%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV387^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:39:26 AM UTC 2026
% Result : Theorem 0.07s 0.27s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of formulae : 99 ( 17 unt; 0 typ; 5 def)
% Number of atoms : 959 ( 214 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 1188 ( 151 ~; 216 |; 276 &; 540 @)
% ( 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,
vOR: $o > $o > $o ).
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,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ~ ( ( X1 @ X4 )
& ( X0 @ X4 ) )
& ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( ( X2 @ X4 )
& ( X0 @ X4 ) )
& ( X1 @ X4 )
& ( X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM44_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] :
( ( ~ ( ( X1 @ X4 )
& ( X0 @ X4 ) )
& ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( ( X2 @ X4 )
& ( X0 @ 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] :
( ( ~ ( ( X1 @ X4 )
& ( X0 @ X4 ) )
& ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( ( X2 @ X4 )
& ( X0 @ 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 )
& ~ ( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ( X1 @ 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 )
& ~ ( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ( X1 @ 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 )
& ~ ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ 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 )
& ~ ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ 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 )
& ~ ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ 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 )
& ~ ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ 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 )
& ~ ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ 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 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $false
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f21]) ).
thf(f24,plain,
( ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f24]) ).
thf(f27,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f25]) ).
thf(f28,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f34,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f35,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f34]) ).
thf(f44,plain,
( ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f45,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f44]) ).
thf(f46,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f45]) ).
thf(f56,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f46]) ).
thf(f57,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f56]) ).
thf(f58,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f62,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f58]) ).
thf(f63,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f62]) ).
thf(f64,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f65,plain,
( ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f64]) ).
thf(f66,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f64]) ).
thf(f67,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f69,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f71,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f69]) ).
thf(f73,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f71]) ).
thf(f75,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f76,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f75]) ).
thf(f98,plain,
( ( $true
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f65]) ).
thf(f99,plain,
( ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f101,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f100]) ).
thf(f103,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f101]) ).
thf(f104,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f103]) ).
thf(f126,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f128,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f129,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f128]) ).
thf(f132,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f129]) ).
thf(f166,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f99]) ).
thf(f167,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f167]) ).
thf(f208,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f209,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f209]) ).
thf(f221,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f222,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f221]) ).
thf(f228,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f229,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f229]) ).
thf(f232,definition,
( spl4_1
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f234,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f236,definition,
( spl4_2
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f238,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f236]) ).
thf(f240,definition,
( spl4_3
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f242,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f240]) ).
thf(f243,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f35,f240,f236,f232]) ).
thf(f245,definition,
( spl4_4
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f247,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f249,definition,
( spl4_5
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f251,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f252,plain,
( spl4_4
| spl4_2
| spl4_5 ),
inference(avatar_split_clause,[],[f63,f249,f236,f245]) ).
thf(f263,plain,
( spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f132,f240,f249]) ).
thf(f265,plain,
( spl4_2
| spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f230,f232,f245,f236]) ).
thf(f268,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_4 ),
inference(constrained_superposition,[],[f242,f247]) ).
thf(f269,plain,
( $false
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f268]) ).
thf(f270,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f269]) ).
thf(f277,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_5 ),
inference(forward_demodulation,[],[f251,f234]) ).
thf(f278,plain,
( $false
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f277]) ).
thf(f279,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f278]) ).
thf(f284,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f76,f238]) ).
thf(f285,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f284]) ).
thf(f286,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f285]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f243]) ).
cnf(s2,plain,
( spl4_2
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f252]) ).
cnf(s9,plain,
( spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f263]) ).
cnf(s11,plain,
( spl4_1
| spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f265]) ).
cnf(s12,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f270]) ).
cnf(s14,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f279]) ).
cnf(s15,plain,
~ spl4_2,
inference(sat_conversion,[],[f286]) ).
cnf(s16,plain,
( spl4_1
| spl4_4 ),
inference(rat,[],[s11,s15]) ).
cnf(s17,plain,
( spl4_4
| spl4_5 ),
inference(rat,[],[s2,s15]) ).
cnf(s18,plain,
( spl4_1
| spl4_3 ),
inference(rat,[],[s1,s15]) ).
cnf(s19,plain,
spl4_1,
inference(rat,[],[s12,s18,s16]) ).
cnf(s20,plain,
~ spl4_5,
inference(rat,[],[s14,s19]) ).
cnf(s21,plain,
spl4_3,
inference(rat,[],[s9,s20]) ).
cnf(s23,plain,
spl4_4,
inference(rat,[],[s17,s20]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s12,s23,s21]) ).
thf(f287,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV387^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 15:47:03 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.27 % (3691351)Will run a generic schedule for satisfiability detection.
% 0.07/0.27 % (3691363)% WARNING: option uhcvi not known.
% 0.07/0.27 % (3691363)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3435669514:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.27 % (3691363)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.27 % (3691363)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.27 % (3691363) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3691351-3691363"...
% 0.07/0.27 % (3691363)...printing done.
% 0.07/0.27 % (3691363)Refutation found. Thanks to Tanya!
% 0.07/0.27 % SZS status Theorem for theBenchmark
% 0.07/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.27 % (3691363)------------------------------
% 0.07/0.27 % (3691363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.27 % (3691363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.27 % (3691363)CaDiCaL version: 2.1.3
% 0.07/0.27 % (3691363)Termination reason: Refutation
% 0.07/0.27 % (3691363)Time elapsed: 0.004 s
% 0.07/0.27 % (3691363)Peak memory usage: 13 MB
% 0.07/0.27 % (3691363)Instructions burned: 13 (million)
% 0.07/0.27 % (3691351)Success in time 0.033 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------