%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET601^5 : 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 : n001.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 08:23:20 AM UTC 2026
% Result : Theorem 0.24s 0.36s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 104 ( 17 unt; 0 typ; 6 def)
% Number of atoms : 898 ( 214 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 962 ( 41 ~; 302 |; 130 &; 483 @)
% ( 6 <=>; 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 : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 40 ( 0 sgn 12 !; 6 ?; 40 :)
% 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,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_7,type,
sK2: a > $o ).
thf(func_def_10,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X4: a] :
( ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( ( X1 @ X4 )
| ( X0 @ X4 ) )
& ( ( X2 @ X4 )
| ( X0 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ( X0 @ X3 ) )
| ( ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ( X0 @ X3 )
& ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_72_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X4: a] :
( ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( ( X1 @ X4 )
| ( X0 @ X4 ) )
& ( ( X2 @ X4 )
| ( X0 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ( X0 @ X3 ) )
| ( ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ( X0 @ X3 )
& ( X1 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( X2 @ X3 )
| ( X1 @ X3 ) )
& ( ( X1 @ X3 )
| ( X0 @ X3 ) )
& ( ( X2 @ X3 )
| ( X0 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ( X2 @ X4 )
& ( X1 @ X4 ) )
| ( ( X0 @ X4 )
& ( X1 @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
| ( X2 @ Y0 ) )
& ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
| ( X2 @ Y0 ) )
& ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( ( X1 @ Y0 )
| ( X2 @ Y0 ) )
& ( ( X2 @ Y0 )
| ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f12,plain,
( ( $true
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f13,plain,
( ( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) )
@ sK3 )
= $false )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( ( $false
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f17,plain,
( ( ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
= $false )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f24,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f24]) ).
thf(f29,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f30,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f29]) ).
thf(f49,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f50,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f51,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
= $false )
| ( $false
= ( sK2 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f50]) ).
thf(f63,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f51]) ).
thf(f69,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f63]) ).
thf(f72,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f69]) ).
thf(f73,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f74,plain,
( ( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f75]) ).
thf(f89,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f76]) ).
thf(f91,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f89]) ).
thf(f92,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f91]) ).
thf(f98,plain,
( ( $true
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f99,plain,
( ( $true
= ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f99]) ).
thf(f101,plain,
( ( $true
= ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f99]) ).
thf(f102,plain,
( ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f101]) ).
thf(f103,plain,
( ( $true
= ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f101]) ).
thf(f104,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f103]) ).
thf(f105,plain,
( ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f104]) ).
thf(f106,plain,
( ( $true
= ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f105]) ).
thf(f118,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f106]) ).
thf(f125,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f118]) ).
thf(f126,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f125]) ).
thf(f128,plain,
( ( $true
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f102]) ).
thf(f129,plain,
( ( $true
= ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f128]) ).
thf(f131,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f129]) ).
thf(f132,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f131]) ).
thf(f139,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f132]) ).
thf(f140,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f139]) ).
thf(f152,plain,
( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f100]) ).
thf(f167,plain,
( ( $true
= ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f168,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f170,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f170]) ).
thf(f174,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f171]) ).
thf(f180,definition,
( spl4_1
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f182,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f180]) ).
thf(f184,definition,
( spl4_2
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f186,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f184]) ).
thf(f188,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f30,f180,f184]) ).
thf(f190,definition,
( spl4_3
<=> ( ( sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f192,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f190]) ).
thf(f206,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f72,f190,f180]) ).
thf(f211,plain,
( spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f92,f190,f184]) ).
thf(f216,definition,
( spl4_4
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f218,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f216]) ).
thf(f220,definition,
( spl4_5
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f222,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f224,definition,
( spl4_6
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f226,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f233,plain,
( spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f126,f220,f224]) ).
thf(f237,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f140,f216,f220]) ).
thf(f248,plain,
( spl4_6
| spl4_4 ),
inference(avatar_split_clause,[],[f174,f216,f224]) ).
thf(f251,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_demodulation,[],[f222,f186]) ).
thf(f252,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f251]) ).
thf(f253,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f252]) ).
thf(f255,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4 ),
inference(constrained_superposition,[],[f218,f182]) ).
thf(f259,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f255]) ).
thf(f260,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f259]) ).
thf(f262,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f226,f192]) ).
thf(f263,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f262]) ).
thf(f264,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f263]) ).
cnf(s2,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f188]) ).
cnf(s16,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f206]) ).
cnf(s21,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f211]) ).
cnf(s31,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f233]) ).
cnf(s35,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f237]) ).
cnf(s46,plain,
( spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f248]) ).
cnf(s49,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f253]) ).
cnf(s51,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f260]) ).
cnf(s52,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f264]) ).
cnf(s53,plain,
spl4_1,
inference(rat,[],[s31,s49,s52,s2,s16]) ).
cnf(s54,plain,
~ spl4_4,
inference(rat,[],[s51,s53]) ).
cnf(s55,plain,
spl4_6,
inference(rat,[],[s46,s54]) ).
cnf(s56,plain,
spl4_5,
inference(rat,[],[s35,s54]) ).
cnf(s57,plain,
~ spl4_3,
inference(rat,[],[s52,s55]) ).
cnf(s58,plain,
~ spl4_2,
inference(rat,[],[s49,s56]) ).
cnf(s59,plain,
$false,
inference(rat,[],[s21,s57,s58]) ).
thf(f265,plain,
$false,
inference(avatar_sat_refutation,[],[s59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET601^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n001.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 13:44:36 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.08/0.27 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
% 0.24/0.36 % (1255010)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.36 % (1255021)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.36 % (1255021)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
% 0.24/0.36 % (1255016)lrs+10_16_si=on:nwc=1.5:random_seed=185121487:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.36 % (1255017)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2939015134:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.36 % (1255018)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=3123494428: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)
% 0.24/0.36 % (1255021)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=4276545692:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.36 % (1255017)Refutation not found, incomplete strategy
% 0.24/0.36 % (1255017)------------------------------
% 0.24/0.36 % (1255017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (1255017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (1255017)CaDiCaL version: 2.1.3
% 0.24/0.36 % (1255017)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.36 % (1255017)Time elapsed: 0.003 s
% 0.24/0.36 % (1255017)Peak memory usage: 12 MB
% 0.24/0.36 % (1255017)Instructions burned: 1 (million)
% 0.24/0.36 % (1255017)------------------------------
% 0.24/0.36 % (1255017)------------------------------
% 0.24/0.36 % (1255016) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1255010-1255016"...
% 0.24/0.36 % (1255018) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1255010-1255018"...
% 0.24/0.36 % (1255021) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1255010-1255021"...
% 0.24/0.36 % (1255016)...printing done.
% 0.24/0.36 % (1255018)...printing done.
% 0.24/0.36 % (1255021)...printing done.
% 0.24/0.36 % (1255016)Refutation found. Thanks to Tanya!
% 0.24/0.36 % SZS status Theorem for theBenchmark
% 0.24/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.36 % (1255016)------------------------------
% 0.24/0.36 % (1255016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (1255016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (1255016)CaDiCaL version: 2.1.3
% 0.24/0.36 % (1255016)Termination reason: Refutation
% 0.24/0.36 % (1255016)Time elapsed: 0.012 s
% 0.24/0.36 % (1255016)Peak memory usage: 13 MB
% 0.24/0.36 % (1255016)Instructions burned: 11 (million)
% 0.24/0.36 % (1255010)Success in time 0.076 s
% 0.24/0.36 % Vampire exiting
%------------------------------------------------------------------------------