%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO249^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:53:46 AM UTC 2026
% Result : Theorem 1.80s 1.69s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 94 ( 5 unt; 0 typ; 11 def)
% Number of atoms : 1960 ( 526 equ; 0 cnn)
% Maximal formula atoms : 75 ( 20 avg)
% Number of connectives : 2521 ( 334 ~; 326 |; 244 &;1539 @)
% ( 23 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 15 con; 0-2 aty)
% Number of variables : 290 ( 0 ^; 264 !; 26 ?; 290 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cBIGPHI: $i > $i ).
thf(func_def_1,type,
cHOM_FROM_HH_1: ( $i > $i ) > $o ).
thf(func_def_2,type,
cPHI_2: $i > $i ).
thf(func_def_3,type,
cHOM_FROM_SS_PRIME: ( $i > $i ) > $o ).
thf(func_def_4,type,
cPHI_1: $i > $i ).
thf(func_def_5,type,
cSS_PRIME: $i > $o ).
thf(func_def_6,type,
el1: $i > ( $i > $o ) > $o ).
thf(func_def_7,type,
cHH_1: $i > $o ).
thf(func_def_8,type,
cBIGHI: $i > $i ).
thf(func_def_9,type,
cHH_2: $i > $o ).
thf(func_def_10,type,
cTIMES: $i > $i > $i ).
thf(func_def_14,type,
sK0: ( $i > $i ) > $i ).
thf(func_def_15,type,
sK1: ( $i > $i ) > $i ).
thf(func_def_16,type,
sK2: $i > $i ).
thf(func_def_20,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f1204,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f53,f58,f59,f64,f177,f182,f208,f226,f351,f420,f1090,f1198]) ).
thf(f1198,plain,
( spl5_1
| ~ spl5_4
| ~ spl5_7
| ~ spl5_11
| ~ spl5_19
| ~ spl5_32
| ~ spl5_82 ),
inference(avatar_split_clause,[status(thm)],[f1197,f1051,f418,f349,f199,f179,f61,f46]) ).
thf(f46,definition,
( spl5_1
<=> ( ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) )
= ( cBIGPHI @ ( cTIMES @ sK4 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f61,definition,
( spl5_4
<=> ( ( el1 @ sK4 @ cHH_1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f179,definition,
( spl5_7
<=> ( ( cBIGPHI @ sK4 )
= ( cPHI_2 @ ( sK2 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition]) ).
thf(f199,definition,
( spl5_11
<=> ( ( el1 @ ( sK2 @ sK4 ) @ cSS_PRIME )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_11])],[avatar_definition]) ).
thf(f349,definition,
( spl5_19
<=> ! [X0: $i] :
( ( ( cTIMES @ ( cPHI_2 @ X0 ) @ ( cBIGPHI @ sK3 ) )
= ( cPHI_2 @ ( cTIMES @ X0 @ ( sK2 @ sK3 ) ) ) )
| ( ( el1 @ X0 @ cSS_PRIME )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_19])],[avatar_definition]) ).
thf(f418,definition,
( spl5_32
<=> ! [X0: $i] :
( ( ( cPHI_1 @ ( cTIMES @ X0 @ ( sK2 @ sK3 ) ) )
= ( cTIMES @ ( cPHI_1 @ X0 ) @ sK3 ) )
| ( ( el1 @ X0 @ cSS_PRIME )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_32])],[avatar_definition]) ).
thf(f1051,definition,
( spl5_82
<=> ( ( el1 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) @ cSS_PRIME )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_82])],[avatar_definition]) ).
thf(f1197,plain,
( ( ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) )
= ( cBIGPHI @ ( cTIMES @ sK4 @ sK3 ) ) )
| ~ spl5_4
| ~ spl5_7
| ~ spl5_11
| ~ spl5_19
| ~ spl5_32
| ~ spl5_82 ),
inference(forward_demodulation,[status(thm)],[f1196,f82]) ).
thf(f82,plain,
( ( ( cPHI_1 @ ( sK2 @ sK4 ) )
= sK4 )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $true != $true )
| ( ( cPHI_1 @ ( sK2 @ sK4 ) )
= sK4 )
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f26,f63]) ).
thf(f63,plain,
( ( ( el1 @ sK4 @ cHH_1 )
= $true )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f26,plain,
! [X14: $i] :
( ( $true
!= ( el1 @ X14 @ cHH_1 ) )
| ( ( cPHI_1 @ ( sK2 @ X14 ) )
= X14 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i] :
( ( ( el1 @ ( cBIGPHI @ X0 ) @ cHH_2 )
= $true )
| ( ( el1 @ X0 @ cHH_1 )
!= $true ) )
& ! [X1: $i,X2: $i] :
( ( ( cBIGPHI @ X2 )
= ( cBIGHI @ X1 ) )
| ( X1 != X2 )
| ( ( el1 @ X1 @ cHH_1 )
!= $true )
| ( ( el1 @ X2 @ cHH_1 )
!= $true ) )
& ! [X3: $i > $i] :
( ( ! [X4: $i,X5: $i] :
( ( ( el1 @ X4 @ cSS_PRIME )
!= $true )
| ( ( el1 @ X5 @ cSS_PRIME )
!= $true )
| ( ( X3 @ ( cTIMES @ X4 @ X5 ) )
= ( cTIMES @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) ) )
| ( ( cHOM_FROM_SS_PRIME @ X3 )
!= $true ) )
& ( ( ( cHOM_FROM_SS_PRIME @ X3 )
= $true )
| ( ( ( el1 @ ( sK0 @ X3 ) @ cSS_PRIME )
= $true )
& ( ( el1 @ ( sK1 @ X3 ) @ cSS_PRIME )
= $true )
& ( ( cTIMES @ ( X3 @ ( sK0 @ X3 ) ) @ ( X3 @ ( sK1 @ X3 ) ) )
!= ( X3 @ ( cTIMES @ ( sK0 @ X3 ) @ ( sK1 @ X3 ) ) ) ) ) ) )
& ! [X8: $i] :
( ( ( el1 @ ( cPHI_2 @ X8 ) @ cHH_2 )
= $true )
| ( $true
!= ( el1 @ X8 @ cSS_PRIME ) ) )
& ! [X9: $i,X10: $i,X11: $i,X12: $i] :
( ( ( el1 @ X10 @ cHH_2 )
!= $true )
| ( ( cTIMES @ X12 @ X11 )
= ( cTIMES @ X10 @ X9 ) )
| ( ( el1 @ X11 @ cHH_2 )
!= $true )
| ( ( el1 @ X12 @ cHH_2 )
!= $true )
| ( $true
!= ( el1 @ X9 @ cHH_2 ) )
| ( X10 != X12 )
| ( X9 != X11 ) )
& ! [X13: $i] :
( ( ( el1 @ X13 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cPHI_1 @ X13 ) @ cHH_1 )
= $true ) )
& ! [X14: $i] :
( ( $true
!= ( el1 @ X14 @ cHH_1 ) )
| ( ( ( el1 @ ( sK2 @ X14 ) @ cSS_PRIME )
= $true )
& ( ( cPHI_1 @ ( sK2 @ X14 ) )
= X14 ) ) )
& ! [X16: $i,X17: $i] :
( ( ( el1 @ X16 @ cHH_1 )
!= $true )
| ( ( el1 @ X17 @ cHH_1 )
!= $true )
| ( ( el1 @ ( cTIMES @ X16 @ X17 ) @ cHH_1 )
= $true ) )
& ( ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true )
| ( ( ( el1 @ sK4 @ cHH_1 )
= $true )
& ( ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) )
!= ( cBIGPHI @ ( cTIMES @ sK4 @ sK3 ) ) )
& ( ( el1 @ sK3 @ cHH_1 )
= $true ) ) )
& ( ! [X20: $i,X21: $i] :
( ( $true
!= ( el1 @ X21 @ cHH_1 ) )
| ( ( cTIMES @ ( cBIGPHI @ X21 ) @ ( cBIGPHI @ X20 ) )
= ( cBIGPHI @ ( cTIMES @ X21 @ X20 ) ) )
| ( ( el1 @ X20 @ cHH_1 )
!= $true ) )
| ( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true ) )
& ! [X22: $i,X23: $i,X24: $i,X25: $i] :
( ( X24 != X25 )
| ( ( el1 @ X24 @ cHH_1 )
!= $true )
| ( ( el1 @ X22 @ cHH_1 )
!= $true )
| ( ( cTIMES @ X24 @ X23 )
= ( cTIMES @ X25 @ X22 ) )
| ( X22 != X23 )
| ( ( el1 @ X25 @ cHH_1 )
!= $true )
| ( $true
!= ( el1 @ X23 @ cHH_1 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_1 )
= $true )
& ! [X26: $i] :
( ( ( el1 @ X26 @ cSS_PRIME )
!= $true )
| ( ( cBIGPHI @ ( cPHI_1 @ X26 ) )
= ( cPHI_2 @ X26 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_2 )
= $true )
& ! [X27: $i,X28: $i] :
( ( ( el1 @ X28 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cTIMES @ X28 @ X27 ) @ cSS_PRIME )
= $true )
| ( ( el1 @ X27 @ cSS_PRIME )
!= $true ) )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f10,f13,f12,f11]) ).
thf(f11,plain,
! [X3: $i > $i] :
( ? [X6: $i,X7: $i] :
( ( ( el1 @ X6 @ cSS_PRIME )
= $true )
& ( ( el1 @ X7 @ cSS_PRIME )
= $true )
& ( ( X3 @ ( cTIMES @ X6 @ X7 ) )
!= ( cTIMES @ ( X3 @ X6 ) @ ( X3 @ X7 ) ) ) )
=> ( ( ( el1 @ ( sK0 @ X3 ) @ cSS_PRIME )
= $true )
& ( ( el1 @ ( sK1 @ X3 ) @ cSS_PRIME )
= $true )
& ( ( cTIMES @ ( X3 @ ( sK0 @ X3 ) ) @ ( X3 @ ( sK1 @ X3 ) ) )
!= ( X3 @ ( cTIMES @ ( sK0 @ X3 ) @ ( sK1 @ X3 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X14: $i] :
( ? [X15: $i] :
( ( ( el1 @ X15 @ cSS_PRIME )
= $true )
& ( ( cPHI_1 @ X15 )
= X14 ) )
=> ( ( ( el1 @ ( sK2 @ X14 ) @ cSS_PRIME )
= $true )
& ( ( cPHI_1 @ ( sK2 @ X14 ) )
= X14 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X18: $i,X19: $i] :
( ( ( el1 @ X19 @ cHH_1 )
= $true )
& ( ( cBIGPHI @ ( cTIMES @ X19 @ X18 ) )
!= ( cTIMES @ ( cBIGPHI @ X19 ) @ ( cBIGPHI @ X18 ) ) )
& ( ( el1 @ X18 @ cHH_1 )
= $true ) )
=> ( ( ( el1 @ sK4 @ cHH_1 )
= $true )
& ( ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) )
!= ( cBIGPHI @ ( cTIMES @ sK4 @ sK3 ) ) )
& ( ( el1 @ sK3 @ cHH_1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ! [X0: $i] :
( ( ( el1 @ ( cBIGPHI @ X0 ) @ cHH_2 )
= $true )
| ( ( el1 @ X0 @ cHH_1 )
!= $true ) )
& ! [X1: $i,X2: $i] :
( ( ( cBIGPHI @ X2 )
= ( cBIGHI @ X1 ) )
| ( X1 != X2 )
| ( ( el1 @ X1 @ cHH_1 )
!= $true )
| ( ( el1 @ X2 @ cHH_1 )
!= $true ) )
& ! [X3: $i > $i] :
( ( ! [X4: $i,X5: $i] :
( ( ( el1 @ X4 @ cSS_PRIME )
!= $true )
| ( ( el1 @ X5 @ cSS_PRIME )
!= $true )
| ( ( X3 @ ( cTIMES @ X4 @ X5 ) )
= ( cTIMES @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) ) )
| ( ( cHOM_FROM_SS_PRIME @ X3 )
!= $true ) )
& ( ( ( cHOM_FROM_SS_PRIME @ X3 )
= $true )
| ? [X6: $i,X7: $i] :
( ( ( el1 @ X6 @ cSS_PRIME )
= $true )
& ( ( el1 @ X7 @ cSS_PRIME )
= $true )
& ( ( X3 @ ( cTIMES @ X6 @ X7 ) )
!= ( cTIMES @ ( X3 @ X6 ) @ ( X3 @ X7 ) ) ) ) ) )
& ! [X8: $i] :
( ( ( el1 @ ( cPHI_2 @ X8 ) @ cHH_2 )
= $true )
| ( $true
!= ( el1 @ X8 @ cSS_PRIME ) ) )
& ! [X9: $i,X10: $i,X11: $i,X12: $i] :
( ( ( el1 @ X10 @ cHH_2 )
!= $true )
| ( ( cTIMES @ X12 @ X11 )
= ( cTIMES @ X10 @ X9 ) )
| ( ( el1 @ X11 @ cHH_2 )
!= $true )
| ( ( el1 @ X12 @ cHH_2 )
!= $true )
| ( $true
!= ( el1 @ X9 @ cHH_2 ) )
| ( X10 != X12 )
| ( X9 != X11 ) )
& ! [X13: $i] :
( ( ( el1 @ X13 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cPHI_1 @ X13 ) @ cHH_1 )
= $true ) )
& ! [X14: $i] :
( ( $true
!= ( el1 @ X14 @ cHH_1 ) )
| ? [X15: $i] :
( ( ( el1 @ X15 @ cSS_PRIME )
= $true )
& ( ( cPHI_1 @ X15 )
= X14 ) ) )
& ! [X16: $i,X17: $i] :
( ( ( el1 @ X16 @ cHH_1 )
!= $true )
| ( ( el1 @ X17 @ cHH_1 )
!= $true )
| ( ( el1 @ ( cTIMES @ X16 @ X17 ) @ cHH_1 )
= $true ) )
& ( ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true )
| ? [X18: $i,X19: $i] :
( ( ( el1 @ X19 @ cHH_1 )
= $true )
& ( ( cBIGPHI @ ( cTIMES @ X19 @ X18 ) )
!= ( cTIMES @ ( cBIGPHI @ X19 ) @ ( cBIGPHI @ X18 ) ) )
& ( ( el1 @ X18 @ cHH_1 )
= $true ) ) )
& ( ! [X20: $i,X21: $i] :
( ( $true
!= ( el1 @ X21 @ cHH_1 ) )
| ( ( cTIMES @ ( cBIGPHI @ X21 ) @ ( cBIGPHI @ X20 ) )
= ( cBIGPHI @ ( cTIMES @ X21 @ X20 ) ) )
| ( ( el1 @ X20 @ cHH_1 )
!= $true ) )
| ( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true ) )
& ! [X22: $i,X23: $i,X24: $i,X25: $i] :
( ( X24 != X25 )
| ( ( el1 @ X24 @ cHH_1 )
!= $true )
| ( ( el1 @ X22 @ cHH_1 )
!= $true )
| ( ( cTIMES @ X24 @ X23 )
= ( cTIMES @ X25 @ X22 ) )
| ( X22 != X23 )
| ( ( el1 @ X25 @ cHH_1 )
!= $true )
| ( $true
!= ( el1 @ X23 @ cHH_1 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_1 )
= $true )
& ! [X26: $i] :
( ( ( el1 @ X26 @ cSS_PRIME )
!= $true )
| ( ( cBIGPHI @ ( cPHI_1 @ X26 ) )
= ( cPHI_2 @ X26 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_2 )
= $true )
& ! [X27: $i,X28: $i] :
( ( ( el1 @ X28 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cTIMES @ X28 @ X27 ) @ cSS_PRIME )
= $true )
| ( ( el1 @ X27 @ cSS_PRIME )
!= $true ) )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X20: $i] :
( ( ( el1 @ ( cBIGPHI @ X20 ) @ cHH_2 )
= $true )
| ( ( el1 @ X20 @ cHH_1 )
!= $true ) )
& ! [X12: $i,X13: $i] :
( ( ( cBIGHI @ X12 )
= ( cBIGPHI @ X13 ) )
| ( X12 != X13 )
| ( $true
!= ( el1 @ X12 @ cHH_1 ) )
| ( $true
!= ( el1 @ X13 @ cHH_1 ) ) )
& ! [X14: $i > $i] :
( ( ! [X15: $i,X16: $i] :
( ( ( el1 @ X15 @ cSS_PRIME )
!= $true )
| ( ( el1 @ X16 @ cSS_PRIME )
!= $true )
| ( ( cTIMES @ ( X14 @ X15 ) @ ( X14 @ X16 ) )
= ( X14 @ ( cTIMES @ X15 @ X16 ) ) ) )
| ( $true
!= ( cHOM_FROM_SS_PRIME @ X14 ) ) )
& ( ( $true
= ( cHOM_FROM_SS_PRIME @ X14 ) )
| ? [X15: $i,X16: $i] :
( ( ( el1 @ X15 @ cSS_PRIME )
= $true )
& ( ( el1 @ X16 @ cSS_PRIME )
= $true )
& ( ( cTIMES @ ( X14 @ X15 ) @ ( X14 @ X16 ) )
!= ( X14 @ ( cTIMES @ X15 @ X16 ) ) ) ) ) )
& ! [X7: $i] :
( ( ( el1 @ ( cPHI_2 @ X7 ) @ cHH_2 )
= $true )
| ( ( el1 @ X7 @ cSS_PRIME )
!= $true ) )
& ! [X9: $i,X8: $i,X10: $i,X11: $i] :
( ( ( el1 @ X8 @ cHH_2 )
!= $true )
| ( ( cTIMES @ X11 @ X10 )
= ( cTIMES @ X8 @ X9 ) )
| ( ( el1 @ X10 @ cHH_2 )
!= $true )
| ( ( el1 @ X11 @ cHH_2 )
!= $true )
| ( $true
!= ( el1 @ X9 @ cHH_2 ) )
| ( X8 != X11 )
| ( X9 != X10 ) )
& ! [X17: $i] :
( ( ( el1 @ X17 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cPHI_1 @ X17 ) @ cHH_1 )
= $true ) )
& ! [X2: $i] :
( ( ( el1 @ X2 @ cHH_1 )
!= $true )
| ? [X3: $i] :
( ( ( el1 @ X3 @ cSS_PRIME )
= $true )
& ( ( cPHI_1 @ X3 )
= X2 ) ) )
& ! [X0: $i,X1: $i] :
( ( ( el1 @ X0 @ cHH_1 )
!= $true )
| ( ( el1 @ X1 @ cHH_1 )
!= $true )
| ( $true
= ( el1 @ ( cTIMES @ X0 @ X1 ) @ cHH_1 ) ) )
& ( ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true )
| ? [X5: $i,X6: $i] :
( ( ( el1 @ X6 @ cHH_1 )
= $true )
& ( ( cBIGPHI @ ( cTIMES @ X6 @ X5 ) )
!= ( cTIMES @ ( cBIGPHI @ X6 ) @ ( cBIGPHI @ X5 ) ) )
& ( ( el1 @ X5 @ cHH_1 )
= $true ) ) )
& ( ! [X5: $i,X6: $i] :
( ( ( el1 @ X6 @ cHH_1 )
!= $true )
| ( ( cBIGPHI @ ( cTIMES @ X6 @ X5 ) )
= ( cTIMES @ ( cBIGPHI @ X6 ) @ ( cBIGPHI @ X5 ) ) )
| ( ( el1 @ X5 @ cHH_1 )
!= $true ) )
| ( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true ) )
& ! [X21: $i,X23: $i,X24: $i,X22: $i] :
( ( X22 != X24 )
| ( ( el1 @ X24 @ cHH_1 )
!= $true )
| ( $true
!= ( el1 @ X21 @ cHH_1 ) )
| ( ( cTIMES @ X24 @ X23 )
= ( cTIMES @ X22 @ X21 ) )
| ( X21 != X23 )
| ( ( el1 @ X22 @ cHH_1 )
!= $true )
| ( $true
!= ( el1 @ X23 @ cHH_1 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_1 )
= $true )
& ! [X4: $i] :
( ( ( el1 @ X4 @ cSS_PRIME )
!= $true )
| ( ( cBIGPHI @ ( cPHI_1 @ X4 ) )
= ( cPHI_2 @ X4 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_2 )
= $true )
& ! [X18: $i,X19: $i] :
( ( ( el1 @ X19 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cTIMES @ X19 @ X18 ) @ cSS_PRIME )
= $true )
| ( ( el1 @ X18 @ cSS_PRIME )
!= $true ) )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X20: $i] :
( ( ( el1 @ ( cBIGPHI @ X20 ) @ cHH_2 )
= $true )
| ( ( el1 @ X20 @ cHH_1 )
!= $true ) )
& ! [X12: $i,X13: $i] :
( ( ( cBIGHI @ X12 )
= ( cBIGPHI @ X13 ) )
| ( X12 != X13 )
| ( $true
!= ( el1 @ X12 @ cHH_1 ) )
| ( $true
!= ( el1 @ X13 @ cHH_1 ) ) )
& ! [X14: $i > $i] :
( ( ! [X15: $i,X16: $i] :
( ( ( el1 @ X15 @ cSS_PRIME )
!= $true )
| ( ( el1 @ X16 @ cSS_PRIME )
!= $true )
| ( ( cTIMES @ ( X14 @ X15 ) @ ( X14 @ X16 ) )
= ( X14 @ ( cTIMES @ X15 @ X16 ) ) ) )
| ( $true
!= ( cHOM_FROM_SS_PRIME @ X14 ) ) )
& ( ( $true
= ( cHOM_FROM_SS_PRIME @ X14 ) )
| ? [X15: $i,X16: $i] :
( ( ( el1 @ X15 @ cSS_PRIME )
= $true )
& ( ( el1 @ X16 @ cSS_PRIME )
= $true )
& ( ( cTIMES @ ( X14 @ X15 ) @ ( X14 @ X16 ) )
!= ( X14 @ ( cTIMES @ X15 @ X16 ) ) ) ) ) )
& ! [X7: $i] :
( ( ( el1 @ ( cPHI_2 @ X7 ) @ cHH_2 )
= $true )
| ( ( el1 @ X7 @ cSS_PRIME )
!= $true ) )
& ! [X9: $i,X8: $i,X10: $i,X11: $i] :
( ( ( el1 @ X8 @ cHH_2 )
!= $true )
| ( ( cTIMES @ X11 @ X10 )
= ( cTIMES @ X8 @ X9 ) )
| ( ( el1 @ X10 @ cHH_2 )
!= $true )
| ( ( el1 @ X11 @ cHH_2 )
!= $true )
| ( $true
!= ( el1 @ X9 @ cHH_2 ) )
| ( X8 != X11 )
| ( X9 != X10 ) )
& ! [X17: $i] :
( ( ( el1 @ X17 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cPHI_1 @ X17 ) @ cHH_1 )
= $true ) )
& ! [X2: $i] :
( ( ( el1 @ X2 @ cHH_1 )
!= $true )
| ? [X3: $i] :
( ( ( el1 @ X3 @ cSS_PRIME )
= $true )
& ( ( cPHI_1 @ X3 )
= X2 ) ) )
& ! [X0: $i,X1: $i] :
( ( ( el1 @ X0 @ cHH_1 )
!= $true )
| ( ( el1 @ X1 @ cHH_1 )
!= $true )
| ( $true
= ( el1 @ ( cTIMES @ X0 @ X1 ) @ cHH_1 ) ) )
& ( ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true )
| ? [X5: $i,X6: $i] :
( ( ( el1 @ X6 @ cHH_1 )
= $true )
& ( ( cBIGPHI @ ( cTIMES @ X6 @ X5 ) )
!= ( cTIMES @ ( cBIGPHI @ X6 ) @ ( cBIGPHI @ X5 ) ) )
& ( ( el1 @ X5 @ cHH_1 )
= $true ) ) )
& ( ! [X5: $i,X6: $i] :
( ( ( el1 @ X6 @ cHH_1 )
!= $true )
| ( ( cBIGPHI @ ( cTIMES @ X6 @ X5 ) )
= ( cTIMES @ ( cBIGPHI @ X6 ) @ ( cBIGPHI @ X5 ) ) )
| ( ( el1 @ X5 @ cHH_1 )
!= $true ) )
| ( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true ) )
& ! [X21: $i,X23: $i,X24: $i,X22: $i] :
( ( X22 != X24 )
| ( ( el1 @ X24 @ cHH_1 )
!= $true )
| ( $true
!= ( el1 @ X21 @ cHH_1 ) )
| ( ( cTIMES @ X24 @ X23 )
= ( cTIMES @ X22 @ X21 ) )
| ( X21 != X23 )
| ( ( el1 @ X22 @ cHH_1 )
!= $true )
| ( $true
!= ( el1 @ X23 @ cHH_1 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_1 )
= $true )
& ! [X4: $i] :
( ( ( el1 @ X4 @ cSS_PRIME )
!= $true )
| ( ( cBIGPHI @ ( cPHI_1 @ X4 ) )
= ( cPHI_2 @ X4 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_2 )
= $true )
& ! [X18: $i,X19: $i] :
( ( ( el1 @ X19 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cTIMES @ X19 @ X18 ) @ cSS_PRIME )
= $true )
| ( ( el1 @ X18 @ cSS_PRIME )
!= $true ) )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X20: $i] :
( ( ( el1 @ ( cBIGPHI @ X20 ) @ cHH_2 )
= $true )
| ( ( el1 @ X20 @ cHH_1 )
!= $true ) )
& ! [X12: $i,X13: $i] :
( ( ( cBIGHI @ X12 )
= ( cBIGPHI @ X13 ) )
| ( X12 != X13 )
| ( $true
!= ( el1 @ X12 @ cHH_1 ) )
| ( $true
!= ( el1 @ X13 @ cHH_1 ) ) )
& ! [X14: $i > $i] :
( ! [X15: $i,X16: $i] :
( ( ( el1 @ X15 @ cSS_PRIME )
!= $true )
| ( ( el1 @ X16 @ cSS_PRIME )
!= $true )
| ( ( cTIMES @ ( X14 @ X15 ) @ ( X14 @ X16 ) )
= ( X14 @ ( cTIMES @ X15 @ X16 ) ) ) )
<=> ( $true
= ( cHOM_FROM_SS_PRIME @ X14 ) ) )
& ! [X7: $i] :
( ( ( el1 @ ( cPHI_2 @ X7 ) @ cHH_2 )
= $true )
| ( ( el1 @ X7 @ cSS_PRIME )
!= $true ) )
& ! [X9: $i,X8: $i,X10: $i,X11: $i] :
( ( ( el1 @ X8 @ cHH_2 )
!= $true )
| ( ( cTIMES @ X11 @ X10 )
= ( cTIMES @ X8 @ X9 ) )
| ( ( el1 @ X10 @ cHH_2 )
!= $true )
| ( ( el1 @ X11 @ cHH_2 )
!= $true )
| ( $true
!= ( el1 @ X9 @ cHH_2 ) )
| ( X8 != X11 )
| ( X9 != X10 ) )
& ! [X17: $i] :
( ( ( el1 @ X17 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cPHI_1 @ X17 ) @ cHH_1 )
= $true ) )
& ! [X2: $i] :
( ( ( el1 @ X2 @ cHH_1 )
!= $true )
| ? [X3: $i] :
( ( ( el1 @ X3 @ cSS_PRIME )
= $true )
& ( ( cPHI_1 @ X3 )
= X2 ) ) )
& ! [X0: $i,X1: $i] :
( ( ( el1 @ X0 @ cHH_1 )
!= $true )
| ( ( el1 @ X1 @ cHH_1 )
!= $true )
| ( $true
= ( el1 @ ( cTIMES @ X0 @ X1 ) @ cHH_1 ) ) )
& ( ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true )
<=> ! [X5: $i,X6: $i] :
( ( ( el1 @ X6 @ cHH_1 )
!= $true )
| ( ( cBIGPHI @ ( cTIMES @ X6 @ X5 ) )
= ( cTIMES @ ( cBIGPHI @ X6 ) @ ( cBIGPHI @ X5 ) ) )
| ( ( el1 @ X5 @ cHH_1 )
!= $true ) ) )
& ! [X21: $i,X23: $i,X24: $i,X22: $i] :
( ( X22 != X24 )
| ( ( el1 @ X24 @ cHH_1 )
!= $true )
| ( $true
!= ( el1 @ X21 @ cHH_1 ) )
| ( ( cTIMES @ X24 @ X23 )
= ( cTIMES @ X22 @ X21 ) )
| ( X21 != X23 )
| ( ( el1 @ X22 @ cHH_1 )
!= $true )
| ( $true
!= ( el1 @ X23 @ cHH_1 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_1 )
= $true )
& ! [X4: $i] :
( ( ( el1 @ X4 @ cSS_PRIME )
!= $true )
| ( ( cBIGPHI @ ( cPHI_1 @ X4 ) )
= ( cPHI_2 @ X4 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_2 )
= $true )
& ! [X18: $i,X19: $i] :
( ( ( el1 @ X19 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cTIMES @ X19 @ X18 ) @ cSS_PRIME )
= $true )
| ( ( el1 @ X18 @ cSS_PRIME )
!= $true ) )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true )
& ! [X19: $i,X18: $i] :
( ( ( el1 @ ( cTIMES @ X19 @ X18 ) @ cSS_PRIME )
= $true )
| ( ( el1 @ X18 @ cSS_PRIME )
!= $true )
| ( ( el1 @ X19 @ cSS_PRIME )
!= $true ) )
& ! [X22: $i,X24: $i,X23: $i,X21: $i] :
( ( ( cTIMES @ X24 @ X23 )
= ( cTIMES @ X22 @ X21 ) )
| ( X21 != X23 )
| ( X22 != X24 )
| ( ( el1 @ X24 @ cHH_1 )
!= $true )
| ( $true
!= ( el1 @ X21 @ cHH_1 ) )
| ( $true
!= ( el1 @ X23 @ cHH_1 ) )
| ( ( el1 @ X22 @ cHH_1 )
!= $true ) )
& ! [X20: $i] :
( ( ( el1 @ ( cBIGPHI @ X20 ) @ cHH_2 )
= $true )
| ( ( el1 @ X20 @ cHH_1 )
!= $true ) )
& ! [X7: $i] :
( ( ( el1 @ ( cPHI_2 @ X7 ) @ cHH_2 )
= $true )
| ( ( el1 @ X7 @ cSS_PRIME )
!= $true ) )
& ! [X17: $i] :
( ( ( el1 @ X17 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( cPHI_1 @ X17 ) @ cHH_1 )
= $true ) )
& ( ! [X6: $i,X5: $i] :
( ( ( cBIGPHI @ ( cTIMES @ X6 @ X5 ) )
= ( cTIMES @ ( cBIGPHI @ X6 ) @ ( cBIGPHI @ X5 ) ) )
| ( ( el1 @ X6 @ cHH_1 )
!= $true )
| ( ( el1 @ X5 @ cHH_1 )
!= $true ) )
<=> ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true ) )
& ! [X11: $i,X8: $i,X9: $i,X10: $i] :
( ( ( cTIMES @ X11 @ X10 )
= ( cTIMES @ X8 @ X9 ) )
| ( X9 != X10 )
| ( ( el1 @ X11 @ cHH_2 )
!= $true )
| ( $true
!= ( el1 @ X9 @ cHH_2 ) )
| ( ( el1 @ X10 @ cHH_2 )
!= $true )
| ( ( el1 @ X8 @ cHH_2 )
!= $true )
| ( X8 != X11 ) )
& ! [X4: $i] :
( ( ( el1 @ X4 @ cSS_PRIME )
!= $true )
| ( ( cBIGPHI @ ( cPHI_1 @ X4 ) )
= ( cPHI_2 @ X4 ) ) )
& ! [X2: $i] :
( ( ( el1 @ X2 @ cHH_1 )
!= $true )
| ? [X3: $i] :
( ( ( el1 @ X3 @ cSS_PRIME )
= $true )
& ( ( cPHI_1 @ X3 )
= X2 ) ) )
& ! [X14: $i > $i] :
( ! [X16: $i,X15: $i] :
( ( ( cTIMES @ ( X14 @ X15 ) @ ( X14 @ X16 ) )
= ( X14 @ ( cTIMES @ X15 @ X16 ) ) )
| ( ( el1 @ X16 @ cSS_PRIME )
!= $true )
| ( ( el1 @ X15 @ cSS_PRIME )
!= $true ) )
<=> ( $true
= ( cHOM_FROM_SS_PRIME @ X14 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_2 )
= $true )
& ! [X0: $i,X1: $i] :
( ( $true
= ( el1 @ ( cTIMES @ X0 @ X1 ) @ cHH_1 ) )
| ( ( el1 @ X1 @ cHH_1 )
!= $true )
| ( ( el1 @ X0 @ cHH_1 )
!= $true ) )
& ! [X12: $i,X13: $i] :
( ( ( cBIGHI @ X12 )
= ( cBIGPHI @ X13 ) )
| ( $true
!= ( el1 @ X13 @ cHH_1 ) )
| ( $true
!= ( el1 @ X12 @ cHH_1 ) )
| ( X12 != X13 ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X19: $i,X18: $i] :
( ( ( ( el1 @ X18 @ cSS_PRIME )
= $true )
& ( ( el1 @ X19 @ cSS_PRIME )
= $true ) )
=> ( ( el1 @ ( cTIMES @ X19 @ X18 ) @ cSS_PRIME )
= $true ) )
& ! [X22: $i,X24: $i,X23: $i,X21: $i] :
( ( ( X21 = X23 )
& ( X22 = X24 )
& ( ( el1 @ X24 @ cHH_1 )
= $true )
& ( $true
= ( el1 @ X21 @ cHH_1 ) )
& ( $true
= ( el1 @ X23 @ cHH_1 ) )
& ( ( el1 @ X22 @ cHH_1 )
= $true ) )
=> ( ( cTIMES @ X24 @ X23 )
= ( cTIMES @ X22 @ X21 ) ) )
& ! [X20: $i] :
( ( ( el1 @ X20 @ cHH_1 )
= $true )
=> ( ( el1 @ ( cBIGPHI @ X20 ) @ cHH_2 )
= $true ) )
& ! [X7: $i] :
( ( ( el1 @ X7 @ cSS_PRIME )
= $true )
=> ( ( el1 @ ( cPHI_2 @ X7 ) @ cHH_2 )
= $true ) )
& ! [X17: $i] :
( ( ( el1 @ X17 @ cSS_PRIME )
= $true )
=> ( ( el1 @ ( cPHI_1 @ X17 ) @ cHH_1 )
= $true ) )
& ( ! [X6: $i,X5: $i] :
( ( ( ( el1 @ X6 @ cHH_1 )
= $true )
& ( ( el1 @ X5 @ cHH_1 )
= $true ) )
=> ( ( cBIGPHI @ ( cTIMES @ X6 @ X5 ) )
= ( cTIMES @ ( cBIGPHI @ X6 ) @ ( cBIGPHI @ X5 ) ) ) )
<=> ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true ) )
& ! [X11: $i,X8: $i,X9: $i,X10: $i] :
( ( ( X9 = X10 )
& ( ( el1 @ X11 @ cHH_2 )
= $true )
& ( $true
= ( el1 @ X9 @ cHH_2 ) )
& ( ( el1 @ X10 @ cHH_2 )
= $true )
& ( ( el1 @ X8 @ cHH_2 )
= $true )
& ( X8 = X11 ) )
=> ( ( cTIMES @ X11 @ X10 )
= ( cTIMES @ X8 @ X9 ) ) )
& ! [X4: $i] :
( ( ( el1 @ X4 @ cSS_PRIME )
= $true )
=> ( ( cBIGPHI @ ( cPHI_1 @ X4 ) )
= ( cPHI_2 @ X4 ) ) )
& ! [X2: $i] :
( ( ( el1 @ X2 @ cHH_1 )
= $true )
=> ? [X3: $i] :
( ( ( el1 @ X3 @ cSS_PRIME )
= $true )
& ( ( cPHI_1 @ X3 )
= X2 ) ) )
& ! [X14: $i > $i] :
( ! [X16: $i,X15: $i] :
( ( ( ( el1 @ X16 @ cSS_PRIME )
= $true )
& ( ( el1 @ X15 @ cSS_PRIME )
= $true ) )
=> ( ( cTIMES @ ( X14 @ X15 ) @ ( X14 @ X16 ) )
= ( X14 @ ( cTIMES @ X15 @ X16 ) ) ) )
<=> ( $true
= ( cHOM_FROM_SS_PRIME @ X14 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_2 )
= $true )
& ! [X0: $i,X1: $i] :
( ( ( ( el1 @ X1 @ cHH_1 )
= $true )
& ( ( el1 @ X0 @ cHH_1 )
= $true ) )
=> ( $true
= ( el1 @ ( cTIMES @ X0 @ X1 ) @ cHH_1 ) ) )
& ! [X12: $i,X13: $i] :
( ( ( $true
= ( el1 @ X13 @ cHH_1 ) )
& ( $true
= ( el1 @ X12 @ cHH_1 ) )
& ( X12 = X13 ) )
=> ( ( cBIGHI @ X12 )
= ( cBIGPHI @ X13 ) ) )
& ( ( cHOM_FROM_SS_PRIME @ cPHI_1 )
= $true ) )
=> ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( ( el1 @ X0 @ cHH_1 )
& ( el1 @ X1 @ cHH_1 ) )
=> ( el1 @ ( cTIMES @ X0 @ X1 ) @ cHH_1 ) )
& ! [X2: $i] :
( ( el1 @ X2 @ cHH_1 )
=> ? [X3: $i] :
( ( el1 @ X3 @ cSS_PRIME )
& ( ( cPHI_1 @ X3 )
= X2 ) ) )
& ! [X4: $i] :
( ( el1 @ X4 @ cSS_PRIME )
=> ( ( cBIGPHI @ ( cPHI_1 @ X4 ) )
= ( cPHI_2 @ X4 ) ) )
& ( cHOM_FROM_SS_PRIME @ cPHI_1 )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
<=> ! [X5: $i,X6: $i] :
( ( ( el1 @ X6 @ cHH_1 )
& ( el1 @ X5 @ cHH_1 ) )
=> ( ( cBIGPHI @ ( cTIMES @ X6 @ X5 ) )
= ( cTIMES @ ( cBIGPHI @ X6 ) @ ( cBIGPHI @ X5 ) ) ) ) )
& ! [X7: $i] :
( ( el1 @ X7 @ cSS_PRIME )
=> ( el1 @ ( cPHI_2 @ X7 ) @ cHH_2 ) )
& ! [X8: $i,X9: $i,X10: $i,X11: $i] :
( ( ( el1 @ X8 @ cHH_2 )
& ( X8 = X11 )
& ( X9 = X10 )
& ( el1 @ X9 @ cHH_2 )
& ( el1 @ X10 @ cHH_2 )
& ( el1 @ X11 @ cHH_2 ) )
=> ( ( cTIMES @ X11 @ X10 )
= ( cTIMES @ X8 @ X9 ) ) )
& ! [X12: $i,X13: $i] :
( ( ( el1 @ X13 @ cHH_1 )
& ( X12 = X13 )
& ( el1 @ X12 @ cHH_1 ) )
=> ( ( cBIGHI @ X12 )
= ( cBIGPHI @ X13 ) ) )
& ! [X14: $i > $i] :
( ! [X15: $i,X16: $i] :
( ( ( el1 @ X16 @ cSS_PRIME )
& ( el1 @ X15 @ cSS_PRIME ) )
=> ( ( cTIMES @ ( X14 @ X15 ) @ ( X14 @ X16 ) )
= ( X14 @ ( cTIMES @ X15 @ X16 ) ) ) )
<=> ( cHOM_FROM_SS_PRIME @ X14 ) )
& ! [X17: $i] :
( ( el1 @ X17 @ cSS_PRIME )
=> ( el1 @ ( cPHI_1 @ X17 ) @ cHH_1 ) )
& ! [X18: $i,X19: $i] :
( ( ( el1 @ X18 @ cSS_PRIME )
& ( el1 @ X19 @ cSS_PRIME ) )
=> ( el1 @ ( cTIMES @ X19 @ X18 ) @ cSS_PRIME ) )
& ! [X20: $i] :
( ( el1 @ X20 @ cHH_1 )
=> ( el1 @ ( cBIGPHI @ X20 ) @ cHH_2 ) )
& ( cHOM_FROM_SS_PRIME @ cPHI_2 )
& ! [X21: $i,X22: $i,X23: $i,X24: $i] :
( ( ( X22 = X24 )
& ( el1 @ X22 @ cHH_1 )
& ( el1 @ X24 @ cHH_1 )
& ( el1 @ X21 @ cHH_1 )
& ( el1 @ X23 @ cHH_1 )
& ( X21 = X23 ) )
=> ( ( cTIMES @ X24 @ X23 )
= ( cTIMES @ X22 @ X21 ) ) ) )
=> ( cHOM_FROM_HH_1 @ cBIGPHI ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X5: $i,X6: $i] :
( ( ( el1 @ X5 @ cHH_1 )
& ( el1 @ X6 @ cHH_1 ) )
=> ( el1 @ ( cTIMES @ X5 @ X6 ) @ cHH_1 ) )
& ! [X6: $i] :
( ( el1 @ X6 @ cHH_1 )
=> ? [X5: $i] :
( ( el1 @ X5 @ cSS_PRIME )
& ( ( cPHI_1 @ X5 )
= X6 ) ) )
& ! [X5: $i] :
( ( el1 @ X5 @ cSS_PRIME )
=> ( ( cPHI_2 @ X5 )
= ( cBIGPHI @ ( cPHI_1 @ X5 ) ) ) )
& ( cHOM_FROM_SS_PRIME @ cPHI_1 )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
<=> ! [X6: $i,X5: $i] :
( ( ( el1 @ X5 @ cHH_1 )
& ( el1 @ X6 @ cHH_1 ) )
=> ( ( cBIGPHI @ ( cTIMES @ X5 @ X6 ) )
= ( cTIMES @ ( cBIGPHI @ X5 ) @ ( cBIGPHI @ X6 ) ) ) ) )
& ! [X5: $i] :
( ( el1 @ X5 @ cSS_PRIME )
=> ( el1 @ ( cPHI_2 @ X5 ) @ cHH_2 ) )
& ! [X0: $i,X2: $i,X3: $i,X1: $i] :
( ( ( el1 @ X0 @ cHH_2 )
& ( X0 = X1 )
& ( X2 = X3 )
& ( el1 @ X2 @ cHH_2 )
& ( el1 @ X3 @ cHH_2 )
& ( el1 @ X1 @ cHH_2 ) )
=> ( ( cTIMES @ X0 @ X2 )
= ( cTIMES @ X1 @ X3 ) ) )
& ! [X5: $i,X6: $i] :
( ( ( el1 @ X6 @ cHH_1 )
& ( X5 = X6 )
& ( el1 @ X5 @ cHH_1 ) )
=> ( ( cBIGPHI @ X6 )
= ( cBIGHI @ X5 ) ) )
& ! [X4: $i > $i] :
( ! [X5: $i,X6: $i] :
( ( ( el1 @ X6 @ cSS_PRIME )
& ( el1 @ X5 @ cSS_PRIME ) )
=> ( ( X4 @ ( cTIMES @ X5 @ X6 ) )
= ( cTIMES @ ( X4 @ X5 ) @ ( X4 @ X6 ) ) ) )
<=> ( cHOM_FROM_SS_PRIME @ X4 ) )
& ! [X5: $i] :
( ( el1 @ X5 @ cSS_PRIME )
=> ( el1 @ ( cPHI_1 @ X5 ) @ cHH_1 ) )
& ! [X1: $i,X0: $i] :
( ( ( el1 @ X1 @ cSS_PRIME )
& ( el1 @ X0 @ cSS_PRIME ) )
=> ( el1 @ ( cTIMES @ X0 @ X1 ) @ cSS_PRIME ) )
& ! [X5: $i] :
( ( el1 @ X5 @ cHH_1 )
=> ( el1 @ ( cBIGPHI @ X5 ) @ cHH_2 ) )
& ( cHOM_FROM_SS_PRIME @ cPHI_2 )
& ! [X3: $i,X1: $i,X2: $i,X0: $i] :
( ( ( X0 = X1 )
& ( el1 @ X1 @ cHH_1 )
& ( el1 @ X0 @ cHH_1 )
& ( el1 @ X3 @ cHH_1 )
& ( el1 @ X2 @ cHH_1 )
& ( X2 = X3 ) )
=> ( ( cTIMES @ X0 @ X2 )
= ( cTIMES @ X1 @ X3 ) ) ) )
=> ( cHOM_FROM_HH_1 @ cBIGPHI ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X5: $i,X6: $i] :
( ( ( el1 @ X5 @ cHH_1 )
& ( el1 @ X6 @ cHH_1 ) )
=> ( el1 @ ( cTIMES @ X5 @ X6 ) @ cHH_1 ) )
& ! [X6: $i] :
( ( el1 @ X6 @ cHH_1 )
=> ? [X5: $i] :
( ( el1 @ X5 @ cSS_PRIME )
& ( ( cPHI_1 @ X5 )
= X6 ) ) )
& ! [X5: $i] :
( ( el1 @ X5 @ cSS_PRIME )
=> ( ( cPHI_2 @ X5 )
= ( cBIGPHI @ ( cPHI_1 @ X5 ) ) ) )
& ( cHOM_FROM_SS_PRIME @ cPHI_1 )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
<=> ! [X6: $i,X5: $i] :
( ( ( el1 @ X5 @ cHH_1 )
& ( el1 @ X6 @ cHH_1 ) )
=> ( ( cBIGPHI @ ( cTIMES @ X5 @ X6 ) )
= ( cTIMES @ ( cBIGPHI @ X5 ) @ ( cBIGPHI @ X6 ) ) ) ) )
& ! [X5: $i] :
( ( el1 @ X5 @ cSS_PRIME )
=> ( el1 @ ( cPHI_2 @ X5 ) @ cHH_2 ) )
& ! [X0: $i,X2: $i,X3: $i,X1: $i] :
( ( ( el1 @ X0 @ cHH_2 )
& ( X0 = X1 )
& ( X2 = X3 )
& ( el1 @ X2 @ cHH_2 )
& ( el1 @ X3 @ cHH_2 )
& ( el1 @ X1 @ cHH_2 ) )
=> ( ( cTIMES @ X0 @ X2 )
= ( cTIMES @ X1 @ X3 ) ) )
& ! [X5: $i,X6: $i] :
( ( ( el1 @ X6 @ cHH_1 )
& ( X5 = X6 )
& ( el1 @ X5 @ cHH_1 ) )
=> ( ( cBIGPHI @ X6 )
= ( cBIGHI @ X5 ) ) )
& ! [X4: $i > $i] :
( ! [X5: $i,X6: $i] :
( ( ( el1 @ X6 @ cSS_PRIME )
& ( el1 @ X5 @ cSS_PRIME ) )
=> ( ( X4 @ ( cTIMES @ X5 @ X6 ) )
= ( cTIMES @ ( X4 @ X5 ) @ ( X4 @ X6 ) ) ) )
<=> ( cHOM_FROM_SS_PRIME @ X4 ) )
& ! [X5: $i] :
( ( el1 @ X5 @ cSS_PRIME )
=> ( el1 @ ( cPHI_1 @ X5 ) @ cHH_1 ) )
& ! [X1: $i,X0: $i] :
( ( ( el1 @ X1 @ cSS_PRIME )
& ( el1 @ X0 @ cSS_PRIME ) )
=> ( el1 @ ( cTIMES @ X0 @ X1 ) @ cSS_PRIME ) )
& ! [X5: $i] :
( ( el1 @ X5 @ cHH_1 )
=> ( el1 @ ( cBIGPHI @ X5 ) @ cHH_2 ) )
& ( cHOM_FROM_SS_PRIME @ cPHI_2 )
& ! [X3: $i,X1: $i,X2: $i,X0: $i] :
( ( ( X0 = X1 )
& ( el1 @ X1 @ cHH_1 )
& ( el1 @ X0 @ cHH_1 )
& ( el1 @ X3 @ cHH_1 )
& ( el1 @ X2 @ cHH_1 )
& ( X2 = X3 ) )
=> ( ( cTIMES @ X0 @ X2 )
= ( cTIMES @ X1 @ X3 ) ) ) )
=> ( cHOM_FROM_HH_1 @ cBIGPHI ) ),
file('/export/starexec/sandbox2/tmp/tmp.IZshy8ygwZ/DTF2THF_21253.p',cPROB757) ).
thf(f1196,plain,
( ( ( cBIGPHI @ ( cTIMES @ ( cPHI_1 @ ( sK2 @ sK4 ) ) @ sK3 ) )
= ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) ) )
| ~ spl5_7
| ~ spl5_11
| ~ spl5_19
| ~ spl5_32
| ~ spl5_82 ),
inference(trivial_inequality_removal,[status(thm)],[f1195]) ).
thf(f1195,plain,
( ( ( cBIGPHI @ ( cTIMES @ ( cPHI_1 @ ( sK2 @ sK4 ) ) @ sK3 ) )
= ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) ) )
| ( $true != $true )
| ~ spl5_7
| ~ spl5_11
| ~ spl5_19
| ~ spl5_32
| ~ spl5_82 ),
inference(forward_demodulation,[status(thm)],[f1186,f200]) ).
thf(f200,plain,
( ( ( el1 @ ( sK2 @ sK4 ) @ cSS_PRIME )
= $true )
| ~ spl5_11 ),
inference(avatar_component_clause,[status(thm)],[f199]) ).
thf(f1186,plain,
( ( ( el1 @ ( sK2 @ sK4 ) @ cSS_PRIME )
!= $true )
| ( ( cBIGPHI @ ( cTIMES @ ( cPHI_1 @ ( sK2 @ sK4 ) ) @ sK3 ) )
= ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) ) )
| ~ spl5_7
| ~ spl5_11
| ~ spl5_19
| ~ spl5_32
| ~ spl5_82 ),
inference(superposition,[status(thm)],[f1099,f419]) ).
thf(f419,plain,
( ! [X0: $i] :
( ( ( cPHI_1 @ ( cTIMES @ X0 @ ( sK2 @ sK3 ) ) )
= ( cTIMES @ ( cPHI_1 @ X0 ) @ sK3 ) )
| ( ( el1 @ X0 @ cSS_PRIME )
!= $true ) )
| ~ spl5_32 ),
inference(avatar_component_clause,[status(thm)],[f418]) ).
thf(f1099,plain,
( ( ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) )
= ( cBIGPHI @ ( cPHI_1 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) ) ) )
| ~ spl5_7
| ~ spl5_11
| ~ spl5_19
| ~ spl5_82 ),
inference(forward_demodulation,[status(thm)],[f1098,f950]) ).
thf(f950,plain,
( ( ( cPHI_2 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) )
= ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) ) )
| ~ spl5_7
| ~ spl5_11
| ~ spl5_19 ),
inference(trivial_inequality_removal,[status(thm)],[f949]) ).
thf(f949,plain,
( ( $true != $true )
| ( ( cPHI_2 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) )
= ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) ) )
| ~ spl5_7
| ~ spl5_11
| ~ spl5_19 ),
inference(forward_demodulation,[status(thm)],[f904,f200]) ).
thf(f904,plain,
( ( ( el1 @ ( sK2 @ sK4 ) @ cSS_PRIME )
!= $true )
| ( ( cPHI_2 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) )
= ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) ) )
| ~ spl5_7
| ~ spl5_19 ),
inference(superposition,[status(thm)],[f350,f181]) ).
thf(f181,plain,
( ( ( cBIGPHI @ sK4 )
= ( cPHI_2 @ ( sK2 @ sK4 ) ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[status(thm)],[f179]) ).
thf(f350,plain,
( ! [X0: $i] :
( ( ( cTIMES @ ( cPHI_2 @ X0 ) @ ( cBIGPHI @ sK3 ) )
= ( cPHI_2 @ ( cTIMES @ X0 @ ( sK2 @ sK3 ) ) ) )
| ( ( el1 @ X0 @ cSS_PRIME )
!= $true ) )
| ~ spl5_19 ),
inference(avatar_component_clause,[status(thm)],[f349]) ).
thf(f1098,plain,
( ( ( cPHI_2 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) )
= ( cBIGPHI @ ( cPHI_1 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) ) ) )
| ~ spl5_82 ),
inference(trivial_inequality_removal,[status(thm)],[f1093]) ).
thf(f1093,plain,
( ( $false = $true )
| ( ( cPHI_2 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) )
= ( cBIGPHI @ ( cPHI_1 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) ) ) )
| ~ spl5_82 ),
inference(superposition,[status(thm)],[f1052,f117]) ).
thf(f117,plain,
! [X26: $i] :
( ( $false
= ( el1 @ X26 @ cSS_PRIME ) )
| ( ( cBIGPHI @ ( cPHI_1 @ X26 ) )
= ( cPHI_2 @ X26 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
! [X26: $i] :
( ( ( cBIGPHI @ ( cPHI_1 @ X26 ) )
= ( cPHI_2 @ X26 ) )
| ( $false
= ( el1 @ X26 @ cSS_PRIME ) )
| ( $true != $true ) ),
inference(fool_paramodulation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X26: $i] :
( ( ( el1 @ X26 @ cSS_PRIME )
!= $true )
| ( ( cBIGPHI @ ( cPHI_1 @ X26 ) )
= ( cPHI_2 @ X26 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f1052,plain,
( ( ( el1 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) @ cSS_PRIME )
= $true )
| ~ spl5_82 ),
inference(avatar_component_clause,[status(thm)],[f1051]) ).
thf(f1090,plain,
( ~ spl5_11
| ~ spl5_8
| spl5_82 ),
inference(avatar_split_clause,[status(thm)],[f1089,f1051,f185,f199]) ).
thf(f185,definition,
( spl5_8
<=> ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition]) ).
thf(f1089,plain,
( ( ( el1 @ ( sK2 @ sK4 ) @ cSS_PRIME )
!= $true )
| ~ spl5_8
| spl5_82 ),
inference(trivial_inequality_removal,[status(thm)],[f1088]) ).
thf(f1088,plain,
( ( ( el1 @ ( sK2 @ sK4 ) @ cSS_PRIME )
!= $true )
| ( $true != $true )
| ~ spl5_8
| spl5_82 ),
inference(forward_demodulation,[status(thm)],[f1084,f186]) ).
thf(f186,plain,
( ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
= $true )
| ~ spl5_8 ),
inference(avatar_component_clause,[status(thm)],[f185]) ).
thf(f1084,plain,
( ( ( el1 @ ( sK2 @ sK4 ) @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
!= $true )
| spl5_82 ),
inference(trivial_inequality_removal,[status(thm)],[f1082]) ).
thf(f1082,plain,
( ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( sK2 @ sK4 ) @ cSS_PRIME )
!= $true )
| ( $true != $true )
| spl5_82 ),
inference(superposition,[status(thm)],[f1053,f16]) ).
thf(f16,plain,
! [X28: $i,X27: $i] :
( ( ( el1 @ ( cTIMES @ X28 @ X27 ) @ cSS_PRIME )
= $true )
| ( ( el1 @ X27 @ cSS_PRIME )
!= $true )
| ( ( el1 @ X28 @ cSS_PRIME )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f1053,plain,
( ( ( el1 @ ( cTIMES @ ( sK2 @ sK4 ) @ ( sK2 @ sK3 ) ) @ cSS_PRIME )
!= $true )
| spl5_82 ),
inference(avatar_component_clause,[status(thm)],[f1051]) ).
thf(f420,plain,
( spl5_32
| ~ spl5_8
| ~ spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f416,f55,f185,f418]) ).
thf(f55,definition,
( spl5_3
<=> ( ( el1 @ sK3 @ cHH_1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f416,plain,
( ! [X0: $i] :
( ( ( cPHI_1 @ ( cTIMES @ X0 @ ( sK2 @ sK3 ) ) )
= ( cTIMES @ ( cPHI_1 @ X0 ) @ sK3 ) )
| ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
!= $true )
| ( ( el1 @ X0 @ cSS_PRIME )
!= $true ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f415]) ).
thf(f415,plain,
( ! [X0: $i] :
( ( ( cPHI_1 @ ( cTIMES @ X0 @ ( sK2 @ sK3 ) ) )
= ( cTIMES @ ( cPHI_1 @ X0 ) @ sK3 ) )
| ( ( el1 @ X0 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
!= $true )
| ( $true != $true ) )
| ~ spl5_3 ),
inference(forward_demodulation,[status(thm)],[f285,f19]) ).
thf(f19,plain,
( ( cHOM_FROM_SS_PRIME @ cPHI_1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f285,plain,
( ! [X0: $i] :
( ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
!= $true )
| ( ( cPHI_1 @ ( cTIMES @ X0 @ ( sK2 @ sK3 ) ) )
= ( cTIMES @ ( cPHI_1 @ X0 ) @ sK3 ) )
| ( ( el1 @ X0 @ cSS_PRIME )
!= $true )
| ( ( cHOM_FROM_SS_PRIME @ cPHI_1 )
!= $true ) )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f34,f83]) ).
thf(f83,plain,
( ( sK3
= ( cPHI_1 @ ( sK2 @ sK3 ) ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true != $true )
| ( sK3
= ( cPHI_1 @ ( sK2 @ sK3 ) ) )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f26,f57]) ).
thf(f57,plain,
( ( ( el1 @ sK3 @ cHH_1 )
= $true )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f34,plain,
! [X3: $i > $i,X4: $i,X5: $i] :
( ( ( X3 @ ( cTIMES @ X4 @ X5 ) )
= ( cTIMES @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) )
| ( ( el1 @ X5 @ cSS_PRIME )
!= $true )
| ( ( cHOM_FROM_SS_PRIME @ X3 )
!= $true )
| ( ( el1 @ X4 @ cSS_PRIME )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f351,plain,
( ~ spl5_8
| spl5_19
| ~ spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f347,f174,f349,f185]) ).
thf(f174,definition,
( spl5_6
<=> ( ( cBIGPHI @ sK3 )
= ( cPHI_2 @ ( sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition]) ).
thf(f347,plain,
( ! [X0: $i] :
( ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
!= $true )
| ( ( cTIMES @ ( cPHI_2 @ X0 ) @ ( cBIGPHI @ sK3 ) )
= ( cPHI_2 @ ( cTIMES @ X0 @ ( sK2 @ sK3 ) ) ) )
| ( ( el1 @ X0 @ cSS_PRIME )
!= $true ) )
| ~ spl5_6 ),
inference(trivial_inequality_removal,[status(thm)],[f346]) ).
thf(f346,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
!= $true )
| ( ( el1 @ X0 @ cSS_PRIME )
!= $true )
| ( ( cTIMES @ ( cPHI_2 @ X0 ) @ ( cBIGPHI @ sK3 ) )
= ( cPHI_2 @ ( cTIMES @ X0 @ ( sK2 @ sK3 ) ) ) ) )
| ~ spl5_6 ),
inference(forward_demodulation,[status(thm)],[f281,f17]) ).
thf(f17,plain,
( ( cHOM_FROM_SS_PRIME @ cPHI_2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f281,plain,
( ! [X0: $i] :
( ( ( cTIMES @ ( cPHI_2 @ X0 ) @ ( cBIGPHI @ sK3 ) )
= ( cPHI_2 @ ( cTIMES @ X0 @ ( sK2 @ sK3 ) ) ) )
| ( ( cHOM_FROM_SS_PRIME @ cPHI_2 )
!= $true )
| ( ( el1 @ X0 @ cSS_PRIME )
!= $true )
| ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
!= $true ) )
| ~ spl5_6 ),
inference(superposition,[status(thm)],[f34,f176]) ).
thf(f176,plain,
( ( ( cBIGPHI @ sK3 )
= ( cPHI_2 @ ( sK2 @ sK3 ) ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[status(thm)],[f174]) ).
thf(f226,plain,
( ~ spl5_4
| spl5_11 ),
inference(avatar_split_clause,[status(thm)],[f225,f199,f61]) ).
thf(f225,plain,
( ( ( el1 @ sK4 @ cHH_1 )
!= $true )
| spl5_11 ),
inference(trivial_inequality_removal,[status(thm)],[f222]) ).
thf(f222,plain,
( ( $true != $true )
| ( ( el1 @ sK4 @ cHH_1 )
!= $true )
| spl5_11 ),
inference(superposition,[status(thm)],[f201,f27]) ).
thf(f27,plain,
! [X14: $i] :
( ( ( el1 @ ( sK2 @ X14 ) @ cSS_PRIME )
= $true )
| ( $true
!= ( el1 @ X14 @ cHH_1 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f201,plain,
( ( ( el1 @ ( sK2 @ sK4 ) @ cSS_PRIME )
!= $true )
| spl5_11 ),
inference(avatar_component_clause,[status(thm)],[f199]) ).
thf(f208,plain,
( ~ spl5_3
| spl5_8 ),
inference(avatar_split_clause,[status(thm)],[f207,f185,f55]) ).
thf(f207,plain,
( ( ( el1 @ sK3 @ cHH_1 )
!= $true )
| spl5_8 ),
inference(trivial_inequality_removal,[status(thm)],[f204]) ).
thf(f204,plain,
( ( $true != $true )
| ( ( el1 @ sK3 @ cHH_1 )
!= $true )
| spl5_8 ),
inference(superposition,[status(thm)],[f187,f27]) ).
thf(f187,plain,
( ( ( el1 @ ( sK2 @ sK3 ) @ cSS_PRIME )
!= $true )
| spl5_8 ),
inference(avatar_component_clause,[status(thm)],[f185]) ).
thf(f182,plain,
( spl5_7
| ~ spl5_4
| ~ spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f169,f61,f61,f179]) ).
thf(f169,plain,
( ( ( cBIGPHI @ sK4 )
= ( cPHI_2 @ ( sK2 @ sK4 ) ) )
| ( ( el1 @ sK4 @ cHH_1 )
!= $true )
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f142,f82]) ).
thf(f142,plain,
! [X0: $i] :
( ( ( cPHI_2 @ ( sK2 @ X0 ) )
= ( cBIGPHI @ ( cPHI_1 @ ( sK2 @ X0 ) ) ) )
| ( ( el1 @ X0 @ cHH_1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
! [X0: $i] :
( ( ( el1 @ X0 @ cHH_1 )
!= $true )
| ( ( cPHI_2 @ ( sK2 @ X0 ) )
= ( cBIGPHI @ ( cPHI_1 @ ( sK2 @ X0 ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f18,f27]) ).
thf(f177,plain,
( spl5_6
| ~ spl5_3
| ~ spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f170,f55,f55,f174]) ).
thf(f170,plain,
( ( ( cBIGPHI @ sK3 )
= ( cPHI_2 @ ( sK2 @ sK3 ) ) )
| ( ( el1 @ sK3 @ cHH_1 )
!= $true )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f142,f83]) ).
thf(f64,plain,
( spl5_4
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f50,f61]) ).
thf(f50,definition,
( spl5_2
<=> ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f24,plain,
( ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true )
| ( ( el1 @ sK4 @ cHH_1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f59,plain,
~ spl5_2,
inference(avatar_split_clause,[status(thm)],[f15,f50]) ).
thf(f15,plain,
( ( cHOM_FROM_HH_1 @ cBIGPHI )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f58,plain,
( spl5_2
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f22,f55,f50]) ).
thf(f22,plain,
( ( ( el1 @ sK3 @ cHH_1 )
= $true )
| ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f53,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f23,f50,f46]) ).
thf(f23,plain,
( ( ( cTIMES @ ( cBIGPHI @ sK4 ) @ ( cBIGPHI @ sK3 ) )
!= ( cBIGPHI @ ( cTIMES @ sK4 @ sK3 ) ) )
| ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO249^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.36 % Computer : n006.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Tue Feb 24 14:26:45 EST 2026
% 0.19/0.37 % CPUTime :
% 0.19/0.37 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SYO249^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.47 % Domain : Syntactic
% 0.30/0.47 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Bro09]
% 0.30/0.47 % Names : tps_1216 [Bro09]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.44 v9.1.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.43 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.30/0.47 % Syntax : Number of formulae : 12 ( 0 unt; 11 typ; 0 def)
% 0.30/0.47 % Number of atoms : 75 ( 12 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 75 ( 75 avg)
% 0.30/0.47 % Number of connectives : 143 ( 0 ~; 0 |; 30 &; 98 @)
% 0.30/0.47 % ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 20 ( 20 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 12 ( 11 usr; 0 con; 1-2 aty)
% 0.30/0.47 % Number of variables : 25 ( 0 ^; 24 !; 1 ?; 25 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(cBIGPHI,type,
% 0.30/0.47 cBIGPHI: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(cHOM_FROM_HH_1,type,
% 0.30/0.47 cHOM_FROM_HH_1: ( $i > $i ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(cPHI_2,type,
% 0.30/0.47 cPHI_2: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(cHOM_FROM_SS_PRIME,type,
% 0.30/0.47 cHOM_FROM_SS_PRIME: ( $i > $i ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(cPHI_1,type,
% 0.30/0.47 cPHI_1: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(cSS_PRIME,type,
% 0.30/0.47 cSS_PRIME: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(el1,type,
% 0.30/0.47 el1: $i > ( $i > $o ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(cHH_1,type,
% 0.30/0.47 cHH_1: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(cBIGHI,type,
% 0.30/0.47 cBIGHI: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(cHH_2,type,
% 0.30/0.47 cHH_2: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(cTIMES,type,
% 0.30/0.47 cTIMES: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(cPROB757,conjecture,
% 0.30/0.47 ( ( ! [Xx1: $i,Xx2: $i,Xy1: $i,Xy2: $i] :
% 0.30/0.47 ( ( ( el1 @ Xx1 @ cHH_2 )
% 0.30/0.47 & ( el1 @ Xx2 @ cHH_2 )
% 0.30/0.47 & ( el1 @ Xy1 @ cHH_2 )
% 0.30/0.47 & ( el1 @ Xy2 @ cHH_2 )
% 0.30/0.47 & ( Xx1 = Xx2 )
% 0.30/0.47 & ( Xy1 = Xy2 ) )
% 0.30/0.47 => ( ( cTIMES @ Xx1 @ Xy1 )
% 0.30/0.47 = ( cTIMES @ Xx2 @ Xy2 ) ) )
% 0.30/0.47 & ! [Xx1: $i,Xx2: $i] :
% 0.30/0.47 ( ( ( el1 @ Xx1 @ cSS_PRIME )
% 0.30/0.47 & ( el1 @ Xx2 @ cSS_PRIME ) )
% 0.30/0.47 => ( el1 @ ( cTIMES @ Xx1 @ Xx2 ) @ cSS_PRIME ) )
% 0.30/0.47 & ! [Xx1: $i,Xx2: $i,Xy1: $i,Xy2: $i] :
% 0.30/0.47 ( ( ( el1 @ Xx1 @ cHH_1 )
% 0.30/0.47 & ( el1 @ Xx2 @ cHH_1 )
% 0.30/0.47 & ( el1 @ Xy1 @ cHH_1 )
% 0.30/0.47 & ( el1 @ Xy2 @ cHH_1 )
% 0.30/0.47 & ( Xx1 = Xx2 )
% 0.30/0.47 & ( Xy1 = Xy2 ) )
% 0.30/0.47 => ( ( cTIMES @ Xx1 @ Xy1 )
% 0.30/0.47 = ( cTIMES @ Xx2 @ Xy2 ) ) )
% 0.30/0.47 & ! [Xphi: $i > $i] :
% 0.30/0.47 ( ( cHOM_FROM_SS_PRIME @ Xphi )
% 0.30/0.47 <=> ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( ( el1 @ Xx @ cSS_PRIME )
% 0.30/0.47 & ( el1 @ Xy @ cSS_PRIME ) )
% 0.30/0.47 => ( ( Xphi @ ( cTIMES @ Xx @ Xy ) )
% 0.30/0.47 = ( cTIMES @ ( Xphi @ Xx ) @ ( Xphi @ Xy ) ) ) ) )
% 0.30/0.47 & ( ( cHOM_FROM_HH_1 @ cBIGPHI )
% 0.30/0.47 <=> ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( ( el1 @ Xx @ cHH_1 )
% 0.30/0.47 & ( el1 @ Xy @ cHH_1 ) )
% 0.30/0.47 => ( ( cBIGPHI @ ( cTIMES @ Xx @ Xy ) )
% 0.30/0.47 = ( cTIMES @ ( cBIGPHI @ Xx ) @ ( cBIGPHI @ Xy ) ) ) ) )
% 0.30/0.47 & ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( ( el1 @ Xx @ cHH_1 )
% 0.30/0.47 & ( el1 @ Xy @ cHH_1 ) )
% 0.30/0.47 => ( el1 @ ( cTIMES @ Xx @ Xy ) @ cHH_1 ) )
% 0.30/0.47 & ! [Xx: $i] :
% 0.30/0.47 ( ( el1 @ Xx @ cSS_PRIME )
% 0.30/0.47 => ( el1 @ ( cPHI_2 @ Xx ) @ cHH_2 ) )
% 0.30/0.47 & ! [Xx: $i] :
% 0.30/0.47 ( ( el1 @ Xx @ cHH_1 )
% 0.30/0.47 => ( el1 @ ( cBIGPHI @ Xx ) @ cHH_2 ) )
% 0.30/0.47 & ! [Xx: $i] :
% 0.30/0.47 ( ( el1 @ Xx @ cSS_PRIME )
% 0.30/0.47 => ( el1 @ ( cPHI_1 @ Xx ) @ cHH_1 ) )
% 0.30/0.47 & ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( ( el1 @ Xx @ cHH_1 )
% 0.30/0.47 & ( el1 @ Xy @ cHH_1 )
% 0.30/0.47 & ( Xx = Xy ) )
% 0.30/0.47 => ( ( cBIGHI @ Xx )
% 0.30/0.47 = ( cBIGPHI @ Xy ) ) )
% 0.30/0.47 & ! [Xx: $i] :
% 0.30/0.47 ( ( el1 @ Xx @ cSS_PRIME )
% 0.30/0.47 => ( ( cBIGPHI @ ( cPHI_1 @ Xx ) )
% 0.30/0.47 = ( cPHI_2 @ Xx ) ) )
% 0.30/0.47 & ! [Xy: $i] :
% 0.30/0.47 ( ( el1 @ Xy @ cHH_1 )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( el1 @ Xx @ cSS_PRIME )
% 0.30/0.47 & ( ( cPHI_1 @ Xx )
% 0.30/0.47 = Xy ) ) )
% 0.30/0.47 & ( cHOM_FROM_SS_PRIME @ cPHI_1 )
% 0.30/0.47 & ( cHOM_FROM_SS_PRIME @ cPHI_2 ) )
% 0.30/0.47 => ( cHOM_FROM_HH_1 @ cBIGPHI ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.75/1.41 ---- Embedded in THF ---
% 1.75/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.75/1.41 %%% Generated on Tue Feb 24 14:26:46 EST 2026
% 1.75/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.75/1.41 %%% Logic specification used:
% 1.75/1.41 %%% thf(spec, logic, $$dhol).
% 1.75/1.41
% 1.75/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.IZshy8ygwZ/DTF2DTF21253.p
% See solution above
% 1.75/1.41 ------------------------
% 1.75/1.42 ---- Cleaned THF ---
% 1.75/1.42 thf(cBIGPHI,type,
% 1.75/1.42 cBIGPHI: $i > $i ).
% 1.75/1.42
% 1.75/1.42 thf(cHOM_FROM_HH_1,type,
% 1.75/1.42 cHOM_FROM_HH_1: ( $i > $i ) > $o ).
% 1.75/1.42
% 1.75/1.42 thf(cPHI_2,type,
% 1.75/1.42 cPHI_2: $i > $i ).
% 1.75/1.42
% 1.75/1.42 thf(cHOM_FROM_SS_PRIME,type,
% 1.75/1.42 cHOM_FROM_SS_PRIME: ( $i > $i ) > $o ).
% 1.75/1.42
% 1.75/1.42 thf(cPHI_1,type,
% 1.75/1.42 cPHI_1: $i > $i ).
% 1.75/1.42
% 1.75/1.42 thf(cSS_PRIME,type,
% 1.75/1.42 cSS_PRIME: $i > $o ).
% 1.75/1.42
% 1.75/1.42 thf(el1,type,
% 1.75/1.42 el1: $i > ( $i > $o ) > $o ).
% 1.75/1.42
% 1.75/1.42 thf(cHH_1,type,
% 1.75/1.42 cHH_1: $i > $o ).
% 1.75/1.42
% 1.75/1.42 thf(cBIGHI,type,
% 1.75/1.42 cBIGHI: $i > $i ).
% 1.75/1.42
% 1.75/1.42 thf(cHH_2,type,
% 1.75/1.42 cHH_2: $i > $o ).
% 1.75/1.42
% 1.75/1.42 thf(cTIMES,type,
% 1.75/1.42 cTIMES: $i > $i > $i ).
% 1.75/1.42
% 1.75/1.42 thf(cPROB757,conjecture,
% 1.75/1.42 ( ( ! [Xx1: $i,Xx2: $i,Xy1: $i,Xy2: $i] :
% 1.75/1.42 ( ( ( el1 @ Xx1 @ cHH_2 )
% 1.75/1.42 & ( el1 @ Xx2 @ cHH_2 )
% 1.75/1.42 & ( el1 @ Xy1 @ cHH_2 )
% 1.75/1.42 & ( el1 @ Xy2 @ cHH_2 )
% 1.75/1.42 & ( Xx1 = Xx2 )
% 1.75/1.42 & ( Xy1 = Xy2 ) )
% 1.75/1.42 => ( ( cTIMES @ Xx1 @ Xy1 )
% 1.75/1.42 = ( cTIMES @ Xx2 @ Xy2 ) ) )
% 1.75/1.42 & ! [Xx1: $i,Xx2: $i] :
% 1.75/1.42 ( ( ( el1 @ Xx1 @ cSS_PRIME )
% 1.75/1.42 & ( el1 @ Xx2 @ cSS_PRIME ) )
% 1.75/1.42 => ( el1 @ ( cTIMES @ Xx1 @ Xx2 ) @ cSS_PRIME ) )
% 1.75/1.42 & ! [Xx1: $i,Xx2: $i,Xy1: $i,Xy2: $i] :
% 1.75/1.42 ( ( ( el1 @ Xx1 @ cHH_1 )
% 1.75/1.42 & ( el1 @ Xx2 @ cHH_1 )
% 1.75/1.42 & ( el1 @ Xy1 @ cHH_1 )
% 1.75/1.42 & ( el1 @ Xy2 @ cHH_1 )
% 1.75/1.42 & ( Xx1 = Xx2 )
% 1.75/1.42 & ( Xy1 = Xy2 ) )
% 1.75/1.42 => ( ( cTIMES @ Xx1 @ Xy1 )
% 1.75/1.42 = ( cTIMES @ Xx2 @ Xy2 ) ) )
% 1.75/1.42 & ! [Xphi: $i > $i] :
% 1.75/1.42 ( ( cHOM_FROM_SS_PRIME @ Xphi )
% 1.75/1.42 <=> ! [Xx: $i,Xy: $i] :
% 1.75/1.42 ( ( ( el1 @ Xx @ cSS_PRIME )
% 1.75/1.42 & ( el1 @ Xy @ cSS_PRIME ) )
% 1.75/1.42 => ( ( Xphi @ ( cTIMES @ Xx @ Xy ) )
% 1.75/1.42 = ( cTIMES @ ( Xphi @ Xx ) @ ( Xphi @ Xy ) ) ) ) )
% 1.75/1.42 & ( ( cHOM_FROM_HH_1 @ cBIGPHI )
% 1.75/1.42 <=> ! [Xx: $i,Xy: $i] :
% 1.75/1.42 ( ( ( el1 @ Xx @ cHH_1 )
% 1.75/1.42 & ( el1 @ Xy @ cHH_1 ) )
% 1.75/1.42 => ( ( cBIGPHI @ ( cTIMES @ Xx @ Xy ) )
% 1.75/1.42 = ( cTIMES @ ( cBIGPHI @ Xx ) @ ( cBIGPHI @ Xy ) ) ) ) )
% 1.75/1.42 & ! [Xx: $i,Xy: $i] :
% 1.75/1.42 ( ( ( el1 @ Xx @ cHH_1 )
% 1.75/1.42 & ( el1 @ Xy @ cHH_1 ) )
% 1.75/1.42 => ( el1 @ ( cTIMES @ Xx @ Xy ) @ cHH_1 ) )
% 1.75/1.42 & ! [Xx: $i] :
% 1.75/1.42 ( ( el1 @ Xx @ cSS_PRIME )
% 1.75/1.42 => ( el1 @ ( cPHI_2 @ Xx ) @ cHH_2 ) )
% 1.75/1.42 & ! [Xx: $i] :
% 1.75/1.42 ( ( el1 @ Xx @ cHH_1 )
% 1.75/1.42 => ( el1 @ ( cBIGPHI @ Xx ) @ cHH_2 ) )
% 1.75/1.42 & ! [Xx: $i] :
% 1.75/1.42 ( ( el1 @ Xx @ cSS_PRIME )
% 1.75/1.42 => ( el1 @ ( cPHI_1 @ Xx ) @ cHH_1 ) )
% 1.75/1.42 & ! [Xx: $i,Xy: $i] :
% 1.75/1.42 ( ( ( el1 @ Xx @ cHH_1 )
% 1.75/1.42 & ( el1 @ Xy @ cHH_1 )
% 1.75/1.42 & ( Xx = Xy ) )
% 1.75/1.42 => ( ( cBIGHI @ Xx )
% 1.75/1.42 = ( cBIGPHI @ Xy ) ) )
% 1.75/1.42 & ! [Xx: $i] :
% 1.75/1.42 ( ( el1 @ Xx @ cSS_PRIME )
% 1.75/1.42 => ( ( cBIGPHI @ ( cPHI_1 @ Xx ) )
% 1.75/1.42 = ( cPHI_2 @ Xx ) ) )
% 1.75/1.42 & ! [Xy: $i] :
% 1.75/1.42 ( ( el1 @ Xy @ cHH_1 )
% 1.75/1.42 => ? [Xx: $i] :
% 1.75/1.42 ( ( el1 @ Xx @ cSS_PRIME )
% 1.75/1.42 & ( ( cPHI_1 @ Xx )
% 1.75/1.42 = Xy ) ) )
% 1.75/1.42 & ( cHOM_FROM_SS_PRIME @ cPHI_1 )
% 1.75/1.42 & ( cHOM_FROM_SS_PRIME @ cPHI_2 ) )
% 1.75/1.42 => ( cHOM_FROM_HH_1 @ cBIGPHI ) ) ).
% 1.75/1.42 ------------------------
% 1.75/1.44 % (21352)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/27Mi)
% 1.75/1.44 % (21351)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/4Mi)
% 1.75/1.44 % (21350)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/183Mi)
% 1.75/1.44 % (21356)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/18Mi)
% 1.75/1.44 % (21351)Instruction limit reached!
% 1.75/1.44 % (21351)------------------------------
% 1.75/1.44 % (21351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.44 % (21351)Termination reason: Unknown
% 1.75/1.44 % (21351)Termination phase: Property scanning
% 1.75/1.44
% 1.75/1.44 % (21351)Memory used [KB]: 1023
% 1.75/1.44 % (21351)Time elapsed: 0.004 s
% 1.75/1.44 % (21351)Instructions burned: 5 (million)
% 1.75/1.44 % (21351)------------------------------
% 1.75/1.44 % (21351)------------------------------
% 1.75/1.45 % (21354)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/2Mi)
% 1.75/1.45 % (21355)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/275Mi)
% 1.75/1.45 % (21354)Instruction limit reached!
% 1.75/1.45 % (21354)------------------------------
% 1.75/1.45 % (21354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.45 % (21354)Termination reason: Unknown
% 1.75/1.45 % (21354)Termination phase: shuffling
% 1.75/1.45
% 1.75/1.45 % (21354)Memory used [KB]: 1023
% 1.75/1.45 % (21354)Time elapsed: 0.003 s
% 1.75/1.45 % (21354)Instructions burned: 3 (million)
% 1.75/1.45 % (21354)------------------------------
% 1.75/1.45 % (21354)------------------------------
% 1.75/1.45 % (21356)Instruction limit reached!
% 1.75/1.45 % (21356)------------------------------
% 1.75/1.45 % (21356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.45 % (21356)Termination reason: Unknown
% 1.75/1.45 % (21356)Termination phase: Saturation
% 1.75/1.45
% 1.75/1.45 % (21356)Memory used [KB]: 5628
% 1.75/1.45 % (21356)Time elapsed: 0.011 s
% 1.75/1.45 % (21356)Instructions burned: 18 (million)
% 1.75/1.45 % (21356)------------------------------
% 1.75/1.45 % (21356)------------------------------
% 1.75/1.45 % (21353)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/2Mi)
% 1.75/1.45 % (21353)Instruction limit reached!
% 1.75/1.45 % (21353)------------------------------
% 1.75/1.45 % (21353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.45 % (21353)Termination reason: Unknown
% 1.75/1.45 % (21353)Termination phase: Property scanning
% 1.75/1.45
% 1.75/1.45 % (21353)Memory used [KB]: 1023
% 1.75/1.45 % (21353)Time elapsed: 0.003 s
% 1.75/1.45 % (21353)Instructions burned: 2 (million)
% 1.75/1.45 % (21353)------------------------------
% 1.75/1.45 % (21353)------------------------------
% 1.75/1.46 % (21352)Instruction limit reached!
% 1.75/1.46 % (21352)------------------------------
% 1.75/1.46 % (21352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.46 % (21352)Termination reason: Unknown
% 1.75/1.46 % (21352)Termination phase: Saturation
% 1.75/1.46
% 1.75/1.46 % (21352)Memory used [KB]: 5756
% 1.75/1.46 % (21352)Time elapsed: 0.017 s
% 1.75/1.46 % (21352)Instructions burned: 28 (million)
% 1.75/1.46 % (21352)------------------------------
% 1.75/1.46 % (21352)------------------------------
% 1.75/1.46 % (21357)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/3Mi)
% 1.75/1.46 % (21357)Instruction limit reached!
% 1.75/1.46 % (21357)------------------------------
% 1.75/1.46 % (21357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.46 % (21357)Termination reason: Unknown
% 1.75/1.46 % (21357)Termination phase: Preprocessing 3
% 1.75/1.46
% 1.75/1.46 % (21357)Memory used [KB]: 1023
% 1.75/1.46 % (21357)Time elapsed: 0.003 s
% 1.75/1.46 % (21357)Instructions burned: 3 (million)
% 1.75/1.46 % (21357)------------------------------
% 1.75/1.46 % (21357)------------------------------
% 1.75/1.46 % (21358)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/37Mi)
% 1.75/1.47 % (21359)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/15Mi)
% 1.75/1.47 % (21360)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/3Mi)
% 1.75/1.47 % (21360)Instruction limit reached!
% 1.75/1.47 % (21360)------------------------------
% 1.75/1.47 % (21360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.47 % (21360)Termination reason: Unknown
% 1.75/1.47 % (21360)Termination phase: Preprocessing 3
% 1.75/1.47
% 1.75/1.47 % (21360)Memory used [KB]: 1023
% 1.75/1.47 % (21360)Time elapsed: 0.003 s
% 1.75/1.47 % (21360)Instructions burned: 4 (million)
% 1.75/1.47 % (21360)------------------------------
% 1.75/1.47 % (21360)------------------------------
% 1.75/1.47 % (21361)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/1041Mi)
% 1.75/1.48 % (21359)Instruction limit reached!
% 1.75/1.48 % (21359)------------------------------
% 1.75/1.48 % (21359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.48 % (21359)Termination reason: Unknown
% 1.75/1.48 % (21359)Termination phase: Saturation
% 1.75/1.48
% 1.75/1.48 % (21359)Memory used [KB]: 5756
% 1.75/1.48 % (21359)Time elapsed: 0.010 s
% 1.75/1.48 % (21359)Instructions burned: 16 (million)
% 1.75/1.48 % (21359)------------------------------
% 1.75/1.48 % (21359)------------------------------
% 1.75/1.48 % (21362)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/7Mi)
% 1.75/1.48 % (21362)Instruction limit reached!
% 1.75/1.48 % (21362)------------------------------
% 1.75/1.48 % (21362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.48 % (21362)Termination reason: Unknown
% 1.75/1.48 % (21362)Termination phase: Saturation
% 1.75/1.48
% 1.75/1.48 % (21362)Memory used [KB]: 1151
% 1.75/1.48 % (21362)Time elapsed: 0.006 s
% 1.75/1.48 % (21362)Instructions burned: 8 (million)
% 1.75/1.48 % (21362)------------------------------
% 1.75/1.48 % (21362)------------------------------
% 1.75/1.48 % (21358)Instruction limit reached!
% 1.75/1.48 % (21358)------------------------------
% 1.75/1.48 % (21358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.48 % (21358)Termination reason: Unknown
% 1.75/1.48 % (21358)Termination phase: Saturation
% 1.75/1.48
% 1.75/1.48 % (21358)Memory used [KB]: 5756
% 1.75/1.48 % (21358)Time elapsed: 0.018 s
% 1.75/1.48 % (21358)Instructions burned: 37 (million)
% 1.75/1.48 % (21358)------------------------------
% 1.75/1.48 % (21358)------------------------------
% 1.75/1.49 % (21363)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/16Mi)
% 1.75/1.49 % (21364)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/3Mi)
% 1.75/1.49 % (21364)Instruction limit reached!
% 1.75/1.49 % (21364)------------------------------
% 1.75/1.49 % (21364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.49 % (21364)Termination reason: Unknown
% 1.75/1.49 % (21364)Termination phase: Preprocessing 2
% 1.75/1.49
% 1.75/1.49 % (21364)Memory used [KB]: 1023
% 1.75/1.49 % (21364)Time elapsed: 0.003 s
% 1.75/1.49 % (21364)Instructions burned: 3 (million)
% 1.75/1.49 % (21364)------------------------------
% 1.75/1.49 % (21364)------------------------------
% 1.75/1.49 % (21363)Instruction limit reached!
% 1.75/1.49 % (21363)------------------------------
% 1.75/1.49 % (21363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.49 % (21363)Termination reason: Unknown
% 1.75/1.49 % (21363)Termination phase: Saturation
% 1.75/1.49
% 1.75/1.49 % (21363)Memory used [KB]: 5756
% 1.75/1.49 % (21363)Time elapsed: 0.010 s
% 1.75/1.49 % (21363)Instructions burned: 17 (million)
% 1.75/1.49 % (21363)------------------------------
% 1.75/1.49 % (21363)------------------------------
% 1.75/1.50 % (21365)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/3Mi)
% 1.80/1.50 % (21366)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/7Mi)
% 1.80/1.50 % (21365)Instruction limit reached!
% 1.80/1.50 % (21365)------------------------------
% 1.80/1.50 % (21365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.50 % (21365)Termination reason: Unknown
% 1.80/1.50 % (21365)Termination phase: Preprocessing 3
% 1.80/1.50
% 1.80/1.50 % (21365)Memory used [KB]: 1023
% 1.80/1.50 % (21365)Time elapsed: 0.003 s
% 1.80/1.50 % (21365)Instructions burned: 4 (million)
% 1.80/1.50 % (21365)------------------------------
% 1.80/1.50 % (21365)------------------------------
% 1.80/1.50 % (21366)Instruction limit reached!
% 1.80/1.50 % (21366)------------------------------
% 1.80/1.50 % (21366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.50 % (21366)Termination reason: Unknown
% 1.80/1.50 % (21366)Termination phase: Saturation
% 1.80/1.50
% 1.80/1.50 % (21366)Memory used [KB]: 5500
% 1.80/1.50 % (21366)Time elapsed: 0.005 s
% 1.80/1.50 % (21366)Instructions burned: 7 (million)
% 1.80/1.50 % (21366)------------------------------
% 1.80/1.50 % (21366)------------------------------
% 1.80/1.51 % (21367)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/3Mi)
% 1.80/1.51 % (21367)Instruction limit reached!
% 1.80/1.51 % (21367)------------------------------
% 1.80/1.51 % (21367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.51 % (21367)Termination reason: Unknown
% 1.80/1.51 % (21367)Termination phase: Property scanning
% 1.80/1.51
% 1.80/1.51 % (21367)Memory used [KB]: 1023
% 1.80/1.51 % (21367)Time elapsed: 0.003 s
% 1.80/1.51 % (21367)Instructions burned: 4 (million)
% 1.80/1.51 % (21367)------------------------------
% 1.80/1.51 % (21367)------------------------------
% 1.80/1.51 % (21368)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/4Mi)
% 1.80/1.51 % (21368)Instruction limit reached!
% 1.80/1.51 % (21368)------------------------------
% 1.80/1.51 % (21368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.51 % (21368)Termination reason: Unknown
% 1.80/1.51 % (21368)Termination phase: Preprocessing 3
% 1.80/1.51
% 1.80/1.51 % (21368)Memory used [KB]: 1023
% 1.80/1.51 % (21368)Time elapsed: 0.003 s
% 1.80/1.51 % (21368)Instructions burned: 4 (million)
% 1.80/1.51 % (21368)------------------------------
% 1.80/1.51 % (21368)------------------------------
% 1.80/1.51 % (21369)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/18Mi)
% 1.80/1.52 % (21370)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/710Mi)
% 1.80/1.52 % (21369)Instruction limit reached!
% 1.80/1.52 % (21369)------------------------------
% 1.80/1.52 % (21369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.52 % (21369)Termination reason: Unknown
% 1.80/1.52 % (21369)Termination phase: Saturation
% 1.80/1.52
% 1.80/1.52 % (21369)Memory used [KB]: 5628
% 1.80/1.52 % (21369)Time elapsed: 0.011 s
% 1.80/1.52 % (21369)Instructions burned: 18 (million)
% 1.80/1.52 % (21369)------------------------------
% 1.80/1.52 % (21369)------------------------------
% 1.80/1.53 % (21371)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/6Mi)
% 1.80/1.53 % (21372)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/902Mi)
% 1.80/1.53 % (21371)Instruction limit reached!
% 1.80/1.53 % (21371)------------------------------
% 1.80/1.53 % (21371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.53 % (21371)Termination reason: Unknown
% 1.80/1.53 % (21371)Termination phase: Property scanning
% 1.80/1.53
% 1.80/1.53 % (21371)Memory used [KB]: 1023
% 1.80/1.53 % (21371)Time elapsed: 0.004 s
% 1.80/1.53 % (21371)Instructions burned: 6 (million)
% 1.80/1.53 % (21371)------------------------------
% 1.80/1.53 % (21371)------------------------------
% 1.80/1.53 % (21350)Instruction limit reached!
% 1.80/1.53 % (21350)------------------------------
% 1.80/1.53 % (21350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.53 % (21350)Termination reason: Unknown
% 1.80/1.53 % (21350)Termination phase: Saturation
% 1.80/1.53
% 1.80/1.53 % (21350)Memory used [KB]: 6524
% 1.80/1.53 % (21350)Time elapsed: 0.096 s
% 1.80/1.53 % (21350)Instructions burned: 183 (million)
% 1.80/1.53 % (21350)------------------------------
% 1.80/1.53 % (21350)------------------------------
% 1.80/1.54 % (21373)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/21Mi)
% 1.80/1.54 % (21374)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21253 for (2999ds/5Mi)
% 1.80/1.55 % (21374)Instruction limit reached!
% 1.80/1.55 % (21374)------------------------------
% 1.80/1.55 % (21374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.55 % (21374)Termination reason: Unknown
% 1.80/1.55 % (21374)Termination phase: Saturation
% 1.80/1.55
% 1.80/1.55 % (21374)Memory used [KB]: 1023
% 1.80/1.55 % (21374)Time elapsed: 0.004 s
% 1.80/1.55 % (21374)Instructions burned: 6 (million)
% 1.80/1.55 % (21374)------------------------------
% 1.80/1.55 % (21374)------------------------------
% 1.80/1.55 % (21373)Instruction limit reached!
% 1.80/1.55 % (21373)------------------------------
% 1.80/1.55 % (21373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.55 % (21373)Termination reason: Unknown
% 1.80/1.55 % (21373)Termination phase: Saturation
% 1.80/1.55
% 1.80/1.55 % (21373)Memory used [KB]: 5756
% 1.80/1.55 % (21373)Time elapsed: 0.036 s
% 1.80/1.55 % (21373)Instructions burned: 21 (million)
% 1.80/1.55 % (21373)------------------------------
% 1.80/1.55 % (21373)------------------------------
% 1.80/1.55 % (21375)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_21253 for (2998ds/6Mi)
% 1.80/1.55 % (21375)Instruction limit reached!
% 1.80/1.55 % (21375)------------------------------
% 1.80/1.55 % (21375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.55 % (21375)Termination reason: Unknown
% 1.80/1.55 % (21375)Termination phase: Property scanning
% 1.80/1.55
% 1.80/1.55 % (21375)Memory used [KB]: 1023
% 1.80/1.55 % (21375)Time elapsed: 0.004 s
% 1.80/1.55 % (21375)Instructions burned: 6 (million)
% 1.80/1.55 % (21375)------------------------------
% 1.80/1.55 % (21375)------------------------------
% 1.80/1.56 % (21376)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21253 for (2998ds/377Mi)
% 1.80/1.57 % (21377)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_21253 for (2998ds/779Mi)
% 1.80/1.57 % (21378)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_21253 for (2998ds/19Mi)
% 1.80/1.58 % (21378)Instruction limit reached!
% 1.80/1.58 % (21378)------------------------------
% 1.80/1.58 % (21378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.58 % (21378)Termination reason: Unknown
% 1.80/1.58 % (21378)Termination phase: Saturation
% 1.80/1.58
% 1.80/1.58 % (21378)Memory used [KB]: 5628
% 1.80/1.58 % (21378)Time elapsed: 0.010 s
% 1.80/1.58 % (21378)Instructions burned: 19 (million)
% 1.80/1.58 % (21378)------------------------------
% 1.80/1.58 % (21378)------------------------------
% 1.80/1.58 % (21355)Instruction limit reached!
% 1.80/1.58 % (21355)------------------------------
% 1.80/1.58 % (21355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.58 % (21355)Termination reason: Unknown
% 1.80/1.58 % (21355)Termination phase: Saturation
% 1.80/1.58
% 1.80/1.58 % (21355)Memory used [KB]: 6268
% 1.80/1.58 % (21355)Time elapsed: 0.136 s
% 1.80/1.58 % (21355)Instructions burned: 275 (million)
% 1.80/1.58 % (21355)------------------------------
% 1.80/1.58 % (21355)------------------------------
% 1.80/1.59 % (21379)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21253 for (2998ds/879Mi)
% 1.80/1.60 % (21380)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21253 for (2998ds/17Mi)
% 1.80/1.61 % (21380)Instruction limit reached!
% 1.80/1.61 % (21380)------------------------------
% 1.80/1.61 % (21380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.61 % (21380)Termination reason: Unknown
% 1.80/1.61 % (21380)Termination phase: Saturation
% 1.80/1.61
% 1.80/1.61 % (21380)Memory used [KB]: 5756
% 1.80/1.61 % (21380)Time elapsed: 0.011 s
% 1.80/1.61 % (21380)Instructions burned: 17 (million)
% 1.80/1.61 % (21380)------------------------------
% 1.80/1.61 % (21380)------------------------------
% 1.80/1.62 % (21381)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21253 for (2998ds/3Mi)
% 1.80/1.62 % (21381)Instruction limit reached!
% 1.80/1.62 % (21381)------------------------------
% 1.80/1.62 % (21381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.62 % (21381)Termination reason: Unknown
% 1.80/1.62 % (21381)Termination phase: Preprocessing 2
% 1.80/1.62
% 1.80/1.62 % (21381)Memory used [KB]: 1023
% 1.80/1.62 % (21381)Time elapsed: 0.003 s
% 1.80/1.62 % (21381)Instructions burned: 3 (million)
% 1.80/1.62 % (21381)------------------------------
% 1.80/1.62 % (21381)------------------------------
% 1.80/1.64 % (21382)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21253 for (2997ds/30Mi)
% 1.80/1.66 % (21382)Instruction limit reached!
% 1.80/1.66 % (21382)------------------------------
% 1.80/1.66 % (21382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.66 % (21382)Termination reason: Unknown
% 1.80/1.66 % (21382)Termination phase: Saturation
% 1.80/1.66
% 1.80/1.66 % (21382)Memory used [KB]: 5756
% 1.80/1.66 % (21382)Time elapsed: 0.018 s
% 1.80/1.66 % (21382)Instructions burned: 31 (million)
% 1.80/1.66 % (21382)------------------------------
% 1.80/1.66 % (21382)------------------------------
% 1.80/1.67 % (21383)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_21253 for (2997ds/127Mi)
% 1.80/1.68 % (21376)First to succeed.
% 1.80/1.69 % (21376)Refutation found. Thanks to Tanya!
% 1.80/1.69 % SZS status Theorem for DTF2THF_21253
% 1.80/1.69 % SZS output start Proof for DTF2THF_21253
% 1.80/1.69 thf(func_def_0, type, cBIGPHI: $i > $i).
% 1.80/1.69 thf(func_def_1, type, cHOM_FROM_HH_1: ($i > $i) > $o).
% 1.80/1.69 thf(func_def_2, type, cPHI_2: $i > $i).
% 1.80/1.69 thf(func_def_3, type, cHOM_FROM_SS_PRIME: ($i > $i) > $o).
% 1.80/1.69 thf(func_def_4, type, cPHI_1: $i > $i).
% 1.80/1.69 thf(func_def_5, type, cSS_PRIME: $i > $o).
% 1.80/1.69 thf(func_def_6, type, el1: $i > ($i > $o) > $o).
% 1.80/1.69 thf(func_def_7, type, cHH_1: $i > $o).
% 1.80/1.69 thf(func_def_8, type, cBIGHI: $i > $i).
% 1.80/1.69 thf(func_def_9, type, cHH_2: $i > $o).
% 1.80/1.69 thf(func_def_10, type, cTIMES: $i > $i > $i).
% 1.80/1.69 thf(func_def_14, type, sK0: ($i > $i) > $i).
% 1.80/1.69 thf(func_def_15, type, sK1: ($i > $i) > $i).
% 1.80/1.69 thf(func_def_16, type, sK2: $i > $i).
% 1.80/1.69 thf(func_def_20, type, ph6: !>[X0: $tType]:(X0)).
% 1.80/1.69 thf(f1204,plain,(
% 1.80/1.69 $false),
% 1.80/1.69 inference(avatar_sat_refutation,[status(thm)],[f53,f58,f59,f64,f177,f182,f208,f226,f351,f420,f1090,f1198])).
% 1.80/1.69 thf(f1198,plain,(
% 1.80/1.69 spl5_1 | ~spl5_4 | ~spl5_7 | ~spl5_11 | ~spl5_19 | ~spl5_32 | ~spl5_82),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f1197,f1051,f418,f349,f199,f179,f61,f46])).
% 1.80/1.69 thf(f46,definition,(
% 1.80/1.69 spl5_1 <=> ((cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3)) = (cBIGPHI @ (cTIMES @ sK4 @ sK3)))),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.80/1.69 thf(f61,definition,(
% 1.80/1.69 spl5_4 <=> ((el1 @ sK4 @ cHH_1) = $true)),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.80/1.69 thf(f179,definition,(
% 1.80/1.69 spl5_7 <=> ((cBIGPHI @ sK4) = (cPHI_2 @ (sK2 @ sK4)))),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition])).
% 1.80/1.69 thf(f199,definition,(
% 1.80/1.69 spl5_11 <=> ((el1 @ (sK2 @ sK4) @ cSS_PRIME) = $true)),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_11])],[avatar_definition])).
% 1.80/1.69 thf(f349,definition,(
% 1.80/1.69 spl5_19 <=> ! [X0 : $i] : (((cTIMES @ (cPHI_2 @ X0) @ (cBIGPHI @ sK3)) = (cPHI_2 @ (cTIMES @ X0 @ (sK2 @ sK3)))) | ((el1 @ X0 @ cSS_PRIME) != $true))),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_19])],[avatar_definition])).
% 1.80/1.69 thf(f418,definition,(
% 1.80/1.69 spl5_32 <=> ! [X0 : $i] : (((cPHI_1 @ (cTIMES @ X0 @ (sK2 @ sK3))) = (cTIMES @ (cPHI_1 @ X0) @ sK3)) | ((el1 @ X0 @ cSS_PRIME) != $true))),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_32])],[avatar_definition])).
% 1.80/1.69 thf(f1051,definition,(
% 1.80/1.69 spl5_82 <=> ((el1 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3)) @ cSS_PRIME) = $true)),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_82])],[avatar_definition])).
% 1.80/1.69 thf(f1197,plain,(
% 1.80/1.69 ((cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3)) = (cBIGPHI @ (cTIMES @ sK4 @ sK3))) | (~spl5_4 | ~spl5_7 | ~spl5_11 | ~spl5_19 | ~spl5_32 | ~spl5_82)),
% 1.80/1.69 inference(forward_demodulation,[status(thm)],[f1196,f82])).
% 1.80/1.69 thf(f82,plain,(
% 1.80/1.69 ((cPHI_1 @ (sK2 @ sK4)) = sK4) | ~spl5_4),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.80/1.69 thf(f80,plain,(
% 1.80/1.69 ($true != $true) | ((cPHI_1 @ (sK2 @ sK4)) = sK4) | ~spl5_4),
% 1.80/1.69 inference(superposition,[status(thm)],[f26,f63])).
% 1.80/1.69 thf(f63,plain,(
% 1.80/1.69 ((el1 @ sK4 @ cHH_1) = $true) | ~spl5_4),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.80/1.69 thf(f26,plain,(
% 1.80/1.69 ( ! [X14 : $i] : (($true != (el1 @ X14 @ cHH_1)) | ((cPHI_1 @ (sK2 @ X14)) = X14)) )),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 thf(f14,plain,(
% 1.80/1.69 ! [X0 : $i] : (((el1 @ (cBIGPHI @ X0) @ cHH_2) = $true) | ((el1 @ X0 @ cHH_1) != $true)) & ! [X1 : $i,X2 : $i] : (((cBIGPHI @ X2) = (cBIGHI @ X1)) | (X1 != X2) | ((el1 @ X1 @ cHH_1) != $true) | ((el1 @ X2 @ cHH_1) != $true)) & ! [X3 : $i > $i] : ((! [X4 : $i,X5 : $i] : (((el1 @ X4 @ cSS_PRIME) != $true) | ((el1 @ X5 @ cSS_PRIME) != $true) | ((X3 @ (cTIMES @ X4 @ X5)) = (cTIMES @ (X3 @ X4) @ (X3 @ X5)))) | ((cHOM_FROM_SS_PRIME @ X3) != $true)) & (((cHOM_FROM_SS_PRIME @ X3) = $true) | (((el1 @ (sK0 @ X3) @ cSS_PRIME) = $true) & ((el1 @ (sK1 @ X3) @ cSS_PRIME) = $true) & ((cTIMES @ (X3 @ (sK0 @ X3)) @ (X3 @ (sK1 @ X3))) != (X3 @ (cTIMES @ (sK0 @ X3) @ (sK1 @ X3))))))) & ! [X8 : $i] : (((el1 @ (cPHI_2 @ X8) @ cHH_2) = $true) | ($true != (el1 @ X8 @ cSS_PRIME))) & ! [X9 : $i,X10 : $i,X11 : $i,X12 : $i] : (((el1 @ X10 @ cHH_2) != $true) | ((cTIMES @ X12 @ X11) = (cTIMES @ X10 @ X9)) | ((el1 @ X11 @ cHH_2) != $true) | ((el1 @ X12 @ cHH_2) != $true) | ($true != (el1 @ X9 @ cHH_2)) | (X10 != X12) | (X9 != X11)) & ! [X13 : $i] : (((el1 @ X13 @ cSS_PRIME) != $true) | ((el1 @ (cPHI_1 @ X13) @ cHH_1) = $true)) & ! [X14 : $i] : (($true != (el1 @ X14 @ cHH_1)) | (((el1 @ (sK2 @ X14) @ cSS_PRIME) = $true) & ((cPHI_1 @ (sK2 @ X14)) = X14))) & ! [X16 : $i,X17 : $i] : (((el1 @ X16 @ cHH_1) != $true) | ((el1 @ X17 @ cHH_1) != $true) | ((el1 @ (cTIMES @ X16 @ X17) @ cHH_1) = $true)) & (((cHOM_FROM_HH_1 @ cBIGPHI) = $true) | (((el1 @ sK4 @ cHH_1) = $true) & ((cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3)) != (cBIGPHI @ (cTIMES @ sK4 @ sK3))) & ((el1 @ sK3 @ cHH_1) = $true))) & (! [X20 : $i,X21 : $i] : (($true != (el1 @ X21 @ cHH_1)) | ((cTIMES @ (cBIGPHI @ X21) @ (cBIGPHI @ X20)) = (cBIGPHI @ (cTIMES @ X21 @ X20))) | ((el1 @ X20 @ cHH_1) != $true)) | ((cHOM_FROM_HH_1 @ cBIGPHI) != $true)) & ! [X22 : $i,X23 : $i,X24 : $i,X25 : $i] : ((X24 != X25) | ((el1 @ X24 @ cHH_1) != $true) | ((el1 @ X22 @ cHH_1) != $true) | ((cTIMES @ X24 @ X23) = (cTIMES @ X25 @ X22)) | (X22 != X23) | ((el1 @ X25 @ cHH_1) != $true) | ($true != (el1 @ X23 @ cHH_1))) & ((cHOM_FROM_SS_PRIME @ cPHI_1) = $true) & ! [X26 : $i] : (((el1 @ X26 @ cSS_PRIME) != $true) | ((cBIGPHI @ (cPHI_1 @ X26)) = (cPHI_2 @ X26))) & ((cHOM_FROM_SS_PRIME @ cPHI_2) = $true) & ! [X27 : $i,X28 : $i] : (((el1 @ X28 @ cSS_PRIME) != $true) | ((el1 @ (cTIMES @ X28 @ X27) @ cSS_PRIME) = $true) | ((el1 @ X27 @ cSS_PRIME) != $true)) & ((cHOM_FROM_HH_1 @ cBIGPHI) != $true)),
% 1.80/1.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f10,f13,f12,f11])).
% 1.80/1.69 thf(f11,plain,(
% 1.80/1.69 ! [X3 : $i > $i] : (? [X6 : $i,X7 : $i] : (((el1 @ X6 @ cSS_PRIME) = $true) & ((el1 @ X7 @ cSS_PRIME) = $true) & ((X3 @ (cTIMES @ X6 @ X7)) != (cTIMES @ (X3 @ X6) @ (X3 @ X7)))) => (((el1 @ (sK0 @ X3) @ cSS_PRIME) = $true) & ((el1 @ (sK1 @ X3) @ cSS_PRIME) = $true) & ((cTIMES @ (X3 @ (sK0 @ X3)) @ (X3 @ (sK1 @ X3))) != (X3 @ (cTIMES @ (sK0 @ X3) @ (sK1 @ X3))))))),
% 1.80/1.69 introduced(definition,[],[choice_axiom])).
% 1.80/1.69 thf(f12,plain,(
% 1.80/1.69 ! [X14 : $i] : (? [X15 : $i] : (((el1 @ X15 @ cSS_PRIME) = $true) & ((cPHI_1 @ X15) = X14)) => (((el1 @ (sK2 @ X14) @ cSS_PRIME) = $true) & ((cPHI_1 @ (sK2 @ X14)) = X14)))),
% 1.80/1.69 introduced(definition,[],[choice_axiom])).
% 1.80/1.69 thf(f13,plain,(
% 1.80/1.69 ? [X18 : $i,X19 : $i] : (((el1 @ X19 @ cHH_1) = $true) & ((cBIGPHI @ (cTIMES @ X19 @ X18)) != (cTIMES @ (cBIGPHI @ X19) @ (cBIGPHI @ X18))) & ((el1 @ X18 @ cHH_1) = $true)) => (((el1 @ sK4 @ cHH_1) = $true) & ((cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3)) != (cBIGPHI @ (cTIMES @ sK4 @ sK3))) & ((el1 @ sK3 @ cHH_1) = $true))),
% 1.80/1.69 introduced(definition,[],[choice_axiom])).
% 1.80/1.69 thf(f10,plain,(
% 1.80/1.69 ! [X0 : $i] : (((el1 @ (cBIGPHI @ X0) @ cHH_2) = $true) | ((el1 @ X0 @ cHH_1) != $true)) & ! [X1 : $i,X2 : $i] : (((cBIGPHI @ X2) = (cBIGHI @ X1)) | (X1 != X2) | ((el1 @ X1 @ cHH_1) != $true) | ((el1 @ X2 @ cHH_1) != $true)) & ! [X3 : $i > $i] : ((! [X4 : $i,X5 : $i] : (((el1 @ X4 @ cSS_PRIME) != $true) | ((el1 @ X5 @ cSS_PRIME) != $true) | ((X3 @ (cTIMES @ X4 @ X5)) = (cTIMES @ (X3 @ X4) @ (X3 @ X5)))) | ((cHOM_FROM_SS_PRIME @ X3) != $true)) & (((cHOM_FROM_SS_PRIME @ X3) = $true) | ? [X6 : $i,X7 : $i] : (((el1 @ X6 @ cSS_PRIME) = $true) & ((el1 @ X7 @ cSS_PRIME) = $true) & ((X3 @ (cTIMES @ X6 @ X7)) != (cTIMES @ (X3 @ X6) @ (X3 @ X7)))))) & ! [X8 : $i] : (((el1 @ (cPHI_2 @ X8) @ cHH_2) = $true) | ($true != (el1 @ X8 @ cSS_PRIME))) & ! [X9 : $i,X10 : $i,X11 : $i,X12 : $i] : (((el1 @ X10 @ cHH_2) != $true) | ((cTIMES @ X12 @ X11) = (cTIMES @ X10 @ X9)) | ((el1 @ X11 @ cHH_2) != $true) | ((el1 @ X12 @ cHH_2) != $true) | ($true != (el1 @ X9 @ cHH_2)) | (X10 != X12) | (X9 != X11)) & ! [X13 : $i] : (((el1 @ X13 @ cSS_PRIME) != $true) | ((el1 @ (cPHI_1 @ X13) @ cHH_1) = $true)) & ! [X14 : $i] : (($true != (el1 @ X14 @ cHH_1)) | ? [X15 : $i] : (((el1 @ X15 @ cSS_PRIME) = $true) & ((cPHI_1 @ X15) = X14))) & ! [X16 : $i,X17 : $i] : (((el1 @ X16 @ cHH_1) != $true) | ((el1 @ X17 @ cHH_1) != $true) | ((el1 @ (cTIMES @ X16 @ X17) @ cHH_1) = $true)) & (((cHOM_FROM_HH_1 @ cBIGPHI) = $true) | ? [X18 : $i,X19 : $i] : (((el1 @ X19 @ cHH_1) = $true) & ((cBIGPHI @ (cTIMES @ X19 @ X18)) != (cTIMES @ (cBIGPHI @ X19) @ (cBIGPHI @ X18))) & ((el1 @ X18 @ cHH_1) = $true))) & (! [X20 : $i,X21 : $i] : (($true != (el1 @ X21 @ cHH_1)) | ((cTIMES @ (cBIGPHI @ X21) @ (cBIGPHI @ X20)) = (cBIGPHI @ (cTIMES @ X21 @ X20))) | ((el1 @ X20 @ cHH_1) != $true)) | ((cHOM_FROM_HH_1 @ cBIGPHI) != $true)) & ! [X22 : $i,X23 : $i,X24 : $i,X25 : $i] : ((X24 != X25) | ((el1 @ X24 @ cHH_1) != $true) | ((el1 @ X22 @ cHH_1) != $true) | ((cTIMES @ X24 @ X23) = (cTIMES @ X25 @ X22)) | (X22 != X23) | ((el1 @ X25 @ cHH_1) != $true) | ($true != (el1 @ X23 @ cHH_1))) & ((cHOM_FROM_SS_PRIME @ cPHI_1) = $true) & ! [X26 : $i] : (((el1 @ X26 @ cSS_PRIME) != $true) | ((cBIGPHI @ (cPHI_1 @ X26)) = (cPHI_2 @ X26))) & ((cHOM_FROM_SS_PRIME @ cPHI_2) = $true) & ! [X27 : $i,X28 : $i] : (((el1 @ X28 @ cSS_PRIME) != $true) | ((el1 @ (cTIMES @ X28 @ X27) @ cSS_PRIME) = $true) | ((el1 @ X27 @ cSS_PRIME) != $true)) & ((cHOM_FROM_HH_1 @ cBIGPHI) != $true)),
% 1.80/1.69 inference(rectify,[status(thm)],[f9])).
% 1.80/1.69 thf(f9,plain,(
% 1.80/1.69 ! [X20 : $i] : (((el1 @ (cBIGPHI @ X20) @ cHH_2) = $true) | ((el1 @ X20 @ cHH_1) != $true)) & ! [X12 : $i,X13 : $i] : (((cBIGHI @ X12) = (cBIGPHI @ X13)) | (X12 != X13) | ($true != (el1 @ X12 @ cHH_1)) | ($true != (el1 @ X13 @ cHH_1))) & ! [X14 : $i > $i] : ((! [X15 : $i,X16 : $i] : (((el1 @ X15 @ cSS_PRIME) != $true) | ((el1 @ X16 @ cSS_PRIME) != $true) | ((cTIMES @ (X14 @ X15) @ (X14 @ X16)) = (X14 @ (cTIMES @ X15 @ X16)))) | ($true != (cHOM_FROM_SS_PRIME @ X14))) & (($true = (cHOM_FROM_SS_PRIME @ X14)) | ? [X15 : $i,X16 : $i] : (((el1 @ X15 @ cSS_PRIME) = $true) & ((el1 @ X16 @ cSS_PRIME) = $true) & ((cTIMES @ (X14 @ X15) @ (X14 @ X16)) != (X14 @ (cTIMES @ X15 @ X16)))))) & ! [X7 : $i] : (((el1 @ (cPHI_2 @ X7) @ cHH_2) = $true) | ((el1 @ X7 @ cSS_PRIME) != $true)) & ! [X9 : $i,X8 : $i,X10 : $i,X11 : $i] : (((el1 @ X8 @ cHH_2) != $true) | ((cTIMES @ X11 @ X10) = (cTIMES @ X8 @ X9)) | ((el1 @ X10 @ cHH_2) != $true) | ((el1 @ X11 @ cHH_2) != $true) | ($true != (el1 @ X9 @ cHH_2)) | (X8 != X11) | (X9 != X10)) & ! [X17 : $i] : (((el1 @ X17 @ cSS_PRIME) != $true) | ((el1 @ (cPHI_1 @ X17) @ cHH_1) = $true)) & ! [X2 : $i] : (((el1 @ X2 @ cHH_1) != $true) | ? [X3 : $i] : (((el1 @ X3 @ cSS_PRIME) = $true) & ((cPHI_1 @ X3) = X2))) & ! [X0 : $i,X1 : $i] : (((el1 @ X0 @ cHH_1) != $true) | ((el1 @ X1 @ cHH_1) != $true) | ($true = (el1 @ (cTIMES @ X0 @ X1) @ cHH_1))) & (((cHOM_FROM_HH_1 @ cBIGPHI) = $true) | ? [X5 : $i,X6 : $i] : (((el1 @ X6 @ cHH_1) = $true) & ((cBIGPHI @ (cTIMES @ X6 @ X5)) != (cTIMES @ (cBIGPHI @ X6) @ (cBIGPHI @ X5))) & ((el1 @ X5 @ cHH_1) = $true))) & (! [X5 : $i,X6 : $i] : (((el1 @ X6 @ cHH_1) != $true) | ((cBIGPHI @ (cTIMES @ X6 @ X5)) = (cTIMES @ (cBIGPHI @ X6) @ (cBIGPHI @ X5))) | ((el1 @ X5 @ cHH_1) != $true)) | ((cHOM_FROM_HH_1 @ cBIGPHI) != $true)) & ! [X21 : $i,X23 : $i,X24 : $i,X22 : $i] : ((X22 != X24) | ((el1 @ X24 @ cHH_1) != $true) | ($true != (el1 @ X21 @ cHH_1)) | ((cTIMES @ X24 @ X23) = (cTIMES @ X22 @ X21)) | (X21 != X23) | ((el1 @ X22 @ cHH_1) != $true) | ($true != (el1 @ X23 @ cHH_1))) & ((cHOM_FROM_SS_PRIME @ cPHI_1) = $true) & ! [X4 : $i] : (((el1 @ X4 @ cSS_PRIME) != $true) | ((cBIGPHI @ (cPHI_1 @ X4)) = (cPHI_2 @ X4))) & ((cHOM_FROM_SS_PRIME @ cPHI_2) = $true) & ! [X18 : $i,X19 : $i] : (((el1 @ X19 @ cSS_PRIME) != $true) | ((el1 @ (cTIMES @ X19 @ X18) @ cSS_PRIME) = $true) | ((el1 @ X18 @ cSS_PRIME) != $true)) & ((cHOM_FROM_HH_1 @ cBIGPHI) != $true)),
% 1.80/1.69 inference(flattening,[status(thm)],[f8])).
% 1.80/1.69 thf(f8,plain,(
% 1.80/1.69 ! [X20 : $i] : (((el1 @ (cBIGPHI @ X20) @ cHH_2) = $true) | ((el1 @ X20 @ cHH_1) != $true)) & ! [X12 : $i,X13 : $i] : (((cBIGHI @ X12) = (cBIGPHI @ X13)) | (X12 != X13) | ($true != (el1 @ X12 @ cHH_1)) | ($true != (el1 @ X13 @ cHH_1))) & ! [X14 : $i > $i] : ((! [X15 : $i,X16 : $i] : (((el1 @ X15 @ cSS_PRIME) != $true) | ((el1 @ X16 @ cSS_PRIME) != $true) | ((cTIMES @ (X14 @ X15) @ (X14 @ X16)) = (X14 @ (cTIMES @ X15 @ X16)))) | ($true != (cHOM_FROM_SS_PRIME @ X14))) & (($true = (cHOM_FROM_SS_PRIME @ X14)) | ? [X15 : $i,X16 : $i] : (((el1 @ X15 @ cSS_PRIME) = $true) & ((el1 @ X16 @ cSS_PRIME) = $true) & ((cTIMES @ (X14 @ X15) @ (X14 @ X16)) != (X14 @ (cTIMES @ X15 @ X16)))))) & ! [X7 : $i] : (((el1 @ (cPHI_2 @ X7) @ cHH_2) = $true) | ((el1 @ X7 @ cSS_PRIME) != $true)) & ! [X9 : $i,X8 : $i,X10 : $i,X11 : $i] : (((el1 @ X8 @ cHH_2) != $true) | ((cTIMES @ X11 @ X10) = (cTIMES @ X8 @ X9)) | ((el1 @ X10 @ cHH_2) != $true) | ((el1 @ X11 @ cHH_2) != $true) | ($true != (el1 @ X9 @ cHH_2)) | (X8 != X11) | (X9 != X10)) & ! [X17 : $i] : (((el1 @ X17 @ cSS_PRIME) != $true) | ((el1 @ (cPHI_1 @ X17) @ cHH_1) = $true)) & ! [X2 : $i] : (((el1 @ X2 @ cHH_1) != $true) | ? [X3 : $i] : (((el1 @ X3 @ cSS_PRIME) = $true) & ((cPHI_1 @ X3) = X2))) & ! [X0 : $i,X1 : $i] : (((el1 @ X0 @ cHH_1) != $true) | ((el1 @ X1 @ cHH_1) != $true) | ($true = (el1 @ (cTIMES @ X0 @ X1) @ cHH_1))) & ((((cHOM_FROM_HH_1 @ cBIGPHI) = $true) | ? [X5 : $i,X6 : $i] : (((el1 @ X6 @ cHH_1) = $true) & ((cBIGPHI @ (cTIMES @ X6 @ X5)) != (cTIMES @ (cBIGPHI @ X6) @ (cBIGPHI @ X5))) & ((el1 @ X5 @ cHH_1) = $true))) & (! [X5 : $i,X6 : $i] : (((el1 @ X6 @ cHH_1) != $true) | ((cBIGPHI @ (cTIMES @ X6 @ X5)) = (cTIMES @ (cBIGPHI @ X6) @ (cBIGPHI @ X5))) | ((el1 @ X5 @ cHH_1) != $true)) | ((cHOM_FROM_HH_1 @ cBIGPHI) != $true))) & ! [X21 : $i,X23 : $i,X24 : $i,X22 : $i] : ((X22 != X24) | ((el1 @ X24 @ cHH_1) != $true) | ($true != (el1 @ X21 @ cHH_1)) | ((cTIMES @ X24 @ X23) = (cTIMES @ X22 @ X21)) | (X21 != X23) | ((el1 @ X22 @ cHH_1) != $true) | ($true != (el1 @ X23 @ cHH_1))) & ((cHOM_FROM_SS_PRIME @ cPHI_1) = $true) & ! [X4 : $i] : (((el1 @ X4 @ cSS_PRIME) != $true) | ((cBIGPHI @ (cPHI_1 @ X4)) = (cPHI_2 @ X4))) & ((cHOM_FROM_SS_PRIME @ cPHI_2) = $true) & ! [X18 : $i,X19 : $i] : (((el1 @ X19 @ cSS_PRIME) != $true) | ((el1 @ (cTIMES @ X19 @ X18) @ cSS_PRIME) = $true) | ((el1 @ X18 @ cSS_PRIME) != $true)) & ((cHOM_FROM_HH_1 @ cBIGPHI) != $true)),
% 1.80/1.69 inference(nnf_transformation,[status(thm)],[f7])).
% 1.80/1.69 thf(f7,plain,(
% 1.80/1.69 ! [X20 : $i] : (((el1 @ (cBIGPHI @ X20) @ cHH_2) = $true) | ((el1 @ X20 @ cHH_1) != $true)) & ! [X12 : $i,X13 : $i] : (((cBIGHI @ X12) = (cBIGPHI @ X13)) | (X12 != X13) | ($true != (el1 @ X12 @ cHH_1)) | ($true != (el1 @ X13 @ cHH_1))) & ! [X14 : $i > $i] : (! [X15 : $i,X16 : $i] : (((el1 @ X15 @ cSS_PRIME) != $true) | ((el1 @ X16 @ cSS_PRIME) != $true) | ((cTIMES @ (X14 @ X15) @ (X14 @ X16)) = (X14 @ (cTIMES @ X15 @ X16)))) <=> ($true = (cHOM_FROM_SS_PRIME @ X14))) & ! [X7 : $i] : (((el1 @ (cPHI_2 @ X7) @ cHH_2) = $true) | ((el1 @ X7 @ cSS_PRIME) != $true)) & ! [X9 : $i,X8 : $i,X10 : $i,X11 : $i] : (((el1 @ X8 @ cHH_2) != $true) | ((cTIMES @ X11 @ X10) = (cTIMES @ X8 @ X9)) | ((el1 @ X10 @ cHH_2) != $true) | ((el1 @ X11 @ cHH_2) != $true) | ($true != (el1 @ X9 @ cHH_2)) | (X8 != X11) | (X9 != X10)) & ! [X17 : $i] : (((el1 @ X17 @ cSS_PRIME) != $true) | ((el1 @ (cPHI_1 @ X17) @ cHH_1) = $true)) & ! [X2 : $i] : (((el1 @ X2 @ cHH_1) != $true) | ? [X3 : $i] : (((el1 @ X3 @ cSS_PRIME) = $true) & ((cPHI_1 @ X3) = X2))) & ! [X0 : $i,X1 : $i] : (((el1 @ X0 @ cHH_1) != $true) | ((el1 @ X1 @ cHH_1) != $true) | ($true = (el1 @ (cTIMES @ X0 @ X1) @ cHH_1))) & (((cHOM_FROM_HH_1 @ cBIGPHI) = $true) <=> ! [X5 : $i,X6 : $i] : (((el1 @ X6 @ cHH_1) != $true) | ((cBIGPHI @ (cTIMES @ X6 @ X5)) = (cTIMES @ (cBIGPHI @ X6) @ (cBIGPHI @ X5))) | ((el1 @ X5 @ cHH_1) != $true))) & ! [X21 : $i,X23 : $i,X24 : $i,X22 : $i] : ((X22 != X24) | ((el1 @ X24 @ cHH_1) != $true) | ($true != (el1 @ X21 @ cHH_1)) | ((cTIMES @ X24 @ X23) = (cTIMES @ X22 @ X21)) | (X21 != X23) | ((el1 @ X22 @ cHH_1) != $true) | ($true != (el1 @ X23 @ cHH_1))) & ((cHOM_FROM_SS_PRIME @ cPHI_1) = $true) & ! [X4 : $i] : (((el1 @ X4 @ cSS_PRIME) != $true) | ((cBIGPHI @ (cPHI_1 @ X4)) = (cPHI_2 @ X4))) & ((cHOM_FROM_SS_PRIME @ cPHI_2) = $true) & ! [X18 : $i,X19 : $i] : (((el1 @ X19 @ cSS_PRIME) != $true) | ((el1 @ (cTIMES @ X19 @ X18) @ cSS_PRIME) = $true) | ((el1 @ X18 @ cSS_PRIME) != $true)) & ((cHOM_FROM_HH_1 @ cBIGPHI) != $true)),
% 1.80/1.69 inference(flattening,[status(thm)],[f6])).
% 1.80/1.69 thf(f6,plain,(
% 1.80/1.69 ((cHOM_FROM_HH_1 @ cBIGPHI) != $true) & (! [X19 : $i,X18 : $i] : (((el1 @ (cTIMES @ X19 @ X18) @ cSS_PRIME) = $true) | (((el1 @ X18 @ cSS_PRIME) != $true) | ((el1 @ X19 @ cSS_PRIME) != $true))) & ! [X22 : $i,X24 : $i,X23 : $i,X21 : $i] : (((cTIMES @ X24 @ X23) = (cTIMES @ X22 @ X21)) | ((X21 != X23) | (X22 != X24) | ((el1 @ X24 @ cHH_1) != $true) | ($true != (el1 @ X21 @ cHH_1)) | ($true != (el1 @ X23 @ cHH_1)) | ((el1 @ X22 @ cHH_1) != $true))) & ! [X20 : $i] : (((el1 @ (cBIGPHI @ X20) @ cHH_2) = $true) | ((el1 @ X20 @ cHH_1) != $true)) & ! [X7 : $i] : (((el1 @ (cPHI_2 @ X7) @ cHH_2) = $true) | ((el1 @ X7 @ cSS_PRIME) != $true)) & ! [X17 : $i] : (((el1 @ X17 @ cSS_PRIME) != $true) | ((el1 @ (cPHI_1 @ X17) @ cHH_1) = $true)) & (! [X6 : $i,X5 : $i] : (((cBIGPHI @ (cTIMES @ X6 @ X5)) = (cTIMES @ (cBIGPHI @ X6) @ (cBIGPHI @ X5))) | (((el1 @ X6 @ cHH_1) != $true) | ((el1 @ X5 @ cHH_1) != $true))) <=> ((cHOM_FROM_HH_1 @ cBIGPHI) = $true)) & ! [X11 : $i,X8 : $i,X9 : $i,X10 : $i] : (((cTIMES @ X11 @ X10) = (cTIMES @ X8 @ X9)) | ((X9 != X10) | ((el1 @ X11 @ cHH_2) != $true) | ($true != (el1 @ X9 @ cHH_2)) | ((el1 @ X10 @ cHH_2) != $true) | ((el1 @ X8 @ cHH_2) != $true) | (X8 != X11))) & ! [X4 : $i] : (((el1 @ X4 @ cSS_PRIME) != $true) | ((cBIGPHI @ (cPHI_1 @ X4)) = (cPHI_2 @ X4))) & ! [X2 : $i] : (((el1 @ X2 @ cHH_1) != $true) | ? [X3 : $i] : (((el1 @ X3 @ cSS_PRIME) = $true) & ((cPHI_1 @ X3) = X2))) & ! [X14 : $i > $i] : (! [X16 : $i,X15 : $i] : (((cTIMES @ (X14 @ X15) @ (X14 @ X16)) = (X14 @ (cTIMES @ X15 @ X16))) | (((el1 @ X16 @ cSS_PRIME) != $true) | ((el1 @ X15 @ cSS_PRIME) != $true))) <=> ($true = (cHOM_FROM_SS_PRIME @ X14))) & ((cHOM_FROM_SS_PRIME @ cPHI_2) = $true) & ! [X0 : $i,X1 : $i] : (($true = (el1 @ (cTIMES @ X0 @ X1) @ cHH_1)) | (((el1 @ X1 @ cHH_1) != $true) | ((el1 @ X0 @ cHH_1) != $true))) & ! [X12 : $i,X13 : $i] : (((cBIGHI @ X12) = (cBIGPHI @ X13)) | (($true != (el1 @ X13 @ cHH_1)) | ($true != (el1 @ X12 @ cHH_1)) | (X12 != X13))) & ((cHOM_FROM_SS_PRIME @ cPHI_1) = $true))),
% 1.80/1.69 inference(ennf_transformation,[status(thm)],[f5])).
% 1.80/1.69 thf(f5,plain,(
% 1.80/1.69 ~((! [X19 : $i,X18 : $i] : ((((el1 @ X18 @ cSS_PRIME) = $true) & ((el1 @ X19 @ cSS_PRIME) = $true)) => ((el1 @ (cTIMES @ X19 @ X18) @ cSS_PRIME) = $true)) & ! [X22 : $i,X24 : $i,X23 : $i,X21 : $i] : (((X21 = X23) & (X22 = X24) & ((el1 @ X24 @ cHH_1) = $true) & ($true = (el1 @ X21 @ cHH_1)) & ($true = (el1 @ X23 @ cHH_1)) & ((el1 @ X22 @ cHH_1) = $true)) => ((cTIMES @ X24 @ X23) = (cTIMES @ X22 @ X21))) & ! [X20 : $i] : (((el1 @ X20 @ cHH_1) = $true) => ((el1 @ (cBIGPHI @ X20) @ cHH_2) = $true)) & ! [X7 : $i] : (((el1 @ X7 @ cSS_PRIME) = $true) => ((el1 @ (cPHI_2 @ X7) @ cHH_2) = $true)) & ! [X17 : $i] : (((el1 @ X17 @ cSS_PRIME) = $true) => ((el1 @ (cPHI_1 @ X17) @ cHH_1) = $true)) & (! [X6 : $i,X5 : $i] : ((((el1 @ X6 @ cHH_1) = $true) & ((el1 @ X5 @ cHH_1) = $true)) => ((cBIGPHI @ (cTIMES @ X6 @ X5)) = (cTIMES @ (cBIGPHI @ X6) @ (cBIGPHI @ X5)))) <=> ((cHOM_FROM_HH_1 @ cBIGPHI) = $true)) & ! [X11 : $i,X8 : $i,X9 : $i,X10 : $i] : (((X9 = X10) & ((el1 @ X11 @ cHH_2) = $true) & ($true = (el1 @ X9 @ cHH_2)) & ((el1 @ X10 @ cHH_2) = $true) & ((el1 @ X8 @ cHH_2) = $true) & (X8 = X11)) => ((cTIMES @ X11 @ X10) = (cTIMES @ X8 @ X9))) & ! [X4 : $i] : (((el1 @ X4 @ cSS_PRIME) = $true) => ((cBIGPHI @ (cPHI_1 @ X4)) = (cPHI_2 @ X4))) & ! [X2 : $i] : (((el1 @ X2 @ cHH_1) = $true) => ? [X3 : $i] : (((el1 @ X3 @ cSS_PRIME) = $true) & ((cPHI_1 @ X3) = X2))) & ! [X14 : $i > $i] : (! [X16 : $i,X15 : $i] : ((((el1 @ X16 @ cSS_PRIME) = $true) & ((el1 @ X15 @ cSS_PRIME) = $true)) => ((cTIMES @ (X14 @ X15) @ (X14 @ X16)) = (X14 @ (cTIMES @ X15 @ X16)))) <=> ($true = (cHOM_FROM_SS_PRIME @ X14))) & ((cHOM_FROM_SS_PRIME @ cPHI_2) = $true) & ! [X0 : $i,X1 : $i] : ((((el1 @ X1 @ cHH_1) = $true) & ((el1 @ X0 @ cHH_1) = $true)) => ($true = (el1 @ (cTIMES @ X0 @ X1) @ cHH_1))) & ! [X12 : $i,X13 : $i] : ((($true = (el1 @ X13 @ cHH_1)) & ($true = (el1 @ X12 @ cHH_1)) & (X12 = X13)) => ((cBIGHI @ X12) = (cBIGPHI @ X13))) & ((cHOM_FROM_SS_PRIME @ cPHI_1) = $true)) => ((cHOM_FROM_HH_1 @ cBIGPHI) = $true))),
% 1.80/1.69 inference(fool_elimination,[status(thm)],[f4])).
% 1.80/1.69 thf(f4,plain,(
% 1.80/1.69 ~((! [X0 : $i,X1 : $i] : (((el1 @ X0 @ cHH_1) & (el1 @ X1 @ cHH_1)) => (el1 @ (cTIMES @ X0 @ X1) @ cHH_1)) & ! [X2 : $i] : ((el1 @ X2 @ cHH_1) => ? [X3 : $i] : ((el1 @ X3 @ cSS_PRIME) & ((cPHI_1 @ X3) = X2))) & ! [X4 : $i] : ((el1 @ X4 @ cSS_PRIME) => ((cBIGPHI @ (cPHI_1 @ X4)) = (cPHI_2 @ X4))) & (cHOM_FROM_SS_PRIME @ cPHI_1) & ((cHOM_FROM_HH_1 @ cBIGPHI) <=> ! [X5 : $i,X6 : $i] : (((el1 @ X6 @ cHH_1) & (el1 @ X5 @ cHH_1)) => ((cBIGPHI @ (cTIMES @ X6 @ X5)) = (cTIMES @ (cBIGPHI @ X6) @ (cBIGPHI @ X5))))) & ! [X7 : $i] : ((el1 @ X7 @ cSS_PRIME) => (el1 @ (cPHI_2 @ X7) @ cHH_2)) & ! [X8 : $i,X9 : $i,X10 : $i,X11 : $i] : (((el1 @ X8 @ cHH_2) & (X8 = X11) & (X9 = X10) & (el1 @ X9 @ cHH_2) & (el1 @ X10 @ cHH_2) & (el1 @ X11 @ cHH_2)) => ((cTIMES @ X11 @ X10) = (cTIMES @ X8 @ X9))) & ! [X12 : $i,X13 : $i] : (((el1 @ X13 @ cHH_1) & (X12 = X13) & (el1 @ X12 @ cHH_1)) => ((cBIGHI @ X12) = (cBIGPHI @ X13))) & ! [X14 : $i > $i] : (! [X15 : $i,X16 : $i] : (((el1 @ X16 @ cSS_PRIME) & (el1 @ X15 @ cSS_PRIME)) => ((cTIMES @ (X14 @ X15) @ (X14 @ X16)) = (X14 @ (cTIMES @ X15 @ X16)))) <=> (cHOM_FROM_SS_PRIME @ X14)) & ! [X17 : $i] : ((el1 @ X17 @ cSS_PRIME) => (el1 @ (cPHI_1 @ X17) @ cHH_1)) & ! [X18 : $i,X19 : $i] : (((el1 @ X18 @ cSS_PRIME) & (el1 @ X19 @ cSS_PRIME)) => (el1 @ (cTIMES @ X19 @ X18) @ cSS_PRIME)) & ! [X20 : $i] : ((el1 @ X20 @ cHH_1) => (el1 @ (cBIGPHI @ X20) @ cHH_2)) & (cHOM_FROM_SS_PRIME @ cPHI_2) & ! [X21 : $i,X22 : $i,X23 : $i,X24 : $i] : (((X22 = X24) & (el1 @ X22 @ cHH_1) & (el1 @ X24 @ cHH_1) & (el1 @ X21 @ cHH_1) & (el1 @ X23 @ cHH_1) & (X21 = X23)) => ((cTIMES @ X24 @ X23) = (cTIMES @ X22 @ X21)))) => (cHOM_FROM_HH_1 @ cBIGPHI))),
% 1.80/1.69 inference(rectify,[status(thm)],[f2])).
% 1.80/1.69 thf(f2,negated_conjecture,(
% 1.80/1.69 ~((! [X5 : $i,X6 : $i] : (((el1 @ X5 @ cHH_1) & (el1 @ X6 @ cHH_1)) => (el1 @ (cTIMES @ X5 @ X6) @ cHH_1)) & ! [X6 : $i] : ((el1 @ X6 @ cHH_1) => ? [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) & ((cPHI_1 @ X5) = X6))) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => ((cPHI_2 @ X5) = (cBIGPHI @ (cPHI_1 @ X5)))) & (cHOM_FROM_SS_PRIME @ cPHI_1) & ((cHOM_FROM_HH_1 @ cBIGPHI) <=> ! [X6 : $i,X5 : $i] : (((el1 @ X5 @ cHH_1) & (el1 @ X6 @ cHH_1)) => ((cBIGPHI @ (cTIMES @ X5 @ X6)) = (cTIMES @ (cBIGPHI @ X5) @ (cBIGPHI @ X6))))) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => (el1 @ (cPHI_2 @ X5) @ cHH_2)) & ! [X0 : $i,X2 : $i,X3 : $i,X1 : $i] : (((el1 @ X0 @ cHH_2) & (X0 = X1) & (X2 = X3) & (el1 @ X2 @ cHH_2) & (el1 @ X3 @ cHH_2) & (el1 @ X1 @ cHH_2)) => ((cTIMES @ X0 @ X2) = (cTIMES @ X1 @ X3))) & ! [X5 : $i,X6 : $i] : (((el1 @ X6 @ cHH_1) & (X5 = X6) & (el1 @ X5 @ cHH_1)) => ((cBIGPHI @ X6) = (cBIGHI @ X5))) & ! [X4 : $i > $i] : (! [X5 : $i,X6 : $i] : (((el1 @ X6 @ cSS_PRIME) & (el1 @ X5 @ cSS_PRIME)) => ((X4 @ (cTIMES @ X5 @ X6)) = (cTIMES @ (X4 @ X5) @ (X4 @ X6)))) <=> (cHOM_FROM_SS_PRIME @ X4)) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => (el1 @ (cPHI_1 @ X5) @ cHH_1)) & ! [X1 : $i,X0 : $i] : (((el1 @ X1 @ cSS_PRIME) & (el1 @ X0 @ cSS_PRIME)) => (el1 @ (cTIMES @ X0 @ X1) @ cSS_PRIME)) & ! [X5 : $i] : ((el1 @ X5 @ cHH_1) => (el1 @ (cBIGPHI @ X5) @ cHH_2)) & (cHOM_FROM_SS_PRIME @ cPHI_2) & ! [X3 : $i,X1 : $i,X2 : $i,X0 : $i] : (((X0 = X1) & (el1 @ X1 @ cHH_1) & (el1 @ X0 @ cHH_1) & (el1 @ X3 @ cHH_1) & (el1 @ X2 @ cHH_1) & (X2 = X3)) => ((cTIMES @ X0 @ X2) = (cTIMES @ X1 @ X3)))) => (cHOM_FROM_HH_1 @ cBIGPHI))),
% 1.80/1.69 inference(negated_conjecture,[status(cth)],[f1])).
% 1.80/1.69 thf(f1,conjecture,(
% 1.80/1.69 (! [X5 : $i,X6 : $i] : (((el1 @ X5 @ cHH_1) & (el1 @ X6 @ cHH_1)) => (el1 @ (cTIMES @ X5 @ X6) @ cHH_1)) & ! [X6 : $i] : ((el1 @ X6 @ cHH_1) => ? [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) & ((cPHI_1 @ X5) = X6))) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => ((cPHI_2 @ X5) = (cBIGPHI @ (cPHI_1 @ X5)))) & (cHOM_FROM_SS_PRIME @ cPHI_1) & ((cHOM_FROM_HH_1 @ cBIGPHI) <=> ! [X6 : $i,X5 : $i] : (((el1 @ X5 @ cHH_1) & (el1 @ X6 @ cHH_1)) => ((cBIGPHI @ (cTIMES @ X5 @ X6)) = (cTIMES @ (cBIGPHI @ X5) @ (cBIGPHI @ X6))))) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => (el1 @ (cPHI_2 @ X5) @ cHH_2)) & ! [X0 : $i,X2 : $i,X3 : $i,X1 : $i] : (((el1 @ X0 @ cHH_2) & (X0 = X1) & (X2 = X3) & (el1 @ X2 @ cHH_2) & (el1 @ X3 @ cHH_2) & (el1 @ X1 @ cHH_2)) => ((cTIMES @ X0 @ X2) = (cTIMES @ X1 @ X3))) & ! [X5 : $i,X6 : $i] : (((el1 @ X6 @ cHH_1) & (X5 = X6) & (el1 @ X5 @ cHH_1)) => ((cBIGPHI @ X6) = (cBIGHI @ X5))) & ! [X4 : $i > $i] : (! [X5 : $i,X6 : $i] : (((el1 @ X6 @ cSS_PRIME) & (el1 @ X5 @ cSS_PRIME)) => ((X4 @ (cTIMES @ X5 @ X6)) = (cTIMES @ (X4 @ X5) @ (X4 @ X6)))) <=> (cHOM_FROM_SS_PRIME @ X4)) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => (el1 @ (cPHI_1 @ X5) @ cHH_1)) & ! [X1 : $i,X0 : $i] : (((el1 @ X1 @ cSS_PRIME) & (el1 @ X0 @ cSS_PRIME)) => (el1 @ (cTIMES @ X0 @ X1) @ cSS_PRIME)) & ! [X5 : $i] : ((el1 @ X5 @ cHH_1) => (el1 @ (cBIGPHI @ X5) @ cHH_2)) & (cHOM_FROM_SS_PRIME @ cPHI_2) & ! [X3 : $i,X1 : $i,X2 : $i,X0 : $i] : (((X0 = X1) & (el1 @ X1 @ cHH_1) & (el1 @ X0 @ cHH_1) & (el1 @ X3 @ cHH_1) & (el1 @ X2 @ cHH_1) & (X2 = X3)) => ((cTIMES @ X0 @ X2) = (cTIMES @ X1 @ X3)))) => (cHOM_FROM_HH_1 @ cBIGPHI)),
% 1.80/1.69 file('/export/starexec/sandbox2/tmp/tmp.IZshy8ygwZ/DTF2THF_21253.p',cPROB757)).
% 1.80/1.69 thf(f1196,plain,(
% 1.80/1.69 ((cBIGPHI @ (cTIMES @ (cPHI_1 @ (sK2 @ sK4)) @ sK3)) = (cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3))) | (~spl5_7 | ~spl5_11 | ~spl5_19 | ~spl5_32 | ~spl5_82)),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f1195])).
% 1.80/1.69 thf(f1195,plain,(
% 1.80/1.69 ((cBIGPHI @ (cTIMES @ (cPHI_1 @ (sK2 @ sK4)) @ sK3)) = (cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3))) | ($true != $true) | (~spl5_7 | ~spl5_11 | ~spl5_19 | ~spl5_32 | ~spl5_82)),
% 1.80/1.69 inference(forward_demodulation,[status(thm)],[f1186,f200])).
% 1.80/1.69 thf(f200,plain,(
% 1.80/1.69 ((el1 @ (sK2 @ sK4) @ cSS_PRIME) = $true) | ~spl5_11),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f199])).
% 1.80/1.69 thf(f1186,plain,(
% 1.80/1.69 ((el1 @ (sK2 @ sK4) @ cSS_PRIME) != $true) | ((cBIGPHI @ (cTIMES @ (cPHI_1 @ (sK2 @ sK4)) @ sK3)) = (cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3))) | (~spl5_7 | ~spl5_11 | ~spl5_19 | ~spl5_32 | ~spl5_82)),
% 1.80/1.69 inference(superposition,[status(thm)],[f1099,f419])).
% 1.80/1.69 thf(f419,plain,(
% 1.80/1.69 ( ! [X0 : $i] : (((cPHI_1 @ (cTIMES @ X0 @ (sK2 @ sK3))) = (cTIMES @ (cPHI_1 @ X0) @ sK3)) | ((el1 @ X0 @ cSS_PRIME) != $true)) ) | ~spl5_32),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f418])).
% 1.80/1.69 thf(f1099,plain,(
% 1.80/1.69 ((cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3)) = (cBIGPHI @ (cPHI_1 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3))))) | (~spl5_7 | ~spl5_11 | ~spl5_19 | ~spl5_82)),
% 1.80/1.69 inference(forward_demodulation,[status(thm)],[f1098,f950])).
% 1.80/1.69 thf(f950,plain,(
% 1.80/1.69 ((cPHI_2 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3))) = (cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3))) | (~spl5_7 | ~spl5_11 | ~spl5_19)),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f949])).
% 1.80/1.69 thf(f949,plain,(
% 1.80/1.69 ($true != $true) | ((cPHI_2 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3))) = (cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3))) | (~spl5_7 | ~spl5_11 | ~spl5_19)),
% 1.80/1.69 inference(forward_demodulation,[status(thm)],[f904,f200])).
% 1.80/1.69 thf(f904,plain,(
% 1.80/1.69 ((el1 @ (sK2 @ sK4) @ cSS_PRIME) != $true) | ((cPHI_2 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3))) = (cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3))) | (~spl5_7 | ~spl5_19)),
% 1.80/1.69 inference(superposition,[status(thm)],[f350,f181])).
% 1.80/1.69 thf(f181,plain,(
% 1.80/1.69 ((cBIGPHI @ sK4) = (cPHI_2 @ (sK2 @ sK4))) | ~spl5_7),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f179])).
% 1.80/1.69 thf(f350,plain,(
% 1.80/1.69 ( ! [X0 : $i] : (((cTIMES @ (cPHI_2 @ X0) @ (cBIGPHI @ sK3)) = (cPHI_2 @ (cTIMES @ X0 @ (sK2 @ sK3)))) | ((el1 @ X0 @ cSS_PRIME) != $true)) ) | ~spl5_19),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f349])).
% 1.80/1.69 thf(f1098,plain,(
% 1.80/1.69 ((cPHI_2 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3))) = (cBIGPHI @ (cPHI_1 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3))))) | ~spl5_82),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f1093])).
% 1.80/1.69 thf(f1093,plain,(
% 1.80/1.69 ($false = $true) | ((cPHI_2 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3))) = (cBIGPHI @ (cPHI_1 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3))))) | ~spl5_82),
% 1.80/1.69 inference(superposition,[status(thm)],[f1052,f117])).
% 1.80/1.69 thf(f117,plain,(
% 1.80/1.69 ( ! [X26 : $i] : (($false = (el1 @ X26 @ cSS_PRIME)) | ((cBIGPHI @ (cPHI_1 @ X26)) = (cPHI_2 @ X26))) )),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.80/1.69 thf(f116,plain,(
% 1.80/1.69 ( ! [X26 : $i] : (((cBIGPHI @ (cPHI_1 @ X26)) = (cPHI_2 @ X26)) | ($false = (el1 @ X26 @ cSS_PRIME)) | ($true != $true)) )),
% 1.80/1.69 inference(fool_paramodulation,[status(thm)],[f18])).
% 1.80/1.69 thf(f18,plain,(
% 1.80/1.69 ( ! [X26 : $i] : (((el1 @ X26 @ cSS_PRIME) != $true) | ((cBIGPHI @ (cPHI_1 @ X26)) = (cPHI_2 @ X26))) )),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 thf(f1052,plain,(
% 1.80/1.69 ((el1 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3)) @ cSS_PRIME) = $true) | ~spl5_82),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f1051])).
% 1.80/1.69 thf(f1090,plain,(
% 1.80/1.69 ~spl5_11 | ~spl5_8 | spl5_82),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f1089,f1051,f185,f199])).
% 1.80/1.69 thf(f185,definition,(
% 1.80/1.69 spl5_8 <=> ((el1 @ (sK2 @ sK3) @ cSS_PRIME) = $true)),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition])).
% 1.80/1.69 thf(f1089,plain,(
% 1.80/1.69 ((el1 @ (sK2 @ sK4) @ cSS_PRIME) != $true) | (~spl5_8 | spl5_82)),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f1088])).
% 1.80/1.69 thf(f1088,plain,(
% 1.80/1.69 ((el1 @ (sK2 @ sK4) @ cSS_PRIME) != $true) | ($true != $true) | (~spl5_8 | spl5_82)),
% 1.80/1.69 inference(forward_demodulation,[status(thm)],[f1084,f186])).
% 1.80/1.69 thf(f186,plain,(
% 1.80/1.69 ((el1 @ (sK2 @ sK3) @ cSS_PRIME) = $true) | ~spl5_8),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f185])).
% 1.80/1.69 thf(f1084,plain,(
% 1.80/1.69 ((el1 @ (sK2 @ sK4) @ cSS_PRIME) != $true) | ((el1 @ (sK2 @ sK3) @ cSS_PRIME) != $true) | spl5_82),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f1082])).
% 1.80/1.69 thf(f1082,plain,(
% 1.80/1.69 ((el1 @ (sK2 @ sK3) @ cSS_PRIME) != $true) | ((el1 @ (sK2 @ sK4) @ cSS_PRIME) != $true) | ($true != $true) | spl5_82),
% 1.80/1.69 inference(superposition,[status(thm)],[f1053,f16])).
% 1.80/1.69 thf(f16,plain,(
% 1.80/1.69 ( ! [X28 : $i,X27 : $i] : (((el1 @ (cTIMES @ X28 @ X27) @ cSS_PRIME) = $true) | ((el1 @ X27 @ cSS_PRIME) != $true) | ((el1 @ X28 @ cSS_PRIME) != $true)) )),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 thf(f1053,plain,(
% 1.80/1.69 ((el1 @ (cTIMES @ (sK2 @ sK4) @ (sK2 @ sK3)) @ cSS_PRIME) != $true) | spl5_82),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f1051])).
% 1.80/1.69 thf(f420,plain,(
% 1.80/1.69 spl5_32 | ~spl5_8 | ~spl5_3),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f416,f55,f185,f418])).
% 1.80/1.69 thf(f55,definition,(
% 1.80/1.69 spl5_3 <=> ((el1 @ sK3 @ cHH_1) = $true)),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.80/1.69 thf(f416,plain,(
% 1.80/1.69 ( ! [X0 : $i] : (((cPHI_1 @ (cTIMES @ X0 @ (sK2 @ sK3))) = (cTIMES @ (cPHI_1 @ X0) @ sK3)) | ((el1 @ (sK2 @ sK3) @ cSS_PRIME) != $true) | ((el1 @ X0 @ cSS_PRIME) != $true)) ) | ~spl5_3),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f415])).
% 1.80/1.69 thf(f415,plain,(
% 1.80/1.69 ( ! [X0 : $i] : (((cPHI_1 @ (cTIMES @ X0 @ (sK2 @ sK3))) = (cTIMES @ (cPHI_1 @ X0) @ sK3)) | ((el1 @ X0 @ cSS_PRIME) != $true) | ((el1 @ (sK2 @ sK3) @ cSS_PRIME) != $true) | ($true != $true)) ) | ~spl5_3),
% 1.80/1.69 inference(forward_demodulation,[status(thm)],[f285,f19])).
% 1.80/1.69 thf(f19,plain,(
% 1.80/1.69 ((cHOM_FROM_SS_PRIME @ cPHI_1) = $true)),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 thf(f285,plain,(
% 1.80/1.69 ( ! [X0 : $i] : (((el1 @ (sK2 @ sK3) @ cSS_PRIME) != $true) | ((cPHI_1 @ (cTIMES @ X0 @ (sK2 @ sK3))) = (cTIMES @ (cPHI_1 @ X0) @ sK3)) | ((el1 @ X0 @ cSS_PRIME) != $true) | ((cHOM_FROM_SS_PRIME @ cPHI_1) != $true)) ) | ~spl5_3),
% 1.80/1.69 inference(superposition,[status(thm)],[f34,f83])).
% 1.80/1.69 thf(f83,plain,(
% 1.80/1.69 (sK3 = (cPHI_1 @ (sK2 @ sK3))) | ~spl5_3),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.80/1.69 thf(f79,plain,(
% 1.80/1.69 ($true != $true) | (sK3 = (cPHI_1 @ (sK2 @ sK3))) | ~spl5_3),
% 1.80/1.69 inference(superposition,[status(thm)],[f26,f57])).
% 1.80/1.69 thf(f57,plain,(
% 1.80/1.69 ((el1 @ sK3 @ cHH_1) = $true) | ~spl5_3),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.80/1.69 thf(f34,plain,(
% 1.80/1.69 ( ! [X3 : $i > $i,X4 : $i,X5 : $i] : (((X3 @ (cTIMES @ X4 @ X5)) = (cTIMES @ (X3 @ X4) @ (X3 @ X5))) | ((el1 @ X5 @ cSS_PRIME) != $true) | ((cHOM_FROM_SS_PRIME @ X3) != $true) | ((el1 @ X4 @ cSS_PRIME) != $true)) )),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 thf(f351,plain,(
% 1.80/1.69 ~spl5_8 | spl5_19 | ~spl5_6),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f347,f174,f349,f185])).
% 1.80/1.69 thf(f174,definition,(
% 1.80/1.69 spl5_6 <=> ((cBIGPHI @ sK3) = (cPHI_2 @ (sK2 @ sK3)))),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition])).
% 1.80/1.69 thf(f347,plain,(
% 1.80/1.69 ( ! [X0 : $i] : (((el1 @ (sK2 @ sK3) @ cSS_PRIME) != $true) | ((cTIMES @ (cPHI_2 @ X0) @ (cBIGPHI @ sK3)) = (cPHI_2 @ (cTIMES @ X0 @ (sK2 @ sK3)))) | ((el1 @ X0 @ cSS_PRIME) != $true)) ) | ~spl5_6),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f346])).
% 1.80/1.69 thf(f346,plain,(
% 1.80/1.69 ( ! [X0 : $i] : (($true != $true) | ((el1 @ (sK2 @ sK3) @ cSS_PRIME) != $true) | ((el1 @ X0 @ cSS_PRIME) != $true) | ((cTIMES @ (cPHI_2 @ X0) @ (cBIGPHI @ sK3)) = (cPHI_2 @ (cTIMES @ X0 @ (sK2 @ sK3))))) ) | ~spl5_6),
% 1.80/1.69 inference(forward_demodulation,[status(thm)],[f281,f17])).
% 1.80/1.69 thf(f17,plain,(
% 1.80/1.69 ((cHOM_FROM_SS_PRIME @ cPHI_2) = $true)),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 thf(f281,plain,(
% 1.80/1.69 ( ! [X0 : $i] : (((cTIMES @ (cPHI_2 @ X0) @ (cBIGPHI @ sK3)) = (cPHI_2 @ (cTIMES @ X0 @ (sK2 @ sK3)))) | ((cHOM_FROM_SS_PRIME @ cPHI_2) != $true) | ((el1 @ X0 @ cSS_PRIME) != $true) | ((el1 @ (sK2 @ sK3) @ cSS_PRIME) != $true)) ) | ~spl5_6),
% 1.80/1.69 inference(superposition,[status(thm)],[f34,f176])).
% 1.80/1.69 thf(f176,plain,(
% 1.80/1.69 ((cBIGPHI @ sK3) = (cPHI_2 @ (sK2 @ sK3))) | ~spl5_6),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f174])).
% 1.80/1.69 thf(f226,plain,(
% 1.80/1.69 ~spl5_4 | spl5_11),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f225,f199,f61])).
% 1.80/1.69 thf(f225,plain,(
% 1.80/1.69 ((el1 @ sK4 @ cHH_1) != $true) | spl5_11),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f222])).
% 1.80/1.69 thf(f222,plain,(
% 1.80/1.69 ($true != $true) | ((el1 @ sK4 @ cHH_1) != $true) | spl5_11),
% 1.80/1.69 inference(superposition,[status(thm)],[f201,f27])).
% 1.80/1.69 thf(f27,plain,(
% 1.80/1.69 ( ! [X14 : $i] : (((el1 @ (sK2 @ X14) @ cSS_PRIME) = $true) | ($true != (el1 @ X14 @ cHH_1))) )),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 thf(f201,plain,(
% 1.80/1.69 ((el1 @ (sK2 @ sK4) @ cSS_PRIME) != $true) | spl5_11),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f199])).
% 1.80/1.69 thf(f208,plain,(
% 1.80/1.69 ~spl5_3 | spl5_8),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f207,f185,f55])).
% 1.80/1.69 thf(f207,plain,(
% 1.80/1.69 ((el1 @ sK3 @ cHH_1) != $true) | spl5_8),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f204])).
% 1.80/1.69 thf(f204,plain,(
% 1.80/1.69 ($true != $true) | ((el1 @ sK3 @ cHH_1) != $true) | spl5_8),
% 1.80/1.69 inference(superposition,[status(thm)],[f187,f27])).
% 1.80/1.69 thf(f187,plain,(
% 1.80/1.69 ((el1 @ (sK2 @ sK3) @ cSS_PRIME) != $true) | spl5_8),
% 1.80/1.69 inference(avatar_component_clause,[status(thm)],[f185])).
% 1.80/1.69 thf(f182,plain,(
% 1.80/1.69 spl5_7 | ~spl5_4 | ~spl5_4),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f169,f61,f61,f179])).
% 1.80/1.69 thf(f169,plain,(
% 1.80/1.69 ((cBIGPHI @ sK4) = (cPHI_2 @ (sK2 @ sK4))) | ((el1 @ sK4 @ cHH_1) != $true) | ~spl5_4),
% 1.80/1.69 inference(superposition,[status(thm)],[f142,f82])).
% 1.80/1.69 thf(f142,plain,(
% 1.80/1.69 ( ! [X0 : $i] : (((cPHI_2 @ (sK2 @ X0)) = (cBIGPHI @ (cPHI_1 @ (sK2 @ X0)))) | ((el1 @ X0 @ cHH_1) != $true)) )),
% 1.80/1.69 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.80/1.69 thf(f139,plain,(
% 1.80/1.69 ( ! [X0 : $i] : (((el1 @ X0 @ cHH_1) != $true) | ((cPHI_2 @ (sK2 @ X0)) = (cBIGPHI @ (cPHI_1 @ (sK2 @ X0)))) | ($true != $true)) )),
% 1.80/1.69 inference(superposition,[status(thm)],[f18,f27])).
% 1.80/1.69 thf(f177,plain,(
% 1.80/1.69 spl5_6 | ~spl5_3 | ~spl5_3),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f170,f55,f55,f174])).
% 1.80/1.69 thf(f170,plain,(
% 1.80/1.69 ((cBIGPHI @ sK3) = (cPHI_2 @ (sK2 @ sK3))) | ((el1 @ sK3 @ cHH_1) != $true) | ~spl5_3),
% 1.80/1.69 inference(superposition,[status(thm)],[f142,f83])).
% 1.80/1.69 thf(f64,plain,(
% 1.80/1.69 spl5_4 | spl5_2),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f24,f50,f61])).
% 1.80/1.69 thf(f50,definition,(
% 1.80/1.69 spl5_2 <=> ((cHOM_FROM_HH_1 @ cBIGPHI) = $true)),
% 1.80/1.69 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.80/1.69 thf(f24,plain,(
% 1.80/1.69 ((cHOM_FROM_HH_1 @ cBIGPHI) = $true) | ((el1 @ sK4 @ cHH_1) = $true)),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 thf(f59,plain,(
% 1.80/1.69 ~spl5_2),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f15,f50])).
% 1.80/1.69 thf(f15,plain,(
% 1.80/1.69 ((cHOM_FROM_HH_1 @ cBIGPHI) != $true)),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 thf(f58,plain,(
% 1.80/1.69 spl5_2 | spl5_3),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f22,f55,f50])).
% 1.80/1.69 thf(f22,plain,(
% 1.80/1.69 ((el1 @ sK3 @ cHH_1) = $true) | ((cHOM_FROM_HH_1 @ cBIGPHI) = $true)),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 thf(f53,plain,(
% 1.80/1.69 ~spl5_1 | spl5_2),
% 1.80/1.69 inference(avatar_split_clause,[status(thm)],[f23,f50,f46])).
% 1.80/1.69 thf(f23,plain,(
% 1.80/1.69 ((cTIMES @ (cBIGPHI @ sK4) @ (cBIGPHI @ sK3)) != (cBIGPHI @ (cTIMES @ sK4 @ sK3))) | ((cHOM_FROM_HH_1 @ cBIGPHI) = $true)),
% 1.80/1.69 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.69 % SZS output end Proof for DTF2THF_21253
% 1.80/1.69 % (21376)------------------------------
% 1.80/1.69 % (21376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.69 % (21376)Termination reason: Refutation
% 1.80/1.69
% 1.80/1.69 % (21376)Memory used [KB]: 6780
% 1.80/1.69 % (21376)Time elapsed: 0.128 s
% 1.80/1.69 % (21376)Instructions burned: 232 (million)
% 1.80/1.69 % (21376)------------------------------
% 1.80/1.69 % (21376)------------------------------
% 1.80/1.69 % (21349)Success in time 0.269 s
%------------------------------------------------------------------------------