%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n026.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 08:23:44 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 95 ( 17 unt; 0 typ; 5 def)
% Number of atoms : 826 ( 191 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 986 ( 135 ~; 239 |; 160 &; 447 @)
% ( 5 <=>; 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 : 18 ( 15 usr; 8 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
vOR: $o > $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,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ( X1 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_98_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ( X1 @ 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 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ( X1 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( X0 @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) )
= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( ( X0 @ Y0 )
& ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( ( X0 @ Y0 )
& ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ 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 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f18,plain,
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f27,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f25]) ).
thf(f28,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f29]) ).
thf(f32,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f33,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f32]) ).
thf(f44,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f24]) ).
thf(f45,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f44]) ).
thf(f55,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f56,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f55]) ).
thf(f60,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f56]) ).
thf(f61,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f60]) ).
thf(f62,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f61]) ).
thf(f63,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f64,plain,
( ( $true
= ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f66,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f66]) ).
thf(f70,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f72,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f72]) ).
thf(f91,plain,
( ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f64]) ).
thf(f92,plain,
( ( $false
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f91]) ).
thf(f93,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f91]) ).
thf(f94,plain,
( ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f93]) ).
thf(f95,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f95]) ).
thf(f97,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f96]) ).
thf(f114,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f97]) ).
thf(f117,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f114]) ).
thf(f119,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f117]) ).
thf(f120,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f119]) ).
thf(f122,plain,
( ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f92]) ).
thf(f123,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f122]) ).
thf(f124,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f123]) ).
thf(f126,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f124]) ).
thf(f127,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f136,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f127]) ).
thf(f139,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f136]) ).
thf(f140,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f139]) ).
thf(f143,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f140]) ).
thf(f151,definition,
( spl4_1
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f153,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f151]) ).
thf(f155,definition,
( spl4_2
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f157,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f159,definition,
( spl4_3
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f161,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f159]) ).
thf(f162,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f33,f159,f155,f151]) ).
thf(f164,definition,
( spl4_4
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f166,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f164]) ).
thf(f168,definition,
( spl4_5
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f170,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f168]) ).
thf(f171,plain,
( spl4_2
| spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f62,f168,f164,f155]) ).
thf(f185,plain,
( spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f120,f159,f168]) ).
thf(f189,plain,
( spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f143,f151,f164]) ).
thf(f192,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_4 ),
inference(constrained_superposition,[],[f161,f166]) ).
thf(f193,plain,
( $false
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f192]) ).
thf(f194,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f193]) ).
thf(f200,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_5 ),
inference(constrained_superposition,[],[f170,f153]) ).
thf(f204,plain,
( $false
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f205,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f204]) ).
thf(f210,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f73,f157]) ).
thf(f211,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f210]) ).
thf(f212,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f211]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f162]) ).
cnf(s2,plain,
( spl4_2
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f171]) ).
cnf(s12,plain,
( spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f185]) ).
cnf(s16,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f189]) ).
cnf(s17,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f194]) ).
cnf(s20,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f205]) ).
cnf(s21,plain,
~ spl4_2,
inference(sat_conversion,[],[f212]) ).
cnf(s22,plain,
( spl4_4
| spl4_5 ),
inference(rat,[],[s2,s21]) ).
cnf(s23,plain,
( spl4_1
| spl4_3 ),
inference(rat,[],[s1,s21]) ).
cnf(s24,plain,
spl4_1,
inference(rat,[],[s17,s23,s16]) ).
cnf(s25,plain,
~ spl4_5,
inference(rat,[],[s20,s24]) ).
cnf(s26,plain,
spl4_3,
inference(rat,[],[s12,s25]) ).
cnf(s28,plain,
spl4_4,
inference(rat,[],[s22,s25]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s17,s28,s26]) ).
thf(f213,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET622^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n026.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 13:42:27 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.29 % (606604)Will run a generic schedule for satisfiability detection.
% 0.22/0.29 % (606612)dis+10_1_sil=32000:sp=arity:random_seed=1209682911:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.29 % (606612) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-606604-606612"...
% 0.22/0.29 % (606610)% WARNING: option uhcvi not known.
% 0.22/0.29 % (606612)...printing done.
% 0.22/0.29 % (606612)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (606612)------------------------------
% 0.22/0.29 % (606612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (606612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (606612)CaDiCaL version: 2.1.3
% 0.22/0.29 % (606612)Termination reason: Refutation
% 0.22/0.29 % (606612)Time elapsed: 0.004 s
% 0.22/0.29 % (606612)Peak memory usage: 12 MB
% 0.22/0.29 % (606612)Instructions burned: 10 (million)
% 0.22/0.29 % (606604)Success in time 0.036 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------