%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV387^5 : 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 : n002.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 08:38:33 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 102 ( 18 unt; 0 typ; 6 def)
% Number of atoms : 927 ( 214 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 1129 ( 166 ~; 224 |; 232 &; 501 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 12 !; 3 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vAND: $o > $o > $o ).
thf(func_def_2,type,
vOR: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vNOT: $o > $o ).
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_8,type,
sK2: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(f1,conjecture,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) )
= ( ^ [X4: a] :
( ( ~ ( ( X1 @ X4 )
& ( X0 @ X4 ) )
& ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( ( X0 @ X4 )
& ( X2 @ X4 ) )
& ( X1 @ X4 )
& ( X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM44_pme) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) )
= ( ^ [X4: a] :
( ( ~ ( ( X1 @ X4 )
& ( X0 @ X4 ) )
& ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( ( X0 @ X4 )
& ( X2 @ X4 ) )
& ( X1 @ X4 )
& ( X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( ( ~ ( X0 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X0 @ X3 ) ) ) ) )
= ( ^ [X4: a] :
( ( ~ ( ( X2 @ X4 )
& ( X1 @ X4 ) )
& ( X0 @ X4 )
& ( X1 @ X4 ) )
| ( ~ ( ( X1 @ X4 )
& ( X0 @ X4 ) )
& ( X2 @ X4 )
& ( X1 @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X2 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
| ( ( X1 @ Y0 )
& ( X0 @ Y0 )
& ~ ( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) ) )
= ( ^ [Y0: a] :
( ( ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
& ( X1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X2 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
| ( ( X1 @ Y0 )
& ( X0 @ Y0 )
& ~ ( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
& ( X1 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ( sK1 @ Y0 ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
@ sK3 )
= $true )
| ( ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ( sK1 @ Y0 ) )
@ sK3 )
= $true ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f12,plain,
( ( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
@ sK3 )
= $false )
| ( ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ( sK1 @ Y0 ) )
@ sK3 )
= $false ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f13,plain,
( ( $false
= ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f14,plain,
( ( $false
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f13]) ).
thf(f16,plain,
( ( ( ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $false )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f19]) ).
thf(f31,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f32,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f33]) ).
thf(f38,plain,
( ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f40,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f38]) ).
thf(f41,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f43]) ).
thf(f45,plain,
( ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f44]) ).
thf(f46,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f49,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f46]) ).
thf(f59,plain,
( ( $true
= ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f60,plain,
( ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) )
| ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f59]) ).
thf(f61,plain,
( ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) )
| ( ( ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f60]) ).
thf(f62,plain,
( ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f60]) ).
thf(f64,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f62]) ).
thf(f65,plain,
( ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f64]) ).
thf(f66,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f64]) ).
thf(f68,plain,
( ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f66]) ).
thf(f69,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f86,plain,
( ( sK1 @ sK3 )
= $true ),
inference(duplicate_literal_removal,[],[f69]) ).
thf(f102,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f121,plain,
( ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f122,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f121]) ).
thf(f124,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f122]) ).
thf(f126,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f124]) ).
thf(f127,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f126]) ).
thf(f175,plain,
( ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ( sK1 @ sK3 ) ) )
| ( ( ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true )
| ( ( ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f61]) ).
thf(f218,plain,
( ( ( ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true )
| ( ( ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f175]) ).
thf(f219,plain,
( ( ( ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true )
| ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( ( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f221]) ).
thf(f233,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f222]) ).
thf(f234,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f236,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f239,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f240,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f239]) ).
thf(f247,definition,
( spl4_1
<=> ( ( sK2 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f249,plain,
( ( ( sK2 @ sK3 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f247]) ).
thf(f251,definition,
( spl4_2
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f253,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f255,definition,
( spl4_3
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f257,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f258,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f34,f255,f251,f247]) ).
thf(f260,definition,
( spl4_4
<=> ( ( sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f262,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f264,definition,
( spl4_5
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f266,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f267,plain,
( spl4_4
| spl4_2
| spl4_5 ),
inference(avatar_split_clause,[],[f49,f264,f251,f260]) ).
thf(f269,definition,
( spl4_6
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f271,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f274,plain,
spl4_6,
inference(avatar_split_clause,[],[f86,f269]) ).
thf(f279,plain,
( spl4_3
| spl4_5 ),
inference(avatar_split_clause,[],[f127,f264,f255]) ).
thf(f281,plain,
( spl4_4
| spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f240,f247,f251,f260]) ).
thf(f283,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f253,f271]) ).
thf(f286,plain,
( $false
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f283]) ).
thf(f287,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f286]) ).
thf(f289,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_4 ),
inference(constrained_superposition,[],[f262,f257]) ).
thf(f291,plain,
( $false
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f289]) ).
thf(f292,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f291]) ).
thf(f296,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_5 ),
inference(constrained_superposition,[],[f266,f249]) ).
thf(f300,plain,
( $false
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f301,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f300]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f258]) ).
cnf(s2,plain,
( spl4_2
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f267]) ).
cnf(s5,plain,
spl4_6,
inference(sat_conversion,[],[f274]) ).
cnf(s10,plain,
( spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f279]) ).
cnf(s12,plain,
( spl4_1
| spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f281]) ).
cnf(s14,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(sat_conversion,[],[f287]) ).
cnf(s15,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f292]) ).
cnf(s18,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f301]) ).
cnf(s19,plain,
~ spl4_2,
inference(rat,[],[s14,s5]) ).
cnf(s20,plain,
( spl4_4
| spl4_5 ),
inference(rat,[],[s2,s19]) ).
cnf(s21,plain,
( spl4_1
| spl4_3 ),
inference(rat,[],[s1,s19]) ).
cnf(s22,plain,
spl4_1,
inference(rat,[],[s15,s21,s12,s19]) ).
cnf(s23,plain,
~ spl4_5,
inference(rat,[],[s18,s22]) ).
cnf(s24,plain,
spl4_3,
inference(rat,[],[s10,s23]) ).
cnf(s25,plain,
spl4_4,
inference(rat,[],[s20,s23]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s15,s25,s24]) ).
thf(f302,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV387^5 : 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 : n002.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 15:46:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 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
% 0.21/0.27 % (1450937)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (1450943)lrs+10_16_si=on:nwc=1.5:random_seed=2297716778:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (1450943) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1450937-1450943"...
% 0.21/0.27 % (1450943)...printing done.
% 0.21/0.27 % (1450943)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (1450943)------------------------------
% 0.21/0.27 % (1450943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1450943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1450943)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1450943)Termination reason: Refutation
% 0.21/0.27 % (1450943)Time elapsed: 0.004 s
% 0.21/0.27 % (1450943)Peak memory usage: 13 MB
% 0.21/0.27 % (1450943)Instructions burned: 10 (million)
% 0.21/0.27 % (1450937)Success in time 0.028 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------