%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET601^5 : 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 : n005.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 08:23:40 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 104 ( 16 unt; 0 typ; 6 def)
% Number of atoms : 899 ( 210 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 954 ( 40 ~; 304 |; 125 &; 479 @)
% ( 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 : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 12 !; 3 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
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,
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] :
( ( ^ [X3: a] :
( ( ( X0 @ X3 )
& ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X0 @ X4 )
| ( X2 @ X4 ) )
& ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( ( X1 @ X4 )
| ( X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_72_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( X0 @ X3 )
& ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X0 @ X4 )
| ( X2 @ X4 ) )
& ( ( X2 @ X4 )
| ( X1 @ 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] :
( ( ( X0 @ X3 )
& ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X0 @ X4 )
| ( X2 @ X4 ) )
& ( ( X2 @ X4 )
| ( X1 @ 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 ) )
| ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( ( X1 @ Y0 )
| ( X2 @ Y0 ) )
& ( ( X2 @ Y0 )
| ( X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( ( X1 @ Y0 )
| ( X2 @ Y0 ) )
& ( ( X2 @ Y0 )
| ( X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ 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)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f18,plain,
( ( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f26]) ).
thf(f40,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f42,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f40]) ).
thf(f43,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f42]) ).
thf(f46,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f43]) ).
thf(f51,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f52,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f54,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f52]) ).
thf(f55,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f54]) ).
thf(f57,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f55]) ).
thf(f58,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f57]) ).
thf(f61,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f58]) ).
thf(f77,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f78,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f78]) ).
thf(f92,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f79]) ).
thf(f93,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f92]) ).
thf(f100,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f93]) ).
thf(f101,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f100]) ).
thf(f103,plain,
( ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f104,plain,
( ( $true
= ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f103]) ).
thf(f105,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f106,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f108,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f106]) ).
thf(f109,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f108]) ).
thf(f123,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f109]) ).
thf(f124,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f123]) ).
thf(f126,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f124]) ).
thf(f127,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f130,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f127]) ).
thf(f147,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f105]) ).
thf(f148,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f105]) ).
thf(f150,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f158,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f155]) ).
thf(f175,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f176,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f184,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f177]) ).
thf(f185,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f184]) ).
thf(f188,definition,
( spl4_1
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f190,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f188]) ).
thf(f192,definition,
( spl4_2
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f194,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f192]) ).
thf(f196,definition,
( spl4_3
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f198,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f204,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f46,f196,f188]) ).
thf(f208,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f61,f192,f196]) ).
thf(f221,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f101,f188,f192]) ).
thf(f224,definition,
( spl4_4
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f226,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f228,definition,
( spl4_5
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f230,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f232,definition,
( spl4_6
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f234,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f240,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f130,f232,f228]) ).
thf(f248,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f158,f224,f228]) ).
thf(f257,plain,
( spl4_6
| spl4_4 ),
inference(avatar_split_clause,[],[f185,f224,f232]) ).
thf(f265,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_5 ),
inference(constrained_superposition,[],[f230,f198]) ).
thf(f269,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f265]) ).
thf(f270,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f269]) ).
thf(f274,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f234,f194]) ).
thf(f278,plain,
( $false
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f274]) ).
thf(f279,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f278]) ).
thf(f281,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4 ),
inference(constrained_superposition,[],[f190,f226]) ).
thf(f285,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f281]) ).
thf(f286,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f285]) ).
cnf(s6,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f204]) ).
cnf(s10,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f208]) ).
cnf(s23,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f221]) ).
cnf(s30,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f240]) ).
cnf(s38,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f248]) ).
cnf(s47,plain,
( spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f257]) ).
cnf(s50,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f270]) ).
cnf(s52,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(sat_conversion,[],[f279]) ).
cnf(s54,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f286]) ).
cnf(s55,plain,
spl4_1,
inference(rat,[],[s30,s50,s52,s6,s23]) ).
cnf(s56,plain,
~ spl4_4,
inference(rat,[],[s54,s55]) ).
cnf(s57,plain,
spl4_6,
inference(rat,[],[s47,s56]) ).
cnf(s58,plain,
spl4_5,
inference(rat,[],[s38,s56]) ).
cnf(s59,plain,
~ spl4_2,
inference(rat,[],[s52,s57]) ).
cnf(s60,plain,
~ spl4_3,
inference(rat,[],[s50,s58]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s10,s60,s59]) ).
thf(f288,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET601^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:38:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.18/0.27 % (1674302)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (1674308)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1862737927_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % Exception at run slice level
% 0.18/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.27 % (1674309)% WARNING: option uhcvi not known.
% 0.18/0.27 % (1674310)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=392240783:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (1674309)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3701107934:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (1674311)dis+10_1_sil=32000:sp=arity:random_seed=3709080096:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (1674312)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3998550154:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % (1674314)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2551503805:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.27 % (1674309)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (1674313)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=183933290:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.27 % (1674312)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (1674309)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.27 % (1674316)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1755192493:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.27 % Exception at run slice level
% 0.18/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.27 % (1674309) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1674302-1674309"...
% 0.18/0.27 % (1674311) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1674302-1674311"...
% 0.18/0.27 % (1674312) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1674302-1674312"...
% 0.18/0.27 % (1674314) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1674302-1674314"...
% 0.18/0.27 % (1674310) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1674302-1674310"...
% 0.18/0.27 % (1674313) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1674302-1674313"...
% 0.18/0.27 % (1674311)...printing done.
% 0.18/0.27 % (1674309)...printing done.
% 0.18/0.27 % (1674312)...printing done.
% 0.18/0.27 % (1674314)...printing done.
% 0.18/0.27 % (1674313)...printing done.
% 0.18/0.27 % (1674310)...printing done.
% 0.18/0.27 % (1674314)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (1674314)------------------------------
% 0.18/0.27 % (1674314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (1674314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (1674314)CaDiCaL version: 2.1.3
% 0.18/0.27 % (1674314)Termination reason: Refutation
% 0.18/0.27 % (1674314)Time elapsed: 0.006 s
% 0.18/0.27 % (1674314)Peak memory usage: 13 MB
% 0.18/0.27 % (1674314)Instructions burned: 10 (million)
% 0.18/0.27 % (1674302)Success in time 0.042 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------