%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET622^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:23:23 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 7
% Syntax : Number of formulae : 101 ( 19 unt; 0 typ; 6 def)
% Number of atoms : 824 ( 193 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 1010 ( 163 ~; 233 |; 164 &; 444 @)
% ( 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 : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 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,
vOR: $o > $o > $o ).
thf(func_def_2,type,
vAND: $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,
! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ~ ( ( X1 @ X4 )
| ( X2 @ X4 ) ) )
| ( ( X1 @ X4 )
& ( X0 @ X4 )
& ( X2 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ~ ( ( ( X2 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) ) )
& ( X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_98_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ~ ( ( X1 @ X4 )
| ( X2 @ X4 ) ) )
| ( ( X1 @ X4 )
& ( X0 @ X4 )
& ( X2 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ~ ( ( ( X2 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) ) )
& ( X0 @ X3 ) ) ) ),
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 ) ) )
| ( ( X0 @ X3 )
& ( X1 @ X3 )
& ( X2 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ~ ( ( ( X2 @ X4 )
& ~ ( X0 @ X4 ) )
| ( ( X0 @ X4 )
& ~ ( X2 @ X4 ) ) )
& ( X1 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ~ ( ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) ) )
= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( ( X2 @ Y0 )
| ( X0 @ Y0 ) )
& ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ~ ( ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( ( X2 @ Y0 )
| ( X0 @ Y0 ) )
& ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X2 @ Y0 )
& ( X1 @ Y0 ) )
| ( ~ ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( X2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ~ ( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ~ ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ 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)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ~ ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ~ ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f12,plain,
( ( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) ) )
@ sK3 )
= $true )
| ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ~ ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
@ sK3 )
= $true ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f13,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ~ ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( ( $false
= ( ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $false )
| ( $false
= ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $false
= ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f17,plain,
( ( $false
= ( ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $true )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $true
= ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f27]) ).
thf(f38,plain,
( ( $false
= ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f39,plain,
( ( $true
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $true )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f52,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f56,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f52]) ).
thf(f57,plain,
( ( $true
= ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f58,plain,
( ( ( ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
= $true )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f59,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f60,plain,
( ( ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f59]) ).
thf(f62,plain,
( ( ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f60]) ).
thf(f63,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f62]) ).
thf(f74,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f77,plain,
( ( sK2 @ sK3 )
= $true ),
inference(duplicate_literal_removal,[],[f74]) ).
thf(f84,plain,
( ( $true
= ( ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f58]) ).
thf(f85,plain,
( ( ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true )
| ( ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f84]) ).
thf(f87,plain,
( ( $true
= ( ~ ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) )
| ( ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f85]) ).
thf(f88,plain,
( ( ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f87]) ).
thf(f89,plain,
( ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f88]) ).
thf(f90,plain,
( ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f88]) ).
thf(f92,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f90]) ).
thf(f94,plain,
( ( $false
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f92]) ).
thf(f95,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f95]) ).
thf(f100,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f96]) ).
thf(f101,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f100]) ).
thf(f124,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f89]) ).
thf(f125,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f124]) ).
thf(f129,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f125]) ).
thf(f130,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f129]) ).
thf(f131,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f130]) ).
thf(f165,definition,
( spl4_1
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f167,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f169,definition,
( spl4_2
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f171,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f173,definition,
( spl4_3
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f175,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f173]) ).
thf(f176,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f28,f173,f169,f165]) ).
thf(f178,definition,
( spl4_4
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f180,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f178]) ).
thf(f182,definition,
( spl4_5
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f184,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f182]) ).
thf(f185,plain,
( spl4_4
| spl4_2
| spl4_5 ),
inference(avatar_split_clause,[],[f56,f182,f169,f178]) ).
thf(f187,definition,
( spl4_6
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f189,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f187]) ).
thf(f194,plain,
spl4_6,
inference(avatar_split_clause,[],[f77,f187]) ).
thf(f197,plain,
( spl4_3
| spl4_5 ),
inference(avatar_split_clause,[],[f101,f182,f173]) ).
thf(f200,plain,
( spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f131,f165,f178]) ).
thf(f205,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_demodulation,[],[f180,f175]) ).
thf(f206,plain,
( $false
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f207,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f206]) ).
thf(f209,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_5 ),
inference(forward_demodulation,[],[f184,f167]) ).
thf(f210,plain,
( $false
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f209]) ).
thf(f211,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f210]) ).
thf(f213,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f189,f171]) ).
thf(f217,plain,
( $false
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f213]) ).
thf(f218,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f217]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f176]) ).
cnf(s2,plain,
( spl4_2
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f185]) ).
cnf(s7,plain,
spl4_6,
inference(sat_conversion,[],[f194]) ).
cnf(s10,plain,
( spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f197]) ).
cnf(s13,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f200]) ).
cnf(s18,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f207]) ).
cnf(s19,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f211]) ).
cnf(s21,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(sat_conversion,[],[f218]) ).
cnf(s22,plain,
~ spl4_2,
inference(rat,[],[s21,s7]) ).
cnf(s23,plain,
( spl4_4
| spl4_5 ),
inference(rat,[],[s2,s22]) ).
cnf(s24,plain,
( spl4_1
| spl4_3 ),
inference(rat,[],[s1,s22]) ).
cnf(s25,plain,
spl4_1,
inference(rat,[],[s18,s24,s13]) ).
cnf(s26,plain,
~ spl4_5,
inference(rat,[],[s19,s25]) ).
cnf(s27,plain,
spl4_3,
inference(rat,[],[s10,s26]) ).
cnf(s28,plain,
spl4_4,
inference(rat,[],[s23,s26]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s18,s28,s27]) ).
thf(f219,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET622^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n016.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 13:44:34 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.27 % (363195)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (363202)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=588902450:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (363202)Refutation not found, incomplete strategy
% 0.21/0.27 % (363202)------------------------------
% 0.21/0.27 % (363202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (363202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (363202)CaDiCaL version: 2.1.3
% 0.21/0.27 % (363202)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.27 % (363202)Time elapsed: 0.001 s
% 0.21/0.27 % (363202)Peak memory usage: 12 MB
% 0.21/0.27 % (363202)Instructions burned: 1 (million)
% 0.21/0.27 % (363202)------------------------------
% 0.21/0.27 % (363202)------------------------------
% 0.21/0.27 % (363201)lrs+10_16_si=on:nwc=1.5:random_seed=1602040850:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (363200)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3928559662:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (363203)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=1625875959: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)
% 0.21/0.27 % (363204)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=532104317:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (363201) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-363195-363201"...
% 0.21/0.27 % (363200) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-363195-363200"...
% 0.21/0.27 % (363204) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-363195-363204"...
% 0.21/0.27 % (363203) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-363195-363203"...
% 0.21/0.27 % (363208)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=29515772:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.27 % (363208)Instruction limit reached!
% 0.21/0.27 % (363208)------------------------------
% 0.21/0.27 % (363208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (363208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (363208)CaDiCaL version: 2.1.3
% 0.21/0.27 % (363208)Termination reason: Instruction limit
% 0.21/0.27 % (363208)Termination phase: Saturation
% 0.21/0.27 % (363208)Time elapsed: 0.001 s
% 0.21/0.27 % (363208)Peak memory usage: 12 MB
% 0.21/0.27 % (363208)Instructions burned: 2 (million)
% 0.21/0.27 % (363201)...printing done.
% 0.21/0.27 % (363200)...printing done.
% 0.21/0.27 % (363204)...printing done.
% 0.21/0.27 % (363201)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 % (363201)------------------------------
% 0.21/0.27 % (363201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (363201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (363201)CaDiCaL version: 2.1.3
% 0.21/0.27 % (363201)Termination reason: Refutation
% 0.21/0.27 % (363201)Time elapsed: 0.006 s
% 0.21/0.27 % (363201)Peak memory usage: 13 MB
% 0.21/0.27 % (363201)Instructions burned: 9 (million)
% 0.21/0.27 % (363195)Success in time 0.039 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------