%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET623^5 : 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 : 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 08:23:24 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 7
% Syntax : Number of formulae : 170 ( 17 unt; 0 typ; 6 def)
% Number of atoms : 2291 ( 521 equ; 0 cnn)
% Maximal formula atoms : 6 ( 13 avg)
% Number of connectives : 3126 ( 645 ~; 655 |; 538 &;1282 @)
% ( 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,
vNOT: $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
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,X2: a > $o,X1: a > $o] :
( ( ^ [X3: a] :
( ( ~ ( X0 @ X3 )
& ( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) ) )
| ( ( X0 @ X3 )
& ~ ( ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ) )
= ( ^ [X3: a] :
( ( ~ ( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_99_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ^ [X3: a] :
( ( ~ ( X0 @ X3 )
& ( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) ) )
| ( ( X0 @ X3 )
& ~ ( ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ) )
= ( ^ [X3: a] :
( ( ~ ( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( ( ( X0 @ X3 )
& ~ ( X1 @ 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] :
( ( ~ ( X0 @ X3 )
& ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) ) )
| ( ( X0 @ X3 )
& ~ ( ( ( X2 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) ) ) ) )
= ( ^ [X4: a] :
( ( ~ ( ( ~ ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ( X2 @ X4 )
& ~ ( X0 @ X4 ) ) )
& ( X1 @ X4 ) )
| ( ~ ( X1 @ X4 )
& ( ( ( X0 @ X4 )
& ~ ( X2 @ X4 ) )
| ( ( X2 @ X4 )
& ~ ( X0 @ X4 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) ) )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) ) ) )
= ( ^ [Y0: a] :
( ( ~ ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
& ( X0 @ Y0 ) )
| ( ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
& ~ ( X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) ) )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
& ( X0 @ Y0 ) )
| ( ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
& ~ ( X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
& ( X0 @ Y0 ) )
| ( ( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) )
& ~ ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( ~ ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK0 @ Y0 ) )
| ( ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ~ ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK0 @ Y0 ) )
| ( ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( ( ^ [Y0: a] :
( ( ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ~ ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK0 @ Y0 ) )
| ( ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f19,plain,
( ( ( ^ [Y0: a] :
( ( ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
@ sK3 )
= $true )
| ( $true
= ( ^ [Y0: a] :
( ( ~ ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK0 @ Y0 ) )
| ( ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( ( ^ [Y0: a] :
( ( ~ ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK0 @ Y0 ) )
| ( ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) ) )
@ sK3 )
= $false )
| ( ( ^ [Y0: a] :
( ( ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
@ sK3 )
= $false ) ),
inference(xor_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $false )
| ( ( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
( ( ( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
= $false )
| ( ( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f21]) ).
thf(f24,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f25]) ).
thf(f28,plain,
( ( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f56,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f30]) ).
thf(f69,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f70,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f72]) ).
thf(f79,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f26]) ).
thf(f80,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f79]) ).
thf(f117,plain,
( ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f119,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f117]) ).
thf(f120,plain,
( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f119]) ).
thf(f121,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f120]) ).
thf(f122,plain,
( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f121]) ).
thf(f124,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f122]) ).
thf(f125,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f125]) ).
thf(f130,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f126]) ).
thf(f131,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f130]) ).
thf(f132,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f131]) ).
thf(f155,plain,
( ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f156,plain,
( ( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f157,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $false )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $false )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f161,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f170,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f165]) ).
thf(f171,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f171]) ).
thf(f185,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f186,plain,
( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f188,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f189,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f192]) ).
thf(f203,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f193]) ).
thf(f204,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f204]) ).
thf(f227,plain,
( ( $true
= ( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) )
| ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f228,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f229,plain,
( ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f228]) ).
thf(f232,plain,
( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f230]) ).
thf(f233,plain,
( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f234,plain,
( ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( $true
= ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f237,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f238,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f238]) ).
thf(f241,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f239]) ).
thf(f242,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f272,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f244]) ).
thf(f273,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f272]) ).
thf(f274,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f273]) ).
thf(f290,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f291,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f290]) ).
thf(f393,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f234]) ).
thf(f394,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f393]) ).
thf(f463,plain,
( ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f394]) ).
thf(f517,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f463]) ).
thf(f518,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f517]) ).
thf(f520,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f518]) ).
thf(f522,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f520]) ).
thf(f523,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f522]) ).
thf(f602,plain,
( ( ( ~ ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f229]) ).
thf(f603,plain,
( ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f602]) ).
thf(f604,plain,
( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f603]) ).
thf(f605,plain,
( ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f603]) ).
thf(f606,plain,
( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f605]) ).
thf(f607,plain,
( ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f606]) ).
thf(f1124,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f607]) ).
thf(f1125,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1124]) ).
thf(f1176,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1125]) ).
thf(f1177,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f1176]) ).
thf(f1178,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f1177]) ).
thf(f1179,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f1178]) ).
thf(f1200,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1179]) ).
thf(f1218,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f1200]) ).
thf(f1219,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f1218]) ).
thf(f1220,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f1219]) ).
thf(f1318,plain,
( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f604]) ).
thf(f1408,plain,
( ( $true
= ( ( ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1318]) ).
thf(f1409,plain,
( ( ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( sK2 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1408]) ).
thf(f1458,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $false )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f1409]) ).
thf(f1459,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f1458]) ).
thf(f1460,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1459]) ).
thf(f1461,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK2 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f1460]) ).
thf(f1463,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f1461]) ).
thf(f1464,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f1463]) ).
thf(f1465,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f1464]) ).
thf(f1466,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f1465]) ).
thf(f1467,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f1466]) ).
thf(f1503,definition,
( spl4_1
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f1505,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f1503]) ).
thf(f1507,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f1509,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f1507]) ).
thf(f1511,definition,
( spl4_3
<=> ( ( sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f1513,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f1511]) ).
thf(f1514,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f73,f1511,f1507,f1503]) ).
thf(f1516,definition,
( spl4_4
<=> ( ( sK2 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f1518,plain,
( ( ( sK2 @ sK3 )
= $false )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f1516]) ).
thf(f1520,definition,
( spl4_5
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f1522,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f1520]) ).
thf(f1523,plain,
( spl4_4
| spl4_3
| spl4_5 ),
inference(avatar_split_clause,[],[f132,f1520,f1511,f1516]) ).
thf(f1525,definition,
( spl4_6
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f1527,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f1525]) ).
thf(f1528,plain,
( spl4_5
| spl4_6
| spl4_1 ),
inference(avatar_split_clause,[],[f172,f1503,f1525,f1520]) ).
thf(f1529,plain,
( spl4_2
| spl4_6
| spl4_4 ),
inference(avatar_split_clause,[],[f205,f1516,f1525,f1507]) ).
thf(f1530,plain,
( spl4_1
| spl4_3
| spl4_5 ),
inference(avatar_split_clause,[],[f291,f1520,f1511,f1503]) ).
thf(f1531,plain,
( spl4_6
| spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f523,f1507,f1503,f1525]) ).
thf(f1532,plain,
( spl4_4
| spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f1220,f1520,f1525,f1516]) ).
thf(f1533,plain,
( spl4_4
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f1467,f1511,f1507,f1516]) ).
thf(f1534,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_demodulation,[],[f1522,f1509]) ).
thf(f1535,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f1534]) ).
thf(f1536,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f1535]) ).
thf(f1538,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4 ),
inference(forward_demodulation,[],[f1518,f1505]) ).
thf(f1539,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f1538]) ).
thf(f1540,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f1539]) ).
thf(f1542,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f1513,f1527]) ).
thf(f1543,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f1542]) ).
thf(f1544,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f1543]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f1514]) ).
cnf(s2,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f1523]) ).
cnf(s3,plain,
( spl4_1
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f1528]) ).
cnf(s4,plain,
( spl4_2
| spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f1529]) ).
cnf(s5,plain,
( spl4_1
| spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f1530]) ).
cnf(s6,plain,
( spl4_1
| spl4_2
| spl4_6 ),
inference(sat_conversion,[],[f1531]) ).
cnf(s7,plain,
( spl4_4
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f1532]) ).
cnf(s8,plain,
( spl4_2
| spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f1533]) ).
cnf(s9,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f1536]) ).
cnf(s10,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f1540]) ).
cnf(s11,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f1544]) ).
cnf(s12,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s11,s1,s6]) ).
cnf(s13,plain,
( spl4_5
| spl4_1 ),
inference(rat,[],[s11,s5,s3]) ).
cnf(s14,plain,
spl4_1,
inference(rat,[],[s13,s9,s12]) ).
cnf(s15,plain,
~ spl4_4,
inference(rat,[],[s10,s14]) ).
cnf(s16,plain,
spl4_6,
inference(rat,[],[s9,s4,s7,s15]) ).
cnf(s17,plain,
~ spl4_3,
inference(rat,[],[s11,s16]) ).
cnf(s18,plain,
spl4_5,
inference(rat,[],[s2,s15,s17]) ).
cnf(s19,plain,
spl4_2,
inference(rat,[],[s8,s15,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s9,s18,s19]) ).
thf(f1545,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET623^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n005.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:39:31 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.26 % (1677239)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.26 % (1677256)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.26 % (1677256)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
% 0.18/0.26 % (1677256)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=1874044786:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.18/0.26 % (1677256) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1677239-1677256"...
% 0.18/0.26 % (1677250)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3623538143:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.26 % (1677251)lrs+10_16_si=on:nwc=1.5:random_seed=2057230550:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.26 % (1677252)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3742655778:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.26 % (1677255)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=787983605:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.18/0.26 % (1677253)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=2490428168: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)
% 0.18/0.26 % (1677254)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3203326605:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.26 % (1677252)Refutation not found, incomplete strategy
% 0.18/0.26 % (1677252)------------------------------
% 0.18/0.26 % (1677252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (1677252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (1677252)CaDiCaL version: 2.1.3
% 0.18/0.26 % (1677252)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.26 % (1677252)Time elapsed: 0.002 s
% 0.18/0.26 % (1677252)Peak memory usage: 12 MB
% 0.18/0.26 % (1677252)Instructions burned: 2 (million)
% 0.18/0.26 % (1677252)------------------------------
% 0.18/0.26 % (1677252)------------------------------
% 0.18/0.26 % (1677256)...printing done.
% 0.18/0.26 % (1677256)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.26 % (1677256)------------------------------
% 0.18/0.26 % (1677256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (1677256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (1677256)CaDiCaL version: 2.1.3
% 0.18/0.26 % (1677256)Termination reason: Refutation
% 0.18/0.26 % (1677256)Time elapsed: 0.010 s
% 0.18/0.26 % (1677256)Peak memory usage: 13 MB
% 0.18/0.26 % (1677256)Instructions burned: 40 (million)
% 0.18/0.26 % (1677239)Success in time 0.036 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------