ( cW @ cS )
= $true )
& ( ( cWRH @ cS )
= $true )
& ( ( cUNIQUE @ cS )
= $true ) )
=> ? [X2: $i > $o] :
( ( ? [X3: $i] :
( ( ( cUNIQUE @ X3 )
= $true )
& ( $true
= ( cW @ X3 ) )
& ( ( cLIKE @ cJ @ X3 )
= $true )
& ( $true
= ( cWRH @ X3 ) ) )
<=> ( ( X2 @ cJ )
= $true ) )
& ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( ( X2 @ cJ )
= $true )
<~> ? [X3: $i] :
( ( ( cUNIQUE @ X3 )
= $true )
& ( $true
= ( cW @ X3 ) )
& ( ( cLIKE @ cJ @ X3 )
= $true )
& ( $true
= ( cWRH @ X3 ) ) ) ) )
& ! [X0: $i] :
( ! [X1: $i] :
( ( X0 = X1 )
| ( ( cWRH @ X1 )
!= $true )
| ( ( cW @ X1 )
!= $true ) )
| ( ( cUNIQUE @ X0 )
!= $true ) )
& ( ( cW @ cS )
= $true )
& ( ( cWRH @ cS )
= $true )
& ( ( cUNIQUE @ cS )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( ( X2 @ cJ )
= $true )
<~> ? [X3: $i] :
( ( ( cUNIQUE @ X3 )
= $true )
& ( $true
= ( cW @ X3 ) )
& ( ( cLIKE @ cJ @ X3 )
= $true )
& ( $true
= ( cWRH @ X3 ) ) ) ) )
& ( ( cWRH @ cS )
= $true )
& ! [X0: $i] :
( ! [X1: $i] :
( ( X0 = X1 )
| ( ( cW @ X1 )
!= $true )
| ( ( cWRH @ X1 )
!= $true ) )
| ( ( cUNIQUE @ X0 )
!= $true ) )
& ( ( cW @ cS )
= $true )
& ( ( cUNIQUE @ cS )
= $true ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( ! [X3: $i] :
( ( ( cUNIQUE @ X3 )
!= $true )
| ( $true
!= ( cW @ X3 ) )
| ( ( cLIKE @ cJ @ X3 )
!= $true )
| ( $true
!= ( cWRH @ X3 ) ) )
| ( ( X2 @ cJ )
!= $true ) )
& ( ? [X3: $i] :
( ( ( cUNIQUE @ X3 )
= $true )
& ( $true
= ( cW @ X3 ) )
& ( ( cLIKE @ cJ @ X3 )
= $true )
& ( $true
= ( cWRH @ X3 ) ) )
| ( ( X2 @ cJ )
= $true ) ) ) )
& ( ( cWRH @ cS )
= $true )
& ! [X0: $i] :
( ! [X1: $i] :
( ( X0 = X1 )
| ( ( cW @ X1 )
!= $true )
| ( ( cWRH @ X1 )
!= $true ) )
| ( ( cUNIQUE @ X0 )
!= $true ) )
& ( ( cW @ cS )
= $true )
& ( ( cUNIQUE @ cS )
= $true ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i > $o] :
( ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) )
| ( ( ! [X1: $i] :
( ( $true
!= ( cUNIQUE @ X1 ) )
| ( ( cW @ X1 )
!= $true )
| ( $true
!= ( cLIKE @ cJ @ X1 ) )
| ( ( cWRH @ X1 )
!= $true ) )
| ( $true
!= ( X0 @ cJ ) ) )
& ( ? [X2: $i] :
( ( ( cUNIQUE @ X2 )
= $true )
& ( $true
= ( cW @ X2 ) )
& ( $true
= ( cLIKE @ cJ @ X2 ) )
& ( $true
= ( cWRH @ X2 ) ) )
| ( $true
= ( X0 @ cJ ) ) ) ) )
& ( ( cWRH @ cS )
= $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( X3 = X4 )
| ( $true
!= ( cW @ X4 ) )
| ( $true
!= ( cWRH @ X4 ) ) )
| ( ( cUNIQUE @ X3 )
!= $true ) )
& ( ( cW @ cS )
= $true )
& ( ( cUNIQUE @ cS )
= $true ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ! [X0: $i > $o] :
( ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) )
| ( ( ! [X1: $i] :
( ( $true
!= ( cUNIQUE @ X1 ) )
| ( ( cW @ X1 )
!= $true )
| ( $true
!= ( cLIKE @ cJ @ X1 ) )
| ( ( cWRH @ X1 )
!= $true ) )
| ( $true
!= ( X0 @ cJ ) ) )
& ( ( ( $true
= ( cUNIQUE @ sK0 ) )
& ( $true
= ( cW @ sK0 ) )
& ( $true
= ( cLIKE @ cJ @ sK0 ) )
& ( $true
= ( cWRH @ sK0 ) ) )
| ( $true
= ( X0 @ cJ ) ) ) ) )
& ( ( cWRH @ cS )
= $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( X3 = X4 )
| ( $true
!= ( cW @ X4 ) )
| ( $true
!= ( cWRH @ X4 ) ) )
| ( ( cUNIQUE @ X3 )
!= $true ) )
& ( ( cW @ cS )
= $true )
& ( ( cUNIQUE @ cS )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0)],[f8]) ).
thf(f10,plain,
( ( cUNIQUE @ cS )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( cW @ cS )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( cW @ X4 ) )
| ( X3 = X4 )
| ( ( cUNIQUE @ X3 )
!= $true )
| ( $true
!= ( cWRH @ X4 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( cWRH @ cS )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ cJ ) )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) )
| ( $true
= ( cWRH @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
! [X0: $i > $o] :
( ( $true
= ( cLIKE @ cJ @ sK0 ) )
| ( $true
= ( X0 @ cJ ) )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
! [X0: $i > $o] :
( ( $true
= ( cW @ sK0 ) )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) )
| ( $true
= ( X0 @ cJ ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ cJ ) )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) )
| ( $true
= ( cUNIQUE @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cUNIQUE @ X1 ) )
| ( $true
!= ( X0 @ cJ ) )
| ( $true
!= ( cLIKE @ cJ @ X1 ) )
| ( ( cW @ X1 )
!= $true )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) )
| ( ( cWRH @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f21,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ cJ ) )
| ( $true
= ( cUNIQUE @ sK0 ) )
| ( $true
= ( X0 @ cP ) )
| ( ( cLIKE @ cP @ cS )
= $true ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f22,plain,
! [X0: $i > $o] :
( ( ( X0 @ cP )
= $false )
| ( ( cLIKE @ cP @ cS )
= $false )
| ( $true
= ( X0 @ cJ ) )
| ( $true
= ( cUNIQUE @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f23,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ cJ ) )
| ( ( cWRH @ X1 )
!= $true )
| ( ( cLIKE @ cP @ cS )
= $true )
| ( ( cW @ X1 )
!= $true )
| ( $true
!= ( cUNIQUE @ X1 ) )
| ( $true
= ( X0 @ cP ) )
| ( $true
!= ( cLIKE @ cJ @ X1 ) ) ),
inference(xor_proxy_clausification,[],[f18]) ).
thf(f24,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cUNIQUE @ X1 ) )
| ( ( cW @ X1 )
!= $true )
| ( ( X0 @ cP )
= $false )
| ( $true
!= ( cLIKE @ cJ @ X1 ) )
| ( $true
!= ( X0 @ cJ ) )
| ( ( cWRH @ X1 )
!= $true )
| ( ( cLIKE @ cP @ cS )
= $false ) ),
inference(xor_proxy_clausification,[],[f18]) ).
thf(f25,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ cP ) )
| ( $true
= ( X0 @ cJ ) )
| ( ( cLIKE @ cP @ cS )
= $true )
| ( $true
= ( cLIKE @ cJ @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f26,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ cJ ) )
| ( ( X0 @ cP )
= $false )
| ( $true
= ( cLIKE @ cJ @ sK0 ) )
| ( ( cLIKE @ cP @ cS )
= $false ) ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f27,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ cJ ) )
| ( $true
= ( X0 @ cP ) )
| ( ( cLIKE @ cP @ cS )
= $true )
| ( $true
= ( cW @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f28,plain,
! [X0: $i > $o] :
( ( ( cLIKE @ cP @ cS )
= $false )
| ( $true
= ( X0 @ cJ ) )
| ( $true
= ( cW @ sK0 ) )
| ( ( X0 @ cP )
= $false ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f29,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ cP ) )
| ( ( cLIKE @ cP @ cS )
= $true )
| ( $true
= ( X0 @ cJ ) )
| ( $true
= ( cWRH @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f14]) ).
thf(f30,plain,
! [X0: $i > $o] :
( ( $true
= ( cWRH @ sK0 ) )
| ( ( X0 @ cP )
= $false )
| ( $true
= ( X0 @ cJ ) )
| ( ( cLIKE @ cP @ cS )
= $false ) ),
inference(xor_proxy_clausification,[],[f14]) ).
thf(f32,definition,
( spl1_1
<=> ! [X0: $i > $o] :
( ( ( X0 @ cP )
= $false )
| ( $true
= ( X0 @ cJ ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f33,plain,
( ! [X0: $i > $o] :
( ( $true
= ( X0 @ cJ ) )
| ( ( X0 @ cP )
= $false ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,definition,
( spl1_2
<=> ( $true
= ( cUNIQUE @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f37,plain,
( ( $true
= ( cUNIQUE @ sK0 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f39,definition,
( spl1_3
<=> ( ( cLIKE @ cP @ cS )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f41,plain,
( ( ( cLIKE @ cP @ cS )
= $false )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f22,f39,f35,f32]) ).
thf(f44,definition,
( spl1_4
<=> ( ( cLIKE @ cP @ cS )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f45,plain,
( ( ( cLIKE @ cP @ cS )
!= $true )
| spl1_4 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f46,plain,
( ( ( cLIKE @ cP @ cS )
= $true )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f48,definition,
( spl1_5
<=> ! [X0: $i > $o] :
( ( $true
= ( X0 @ cJ ) )
| ( $true
= ( X0 @ cP ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
thf(f49,plain,
( ! [X0: $i > $o] :
( ( $true
= ( X0 @ cJ ) )
| ( $true
= ( X0 @ cP ) ) )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f50,plain,
( spl1_2
| spl1_4
| spl1_5 ),
inference(avatar_split_clause,[],[f21,f48,f44,f35]) ).
thf(f52,definition,
( spl1_6
<=> ! [X1: $i] :
( ( $true
!= ( cUNIQUE @ X1 ) )
| ( ( cWRH @ X1 )
!= $true )
| ( $true
!= ( cLIKE @ cJ @ X1 ) )
| ( ( cW @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
thf(f53,plain,
( ! [X1: $i] :
( ( $true
!= ( cLIKE @ cJ @ X1 ) )
| ( ( cW @ X1 )
!= $true )
| ( $true
!= ( cUNIQUE @ X1 ) )
| ( ( cWRH @ X1 )
!= $true ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f55,definition,
( spl1_7
<=> ! [X0: $i > $o] :
( ( ( X0 @ cP )
= $false )
| ( $true
!= ( X0 @ cJ ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
thf(f56,plain,
( ! [X0: $i > $o] :
( ( $true
!= ( X0 @ cJ ) )
| ( ( X0 @ cP )
= $false ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f57,plain,
( spl1_6
| spl1_3
| spl1_7 ),
inference(avatar_split_clause,[],[f24,f55,f39,f52]) ).
thf(f59,definition,
( spl1_8
<=> ! [X0: $i > $o] :
( ( $true
!= ( X0 @ cJ ) )
| ( $true
= ( X0 @ cP ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
thf(f60,plain,
( ! [X0: $i > $o] :
( ( $true
!= ( X0 @ cJ ) )
| ( $true
= ( X0 @ cP ) ) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f61,plain,
( spl1_6
| spl1_8
| spl1_4 ),
inference(avatar_split_clause,[],[f23,f44,f59,f52]) ).
thf(f63,definition,
( spl1_9
<=> ( $true
= ( cLIKE @ cJ @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
thf(f65,plain,
( ( $true
= ( cLIKE @ cJ @ sK0 ) )
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f66,plain,
( spl1_3
| spl1_1
| spl1_9 ),
inference(avatar_split_clause,[],[f26,f63,f32,f39]) ).
thf(f67,plain,
( spl1_9
| spl1_4
| spl1_5 ),
inference(avatar_split_clause,[],[f25,f48,f44,f63]) ).
thf(f69,definition,
( spl1_10
<=> ( $true
= ( cW @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
thf(f71,plain,
( ( $true
= ( cW @ sK0 ) )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f72,plain,
( spl1_10
| spl1_1
| spl1_3 ),
inference(avatar_split_clause,[],[f28,f39,f32,f69]) ).
thf(f73,plain,
( spl1_4
| spl1_5
| spl1_10 ),
inference(avatar_split_clause,[],[f27,f69,f48,f44]) ).
thf(f75,definition,
( spl1_11
<=> ( $true
= ( cWRH @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
thf(f77,plain,
( ( $true
= ( cWRH @ sK0 ) )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f75]) ).
thf(f78,plain,
( spl1_1
| spl1_3
| spl1_11 ),
inference(avatar_split_clause,[],[f30,f75,f39,f32]) ).
thf(f79,plain,
( spl1_4
| spl1_5
| spl1_11 ),
inference(avatar_split_clause,[],[f29,f75,f48,f44]) ).
thf(f80,plain,
( ( $true = $false )
| ~ spl1_3
| ~ spl1_4 ),
inference(forward_demodulation,[],[f41,f46]) ).
thf(f81,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f82,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f81]) ).
thf(f85,plain,
( ( $true
= ( ^ [Y0: $i] : $false
@ cP ) )
| ( $true
= ( ^ [Y0: $i] : $false
@ cJ ) )
| ~ spl1_5 ),
inference(primitive_instantiation,[],[f49]) ).
thf(f92,plain,
( ( $true = $false )
| ( $true = $false )
| ~ spl1_5 ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f93,plain,
( ( $true = $false )
| ~ spl1_5 ),
inference(duplicate_literal_removal,[],[f92]) ).
thf(f94,plain,
( $false
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f95,plain,
~ spl1_5,
inference(avatar_contradiction_clause,[],[f94]) ).
thf(f98,plain,
( ( cP = cJ )
| ~ spl1_1 ),
inference(leibniz_equality_elimination,[],[f33]) ).
thf(f121,plain,
! [X0: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ( ( cWRH @ cS )
!= $true )
| ( cS = X0 )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f12,f11]) ).
thf(f124,plain,
! [X0: $i] :
( ( cS = X0 )
| ( ( cUNIQUE @ X0 )
!= $true )
| ( ( cWRH @ cS )
!= $true ) ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f126,plain,
! [X0: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ( cS = X0 ) ),
inference(forward_subsumption_resolution,[],[f124,f13]) ).
thf(f155,plain,
( ! [X0: $i] :
( ( $true
!= ( cLIKE @ cP @ X0 ) )
| ( ( cUNIQUE @ X0 )
!= $true )
| ( ( cW @ X0 )
!= $true )
| ( ( cWRH @ X0 )
!= $true ) )
| ~ spl1_1
| ~ spl1_6 ),
inference(constrained_superposition,[],[f53,f98]) ).
thf(f160,plain,
( ( ( cUNIQUE @ cS )
!= $true )
| ( ( cWRH @ cS )
!= $true )
| ( ( cW @ cS )
!= $true )
| ( $true != $true )
| ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(constrained_superposition,[],[f155,f46]) ).
thf(f164,plain,
( ( ( cWRH @ cS )
!= $true )
| ( ( cW @ cS )
!= $true )
| ( ( cUNIQUE @ cS )
!= $true )
| ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(trivial_inequality_removal,[],[f160]) ).
thf(f166,plain,
( ( ( cUNIQUE @ cS )
!= $true )
| ( ( cW @ cS )
!= $true )
| ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(forward_subsumption_resolution,[],[f164,f13]) ).
thf(f167,plain,
( ( ( cW @ cS )
!= $true )
| ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(forward_subsumption_resolution,[],[f166,f10]) ).
thf(f168,plain,
( $false
| ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(forward_subsumption_resolution,[],[f167,f11]) ).
thf(f169,plain,
( ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f168]) ).
thf(f170,plain,
( ( $true != $true )
| ( cS = sK0 )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f126,f37]) ).
thf(f171,plain,
( ( cS = sK0 )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f170]) ).
thf(f180,plain,
( ( $true
!= ( cUNIQUE @ sK0 ) )
| ( $true
!= ( cWRH @ sK0 ) )
| ( $true != $true )
| ( $true
!= ( cW @ sK0 ) )
| ~ spl1_6
| ~ spl1_9 ),
inference(constrained_superposition,[],[f53,f65]) ).
thf(f181,plain,
( ( $true
!= ( cUNIQUE @ sK0 ) )
| ( $true
!= ( cW @ sK0 ) )
| ( $true
!= ( cWRH @ sK0 ) )
| ~ spl1_6
| ~ spl1_9 ),
inference(trivial_inequality_removal,[],[f180]) ).
thf(f182,plain,
( ( $true
!= ( cWRH @ sK0 ) )
| ( $true
!= ( cW @ sK0 ) )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9 ),
inference(forward_subsumption_resolution,[],[f181,f37]) ).
thf(f183,plain,
( ( $true
!= ( cW @ sK0 ) )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_11 ),
inference(forward_subsumption_resolution,[],[f182,f77]) ).
thf(f184,plain,
( $false
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_10
| ~ spl1_11 ),
inference(forward_subsumption_resolution,[],[f183,f71]) ).
thf(f185,plain,
( ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_10
| ~ spl1_11 ),
inference(avatar_contradiction_clause,[],[f184]) ).
thf(f189,plain,
( ( $true
!= ( ^ [Y0: $i] : $true
@ cJ ) )
| ( ( ^ [Y0: $i] : $true
@ cP )
= $false )
| ~ spl1_7 ),
inference(imitation,[],[f56]) ).
thf(f194,plain,
( ( $true = $false )
| ( $true != $true )
| ~ spl1_7 ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f195,plain,
( $false
| ~ spl1_7 ),
inference(trivial_inequality_removal,[],[f194]) ).
thf(f196,plain,
~ spl1_7,
inference(avatar_contradiction_clause,[],[f195]) ).
thf(f203,plain,
( ( cP = cJ )
| ~ spl1_8 ),
inference(leibniz_equality_elimination,[],[f60]) ).
thf(f217,plain,
( ( $true
= ( cLIKE @ cP @ sK0 ) )
| ~ spl1_8
| ~ spl1_9 ),
inference(constrained_superposition,[],[f65,f203]) ).
thf(f218,plain,
( ( ( cLIKE @ cP @ cS )
= $true )
| ~ spl1_2
| ~ spl1_8
| ~ spl1_9 ),
inference(forward_demodulation,[],[f217,f171]) ).
thf(f221,plain,
( $false
| ~ spl1_2
| spl1_4
| ~ spl1_8
| ~ spl1_9 ),
inference(forward_subsumption_resolution,[],[f218,f45]) ).
thf(f222,plain,
( ~ spl1_2
| spl1_4
| ~ spl1_8
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[],[f221]) ).
cnf(s1,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl1_2
| spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f50]) ).
cnf(s3,plain,
( spl1_3
| spl1_6
| spl1_7 ),
inference(sat_conversion,[],[f57]) ).
cnf(s4,plain,
( spl1_4
| spl1_6
| spl1_8 ),
inference(sat_conversion,[],[f61]) ).
cnf(s5,plain,
( spl1_1
| spl1_3
| spl1_9 ),
inference(sat_conversion,[],[f66]) ).
cnf(s6,plain,
( spl1_4
| spl1_5
| spl1_9 ),
inference(sat_conversion,[],[f67]) ).
cnf(s7,plain,
( spl1_1
| spl1_3
| spl1_10 ),
inference(sat_conversion,[],[f72]) ).
cnf(s8,plain,
( spl1_4
| spl1_5
| spl1_10 ),
inference(sat_conversion,[],[f73]) ).
cnf(s9,plain,
( spl1_1
| spl1_3
| spl1_11 ),
inference(sat_conversion,[],[f78]) ).
cnf(s10,plain,
( spl1_4
| spl1_5
| spl1_11 ),
inference(sat_conversion,[],[f79]) ).
cnf(s11,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f82]) ).
cnf(s12,plain,
~ spl1_5,
inference(sat_conversion,[],[f95]) ).
cnf(s15,plain,
( ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(sat_conversion,[],[f169]) ).
cnf(s16,plain,
( ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_10
| ~ spl1_11 ),
inference(sat_conversion,[],[f185]) ).
cnf(s18,plain,
~ spl1_7,
inference(sat_conversion,[],[f196]) ).
cnf(s21,plain,
( ~ spl1_2
| spl1_4
| ~ spl1_8
| ~ spl1_9 ),
inference(sat_conversion,[],[f222]) ).
cnf(s22,plain,
( spl1_4
| spl1_11 ),
inference(rat,[],[s10,s12]) ).
cnf(s23,plain,
( spl1_4
| spl1_10 ),
inference(rat,[],[s8,s12]) ).
cnf(s24,plain,
( spl1_4
| spl1_9 ),
inference(rat,[],[s6,s12]) ).
cnf(s25,plain,
( spl1_3
| spl1_6 ),
inference(rat,[],[s3,s18]) ).
cnf(s26,plain,
( spl1_2
| spl1_4 ),
inference(rat,[],[s2,s12]) ).
cnf(s27,plain,
( spl1_2
| spl1_1 ),
inference(rat,[],[s11,s1,s26]) ).
cnf(s28,plain,
( spl1_4
| ~ spl1_2 ),
inference(rat,[],[s4,s16,s21,s24,s23,s22]) ).
cnf(s29,plain,
spl1_1,
inference(rat,[],[s16,s5,s7,s9,s25,s11,s28,s27]) ).
cnf(s30,plain,
~ spl1_4,
inference(rat,[],[s25,s15,s11,s29]) ).
cnf(s34,plain,
spl1_2,
inference(rat,[],[s26,s30]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s28,s34,s30]) ).
thf(f223,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO224^5 : 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 : n026.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 16:42:58 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 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
% 0.22/0.27 % (845084)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (845089)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1025838855:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.27 % (845089) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-845084-845089"...
% 0.22/0.27 % (845089)...printing done.
% 0.22/0.27 % (845095)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.27 % (845095)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
% 0.22/0.27 % (845089)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (845089)------------------------------
% 0.22/0.27 % (845089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (845089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (845089)CaDiCaL version: 2.1.3
% 0.22/0.27 % (845089)Termination reason: Refutation
% 0.22/0.27 % (845089)Time elapsed: 0.004 s
% 0.22/0.27 % (845089)Peak memory usage: 13 MB
% 0.22/0.27 % (845089)Instructions burned: 11 (million)
% 0.22/0.27 % (845084)Success in time 0.019 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------