%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU851^5 : 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 : n011.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 08:31:48 AM UTC 2026
% Result : Theorem 0.11s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 77 ( 16 unt; 0 typ; 5 def)
% Number of atoms : 556 ( 124 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 698 ( 143 ~; 177 |; 97 &; 276 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 38 ( 0 sgn 8 !; 4 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vOR: $o > $o > $o ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) ) ) )
= ( ^ [X2: a] :
( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM42_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) ) ) )
= ( ^ [X2: a] :
( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) ) ) )
= ( ^ [X3: a] :
( ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) )
| ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: a > $o,X0: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: a > $o,X0: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,definition,
( spl2_1
<=> ( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f13,plain,
( ( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f11]) ).
thf(f14,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f8,f11]) ).
thf(f15,plain,
( ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK3 ) )
| spl2_1 ),
inference(negative_extensionality,[],[f13]) ).
thf(f16,plain,
( ( $true
= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
@ sK3 ) )
| spl2_1 ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK3 )
= $false )
| ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
@ sK3 )
= $false )
| spl2_1 ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f18,plain,
( ( ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $false )
| ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| spl2_1 ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| spl2_1 ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| spl2_1 ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| spl2_1 ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| spl2_1 ),
inference(or_proxy_clausification,[],[f21]) ).
thf(f27,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| spl2_1 ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f28,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| spl2_1 ),
inference(not_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| spl2_1 ),
inference(duplicate_literal_removal,[],[f28]) ).
thf(f31,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| spl2_1 ),
inference(or_proxy_clausification,[],[f19]) ).
thf(f32,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| spl2_1 ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| spl2_1 ),
inference(not_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| spl2_1 ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f35,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| spl2_1 ),
inference(not_proxy_clausification,[],[f34]) ).
thf(f36,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| spl2_1 ),
inference(duplicate_literal_removal,[],[f35]) ).
thf(f41,plain,
( ( ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( $true
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| spl2_1 ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f42,plain,
( ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| spl2_1 ),
inference(or_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| spl2_1 ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| spl2_1 ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f45,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| spl2_1 ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f61,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| spl2_1 ),
inference(not_proxy_clausification,[],[f45]) ).
thf(f62,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( ( sK0 @ sK3 )
= $false )
| spl2_1 ),
inference(not_proxy_clausification,[],[f61]) ).
thf(f63,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| spl2_1 ),
inference(or_proxy_clausification,[],[f62]) ).
thf(f65,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| spl2_1 ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f67,plain,
( ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $false )
| spl2_1 ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| spl2_1 ),
inference(not_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| spl2_1 ),
inference(not_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| spl2_1 ),
inference(duplicate_literal_removal,[],[f69]) ).
thf(f78,plain,
( ( $true
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| spl2_1 ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f79,plain,
( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| spl2_1 ),
inference(or_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| spl2_1 ),
inference(and_proxy_clausification,[],[f79]) ).
thf(f87,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| spl2_1 ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f91,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| spl2_1 ),
inference(duplicate_literal_removal,[],[f87]) ).
thf(f108,definition,
( spl2_2
<=> ( ( sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f110,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f108]) ).
thf(f112,definition,
( spl2_3
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f114,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f112]) ).
thf(f115,plain,
( spl2_2
| spl2_3
| spl2_1 ),
inference(avatar_split_clause,[],[f29,f11,f112,f108]) ).
thf(f117,definition,
( spl2_4
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f119,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f121,definition,
( spl2_5
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f123,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f121]) ).
thf(f124,plain,
( spl2_4
| spl2_5
| spl2_1 ),
inference(avatar_split_clause,[],[f36,f11,f121,f117]) ).
thf(f125,plain,
( spl2_2
| spl2_5
| spl2_1 ),
inference(avatar_split_clause,[],[f70,f11,f121,f108]) ).
thf(f126,plain,
( spl2_3
| spl2_4
| spl2_1 ),
inference(avatar_split_clause,[],[f91,f11,f117,f112]) ).
thf(f128,plain,
( ( $true = $false )
| ~ spl2_3
| ~ spl2_5 ),
inference(superposition,[],[f114,f123]) ).
thf(f129,plain,
( $false
| ~ spl2_3
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f128]) ).
thf(f130,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f129]) ).
thf(f134,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_demodulation,[],[f119,f110]) ).
thf(f135,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f136,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f135]) ).
cnf(s1,plain,
~ spl2_1,
inference(sat_conversion,[],[f14]) ).
cnf(s2,plain,
( spl2_1
| spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f115]) ).
cnf(s3,plain,
( spl2_1
| spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f124]) ).
cnf(s4,plain,
( spl2_1
| spl2_2
| spl2_5 ),
inference(sat_conversion,[],[f125]) ).
cnf(s5,plain,
( spl2_1
| spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f126]) ).
cnf(s6,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f130]) ).
cnf(s9,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f136]) ).
cnf(s10,plain,
spl2_2,
inference(rat,[],[s6,s2,s4,s1]) ).
cnf(s11,plain,
~ spl2_4,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
spl2_5,
inference(rat,[],[s3,s1,s11]) ).
cnf(s13,plain,
spl2_3,
inference(rat,[],[s5,s1,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s6,s12,s13]) ).
thf(f137,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU851^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n011.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 14:40:01 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.24 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
% 0.11/0.28 % (174125)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.11/0.28 % (174133)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=4050608425: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)
% 0.11/0.28 % (174133) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-174125-174133"...
% 0.11/0.28 % (174133)...printing done.
% 0.11/0.28 % (174133)Refutation found. Thanks to Tanya!
% 0.11/0.28 % SZS status Theorem for theBenchmark
% 0.11/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (174133)------------------------------
% 0.22/0.29 % (174133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (174133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (174133)CaDiCaL version: 2.1.3
% 0.22/0.29 % (174133)Termination reason: Refutation
% 0.22/0.29 % (174133)Time elapsed: 0.003 s
% 0.22/0.29 % (174133)Peak memory usage: 12 MB
% 0.22/0.29 % (174133)Instructions burned: 6 (million)
% 0.22/0.29 % (174125)Success in time 0.032 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------