%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU857^5 : 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 : n014.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 08:31:49 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 7
% Syntax : Number of formulae : 172 ( 17 unt; 0 typ; 6 def)
% Number of atoms : 2183 ( 501 equ; 0 cnn)
% Maximal formula atoms : 6 ( 12 avg)
% Number of connectives : 2939 ( 606 ~; 633 |; 490 &;1204 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ~ ( X2 @ X3 )
& ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) ) )
| ( ~ ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
& ( X2 @ X3 ) ) ) )
= ( ^ [X3: a] :
( ( ( X0 @ X3 )
& ~ ( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) ) )
| ( ( ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ~ ( X1 @ X3 ) ) )
& ~ ( X0 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM43_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ~ ( X2 @ X3 )
& ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) ) )
| ( ~ ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
& ( X2 @ X3 ) ) ) )
= ( ^ [X3: a] :
( ( ( X0 @ X3 )
& ~ ( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) ) )
| ( ( ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ~ ( X1 @ X3 ) ) )
& ~ ( X0 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ~ ( X2 @ X3 )
& ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) ) )
| ( ~ ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
& ( X2 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ~ ( ( ~ ( X2 @ X4 )
& ( X1 @ X4 ) )
| ( ~ ( X1 @ X4 )
& ( X2 @ X4 ) ) ) )
| ( ( ( ( X1 @ X4 )
& ~ ( X2 @ X4 ) )
| ( ( X2 @ X4 )
& ~ ( X1 @ X4 ) ) )
& ~ ( X0 @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ~ ( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ( ( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) )
& ~ ( X2 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
| ( ~ ( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) )
& ( X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ~ ( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ( ( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) )
& ~ ( X2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
| ( ~ ( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) )
& ( X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) )
| ( ( ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
& ~ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( X2 @ Y0 )
& ( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ( ~ ( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
& ( X2 @ Y0 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK2 @ Y0 )
& ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| ( ~ ( ( ( sK1 @ Y0 )
& ~ ( sK0 @ 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] :
( ( ( sK1 @ Y0 )
& ~ ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK2 @ Y0 )
& ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| ( ~ ( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ~ ( sK2 @ Y0 )
& ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| ( ~ ( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f12,plain,
( ( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) )
@ sK3 )
= $true )
| ( $true
= ( ^ [Y0: a] :
( ( ~ ( sK2 @ Y0 )
& ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| ( ~ ( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f13,plain,
( ( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) )
@ sK3 )
= $false )
| ( ( ^ [Y0: a] :
( ( ~ ( sK2 @ Y0 )
& ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| ( ~ ( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ( sK2 @ Y0 ) ) )
@ sK3 )
= $false ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( ( ( ~ ( sK2 @ sK3 )
& ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) ) )
= $false )
| ( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( ( ( ~ ( sK2 @ sK3 )
& ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) ) )
= $false )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f17,plain,
( ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $false )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false )
| ( ( ~ ( sK2 @ sK3 )
& ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f16]) ).
thf(f19,plain,
( ( ( ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false )
| ( ( ~ ( sK2 @ sK3 )
& ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f52,plain,
( ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f23]) ).
thf(f53,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f52]) ).
thf(f65,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f53]) ).
thf(f66,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f67]) ).
thf(f72,plain,
( ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f73,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f113,plain,
( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f75]) ).
thf(f133,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f113]) ).
thf(f134,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f134]) ).
thf(f136,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f136]) ).
thf(f139,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f137]) ).
thf(f141,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f139]) ).
thf(f142,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f143]) ).
thf(f152,plain,
( ( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f15]) ).
thf(f153,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
= $false )
| ( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f15]) ).
thf(f154,plain,
( ( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f170,plain,
( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f156]) ).
thf(f172,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f176]) ).
thf(f183,plain,
( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f184,plain,
( ( $false
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f206,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f184]) ).
thf(f207,plain,
( ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f212,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f210]) ).
thf(f213,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f215,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f213]) ).
thf(f216,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f215]) ).
thf(f228,plain,
( ( ( ( ~ ( sK2 @ sK3 )
& ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) ) )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f229,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( $true
= ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f229]) ).
thf(f232,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f235,plain,
( ( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f236,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f239,plain,
( ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f237]) ).
thf(f240,plain,
( ( ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f240]) ).
thf(f261,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f241]) ).
thf(f262,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f263,plain,
( ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( sK2 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f262]) ).
thf(f265,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f263]) ).
thf(f267,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f265]) ).
thf(f268,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f267]) ).
thf(f269,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f268]) ).
thf(f270,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f269]) ).
thf(f378,plain,
( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f379,plain,
( ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f378]) ).
thf(f390,plain,
( ( ( ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f379]) ).
thf(f391,plain,
( ( ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f390]) ).
thf(f393,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f391]) ).
thf(f394,plain,
( ( $false
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f393]) ).
thf(f401,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f394]) ).
thf(f402,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f401]) ).
thf(f403,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f402]) ).
thf(f404,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f403]) ).
thf(f478,plain,
( ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f230]) ).
thf(f479,plain,
( ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f478]) ).
thf(f1238,plain,
( ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f479]) ).
thf(f1239,plain,
( ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f479]) ).
thf(f1240,plain,
( ( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1239]) ).
thf(f1241,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1240]) ).
thf(f1371,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f1241]) ).
thf(f1372,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f1371]) ).
thf(f1379,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f1372]) ).
thf(f1381,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f1379]) ).
thf(f1382,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f1381]) ).
thf(f1384,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f1382]) ).
thf(f1385,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f1384]) ).
thf(f1386,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f1385]) ).
thf(f1387,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f1386]) ).
thf(f1399,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f1238]) ).
thf(f1481,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f1399]) ).
thf(f1483,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1481]) ).
thf(f1485,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f1483]) ).
thf(f1486,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f1485]) ).
thf(f1487,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f1486]) ).
thf(f1496,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f1487]) ).
thf(f1500,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f1496]) ).
thf(f1552,definition,
( spl4_1
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f1554,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f1552]) ).
thf(f1556,definition,
( spl4_2
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f1558,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f1556]) ).
thf(f1560,definition,
( spl4_3
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f1562,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f1560]) ).
thf(f1563,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f68,f1560,f1556,f1552]) ).
thf(f1565,definition,
( spl4_4
<=> ( ( sK2 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f1567,plain,
( ( ( sK2 @ sK3 )
= $false )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f1565]) ).
thf(f1569,definition,
( spl4_5
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f1571,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f1569]) ).
thf(f1572,plain,
( spl4_4
| spl4_5
| spl4_2 ),
inference(avatar_split_clause,[],[f144,f1556,f1569,f1565]) ).
thf(f1574,definition,
( spl4_6
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f1576,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f1574]) ).
thf(f1577,plain,
( spl4_6
| spl4_1
| spl4_5 ),
inference(avatar_split_clause,[],[f177,f1569,f1552,f1574]) ).
thf(f1578,plain,
( spl4_3
| spl4_4
| spl4_6 ),
inference(avatar_split_clause,[],[f216,f1574,f1565,f1560]) ).
thf(f1579,plain,
( spl4_4
| spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f270,f1574,f1569,f1565]) ).
thf(f1580,plain,
( spl4_3
| spl4_2
| spl4_4 ),
inference(avatar_split_clause,[],[f404,f1565,f1556,f1560]) ).
thf(f1581,plain,
( spl4_1
| spl4_5
| spl4_2 ),
inference(avatar_split_clause,[],[f1387,f1556,f1569,f1552]) ).
thf(f1582,plain,
( spl4_1
| spl4_3
| spl4_6 ),
inference(avatar_split_clause,[],[f1500,f1574,f1560,f1552]) ).
thf(f1583,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f1562,f1571]) ).
thf(f1584,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f1583]) ).
thf(f1585,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f1584]) ).
thf(f1586,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4 ),
inference(constrained_superposition,[],[f1567,f1554]) ).
thf(f1590,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f1586]) ).
thf(f1591,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f1590]) ).
thf(f1593,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f1558,f1576]) ).
thf(f1594,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f1576,f1558]) ).
thf(f1595,plain,
( $false
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f1593]) ).
thf(f1596,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f1595]) ).
thf(f1597,plain,
( $false
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f1594]) ).
thf(f1598,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f1597]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f1563]) ).
cnf(s2,plain,
( spl4_2
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f1572]) ).
cnf(s3,plain,
( spl4_1
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f1577]) ).
cnf(s4,plain,
( spl4_3
| spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f1578]) ).
cnf(s5,plain,
( spl4_4
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f1579]) ).
cnf(s6,plain,
( spl4_2
| spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f1580]) ).
cnf(s7,plain,
( spl4_1
| spl4_2
| spl4_5 ),
inference(sat_conversion,[],[f1581]) ).
cnf(s8,plain,
( spl4_1
| spl4_3
| spl4_6 ),
inference(sat_conversion,[],[f1582]) ).
cnf(s9,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f1585]) ).
cnf(s11,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f1591]) ).
cnf(s12,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(sat_conversion,[],[f1596]) ).
cnf(s13,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(sat_conversion,[],[f1598]) ).
cnf(s14,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s9,s1,s7]) ).
cnf(s15,plain,
( spl4_6
| spl4_1 ),
inference(rat,[],[s9,s3,s8]) ).
cnf(s16,plain,
spl4_1,
inference(rat,[],[s15,s13,s14]) ).
cnf(s17,plain,
~ spl4_4,
inference(rat,[],[s11,s16]) ).
cnf(s18,plain,
spl4_5,
inference(rat,[],[s12,s2,s5,s17]) ).
cnf(s19,plain,
~ spl4_3,
inference(rat,[],[s9,s18]) ).
cnf(s20,plain,
spl4_2,
inference(rat,[],[s6,s17,s19]) ).
cnf(s21,plain,
spl4_6,
inference(rat,[],[s4,s17,s19]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s12,s21,s20]) ).
thf(f1599,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU857^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:40:00 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.30 % (2753571)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (2753578)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2906325109:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (2753578)Refutation not found, incomplete strategy
% 0.22/0.30 % (2753578)------------------------------
% 0.22/0.30 % (2753578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2753578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2753578)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2753578)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.30 % (2753578)Time elapsed: 0.001 s
% 0.22/0.30 % (2753578)Peak memory usage: 12 MB
% 0.22/0.30 % (2753578)Instructions burned: 2 (million)
% 0.22/0.30 % (2753578)------------------------------
% 0.22/0.30 % (2753578)------------------------------
% 0.22/0.30 % (2753582)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (2753582)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.30 % (2753577)lrs+10_16_si=on:nwc=1.5:random_seed=347285900:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (2753576)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1970649457:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (2753580)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2582035413:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (2753579)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=2314523658: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)
% 0.22/0.30 % (2753581)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3261580333:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (2753582)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1034105786:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (2753588)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=723639661:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.30 % (2753577) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2753571-2753577"...
% 0.22/0.30 % (2753576) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2753571-2753576"...
% 0.22/0.30 % (2753588)Instruction limit reached!
% 0.22/0.30 % (2753588)------------------------------
% 0.22/0.30 % (2753588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2753588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2753588)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2753588)Termination reason: Instruction limit
% 0.22/0.30 % (2753588)Termination phase: Saturation
% 0.22/0.30 % (2753588)Time elapsed: 0.001 s
% 0.22/0.30 % (2753588)Peak memory usage: 12 MB
% 0.22/0.30 % (2753588)Instructions burned: 3 (million)
% 0.22/0.30 % (2753579) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2753571-2753579"...
% 0.22/0.30 % (2753581) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2753571-2753581"...
% 0.22/0.30 % (2753580)Instruction limit reached!
% 0.22/0.30 % (2753580)------------------------------
% 0.22/0.30 % (2753580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2753580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2753580)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2753580)Termination reason: Instruction limit
% 0.22/0.30 % (2753580)Termination phase: Saturation
% 0.22/0.30 % (2753580)Time elapsed: 0.010 s
% 0.22/0.30 % (2753580)Peak memory usage: 11 MB
% 0.22/0.30 % (2753580)Instructions burned: 24 (million)
% 0.22/0.30 % (2753582) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2753571-2753582"...
% 0.22/0.30 % (2753577)...printing done.
% 0.22/0.30 % (2753576)...printing done.
% 0.22/0.30 % (2753577)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (2753577)------------------------------
% 0.22/0.30 % (2753577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2753577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2753577)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2753577)Termination reason: Refutation
% 0.22/0.30 % (2753577)Time elapsed: 0.012 s
% 0.22/0.30 % (2753577)Peak memory usage: 13 MB
% 0.22/0.30 % (2753577)Instructions burned: 24 (million)
% 0.22/0.30 % (2753571)Success in time 0.047 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------