%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET601^3 : TPTP v9.3.1. Released v3.6.0.
% 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 08:23:20 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 114 ( 26 unt; 0 typ; 6 def)
% Number of atoms : 1386 ( 222 equ; 0 cnn)
% Maximal formula atoms : 5 ( 12 avg)
% Number of connectives : 1050 ( 42 ~; 289 |; 104 &; 609 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 9 con; 0-4 aty)
% Number of variables : 77 ( 0 sgn 9 !; 6 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
is_a: $i > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
unord_pair: $i > $i > $i > $o ).
thf(func_def_5,type,
singleton: $i > $i > $o ).
thf(func_def_6,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
complement: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_12,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_13,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_14,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vOR: $o > $o > $o ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
vAND: $o > $o > $o ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(func_def_26,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
sK0: $i > $o ).
thf(func_def_29,type,
sK1: $i > $o ).
thf(func_def_30,type,
sK2: $i > $o ).
thf(f6,axiom,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',union) ).
thf(f8,axiom,
( intersection
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',intersection) ).
thf(f15,conjecture,
! [X1: $i > $o,X0: $i > $o,X2: $i > $o] :
( ( union @ ( intersection @ X0 @ X1 ) @ ( union @ ( intersection @ X1 @ X2 ) @ ( intersection @ X2 @ X0 ) ) )
= ( intersection @ ( union @ X0 @ X1 ) @ ( intersection @ ( union @ X1 @ X2 ) @ ( union @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X1: $i > $o,X0: $i > $o,X2: $i > $o] :
( ( union @ ( intersection @ X0 @ X1 ) @ ( union @ ( intersection @ X1 @ X2 ) @ ( intersection @ X2 @ X0 ) ) )
= ( intersection @ ( union @ X0 @ X1 ) @ ( intersection @ ( union @ X1 @ X2 ) @ ( union @ X2 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f18,plain,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f19,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f33,plain,
( intersection
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f34,plain,
( intersection
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f39,plain,
~ ! [X1: $i > $o,X2: $i > $o,X0: $i > $o] :
( ( union @ ( intersection @ X1 @ X0 ) @ ( union @ ( intersection @ X0 @ X2 ) @ ( intersection @ X2 @ X1 ) ) )
= ( intersection @ ( union @ X1 @ X0 ) @ ( intersection @ ( union @ X0 @ X2 ) @ ( union @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f40,plain,
? [X1: $i > $o,X2: $i > $o,X0: $i > $o] :
( ( union @ ( intersection @ X1 @ X0 ) @ ( union @ ( intersection @ X0 @ X2 ) @ ( intersection @ X2 @ X1 ) ) )
!= ( intersection @ ( union @ X1 @ X0 ) @ ( intersection @ ( union @ X0 @ X2 ) @ ( union @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[],[f39]) ).
thf(f41,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( intersection @ ( union @ X0 @ X2 ) @ ( intersection @ ( union @ X2 @ X1 ) @ ( union @ X1 @ X0 ) ) )
!= ( union @ ( intersection @ X0 @ X2 ) @ ( union @ ( intersection @ X2 @ X1 ) @ ( intersection @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f42,plain,
( ( intersection @ ( union @ sK0 @ sK2 ) @ ( intersection @ ( union @ sK2 @ sK1 ) @ ( union @ sK1 @ sK0 ) ) )
!= ( union @ ( intersection @ sK0 @ sK2 ) @ ( union @ ( intersection @ sK2 @ sK1 ) @ ( intersection @ sK1 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f41]) ).
thf(f43,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f50,plain,
( intersection
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f52,plain,
( ( intersection @ ( union @ sK0 @ sK2 ) @ ( intersection @ ( union @ sK2 @ sK1 ) @ ( union @ sK1 @ sK0 ) ) )
!= ( union @ ( intersection @ sK0 @ sK2 ) @ ( union @ ( intersection @ sK2 @ sK1 ) @ ( intersection @ sK1 @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f61,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ sK0
@ sK2 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ sK2
@ sK1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ sK1
@ sK0 ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK0
@ sK2 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK2
@ sK1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK1
@ sK0 ) ) ) ),
inference(definition_unfolding,[],[f52,f50,f43,f50,f43,f43,f43,f50,f43,f50,f50]) ).
thf(f62,plain,
( ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
( ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f62]) ).
thf(f64,plain,
( ( ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ sK3 )
= $true ) ),
inference(xor_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f63]) ).
thf(f66,plain,
( ( $false
= ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
( ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $false )
| ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f69,plain,
( ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f68]) ).
thf(f71,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f73]) ).
thf(f86,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f74]) ).
thf(f93,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f86]) ).
thf(f94,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f93]) ).
thf(f96,plain,
( ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f69]) ).
thf(f98,plain,
( ( ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f99,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f99]) ).
thf(f101,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f100]) ).
thf(f107,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f101]) ).
thf(f110,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f107]) ).
thf(f124,plain,
( ( ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f125,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f125]) ).
thf(f128,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f126]) ).
thf(f129,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f128]) ).
thf(f135,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f129]) ).
thf(f138,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f135]) ).
thf(f149,plain,
( ( $true
= ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f150,plain,
( ( ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f153,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f156]) ).
thf(f159,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f162,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f159]) ).
thf(f167,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f153]) ).
thf(f181,plain,
( ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f182,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f182]) ).
thf(f189,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f183]) ).
thf(f192,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f189]) ).
thf(f193,plain,
( ( $true
= ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK2 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f194,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f193]) ).
thf(f218,plain,
( ( ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f227,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f218]) ).
thf(f228,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f230,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f228]) ).
thf(f231,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f230]) ).
thf(f240,definition,
( spl4_1
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f242,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f240]) ).
thf(f244,definition,
( spl4_2
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f246,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f244]) ).
thf(f248,definition,
( spl4_3
<=> ( ( sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f250,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f257,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f94,f248,f240]) ).
thf(f262,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f110,f244,f240]) ).
thf(f270,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f138,f244,f248]) ).
thf(f276,definition,
( spl4_4
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f278,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f280,definition,
( spl4_5
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f282,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f284,definition,
( spl4_6
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f286,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f288,plain,
( spl4_6
| spl4_4 ),
inference(avatar_split_clause,[],[f162,f276,f284]) ).
thf(f298,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f192,f284,f280]) ).
thf(f307,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f231,f280,f276]) ).
thf(f311,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_4 ),
inference(forward_demodulation,[],[f246,f278]) ).
thf(f312,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f311]) ).
thf(f313,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f312]) ).
thf(f315,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_5 ),
inference(forward_demodulation,[],[f242,f282]) ).
thf(f316,plain,
( $false
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f315]) ).
thf(f317,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f316]) ).
thf(f320,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f286,f250]) ).
thf(f321,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f322,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f321]) ).
cnf(s7,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f257]) ).
cnf(s12,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f262]) ).
cnf(s20,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f270]) ).
cnf(s26,plain,
( spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f288]) ).
cnf(s36,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f298]) ).
cnf(s45,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f307]) ).
cnf(s49,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f313]) ).
cnf(s50,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f317]) ).
cnf(s51,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f322]) ).
cnf(s52,plain,
spl4_1,
inference(rat,[],[s26,s51,s49,s7,s12]) ).
cnf(s53,plain,
~ spl4_5,
inference(rat,[],[s50,s52]) ).
cnf(s54,plain,
spl4_4,
inference(rat,[],[s45,s53]) ).
cnf(s55,plain,
spl4_6,
inference(rat,[],[s36,s53]) ).
cnf(s56,plain,
~ spl4_2,
inference(rat,[],[s49,s54]) ).
cnf(s57,plain,
~ spl4_3,
inference(rat,[],[s51,s55]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s20,s57,s56]) ).
thf(f323,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET601^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:37:37 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.20/0.27 % (2119216)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (2119221)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1946302121:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (2119221) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2119216-2119221"...
% 0.20/0.27 % (2119227)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.27 % (2119227)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
% 0.20/0.27 % (2119221)...printing done.
% 0.20/0.27 % (2119221)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (2119221)------------------------------
% 0.20/0.27 % (2119221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2119221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2119221)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2119221)Termination reason: Refutation
% 0.20/0.27 % (2119221)Time elapsed: 0.004 s
% 0.20/0.27 % (2119221)Peak memory usage: 13 MB
% 0.20/0.27 % (2119221)Instructions burned: 14 (million)
% 0.20/0.27 % (2119216)Success in time 0.038 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------