TSTP Solution File: SEV524^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV524^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 : Thu Aug 31 19:34:51 EDT 2023
% Result : Theorem 20.25s 20.57s
% Output : Proof 20.25s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_c_False,type,
c_False: $o ).
thf(ty_c_Inj0,type,
c_Inj0: $i > $i ).
thf(ty_c_Empty,type,
c_Empty: $i ).
thf(ty_c_Inj1,type,
c_Inj1: $i > $i ).
thf(ty_c_In,type,
c_In: $i > $i > $o ).
thf(ty_c_setsum,type,
c_setsum: $i > $i > $i ).
thf(ty_c_not,type,
c_not: $o > $o ).
thf(sP1,plain,
( sP1
<=> ( c_not
= ( ^ [X1: $o] :
( X1
=> c_False ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( ! [X2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i,X3: $i,X4: $i] :
( ( X1
@ ^ [X5: $i,X6: $i > $i > $i] : c_Empty
@ X4
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X1
@ ^ [X5: $i,X6: $i > $i > $i] : X4
@ ( c_setsum
@ ( X2
@ ^ [X5: ( $i > $i ) > $i > $i] : X4 )
@ X3 )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ~ ( X1
@ ^ [X2: $i,X3: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> c_False ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( c_not
@ ! [X1: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X2: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o,X3: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( ! [X5: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i,X6: $i,X7: $i] :
( ( c_In @ ( c_Inj0 @ X7 ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ X7 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X3
@ ^ [X8: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : X10
@ ( c_setsum
@ ( X5
@ ^ [X8: $i > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( X4
@ ^ [X8: $i,X9: $i > $i > $i] : ( c_Inj0 @ X8 )
@ X6
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( ! [X5: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i,X6: $i,X7: $i] :
( ( X4
@ ^ [X8: $i,X9: $i > $i > $i] : c_Empty
@ X7
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X4
@ ^ [X8: $i,X9: $i > $i > $i] : X7
@ ( c_setsum
@ ( X5
@ ^ [X8: ( $i > $i ) > $i > $i] : X7 )
@ X6 )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ! [X5: $i > ( ( $i > $i ) > $i > $i ) > $i,X6: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i,X7: $i] :
( ( c_In @ ( c_Inj0 @ c_Empty )
@ ( c_setsum @ c_Empty
@ ( X5 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj0 @ c_Empty ) ) ) )
=> ( ( X1
@ ^ [X8: $i,X9: $i,X10: ( $i > $i ) > $i > $i] : X8
@ X7
@ ( X6
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj1 @ c_Empty )
@ ^ [X8: $i,X9: $i] : c_Empty ) )
=> ( X3
@ ^ [X8: $i] : X8
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : X10
@ ( c_setsum @ ( c_Inj0 @ c_Empty )
@ ( X6
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj0 @ c_Empty )
@ ^ [X8: $i,X9: $i] : X9 ) ) ) ) )
=> ( ! [X5: $i > $i > $i,X6: $i > $i,X7: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( X5 @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X3
@ ^ [X8: $i] : c_Empty
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_Inj1 @ X7 ) ) )
=> ( X2
@ ^ [X8: $i,X9: ( $i > $i ) > $i] : ( c_Inj0 @ c_Empty )
@ ( X5 @ c_Empty @ ( X6 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ( ( X4
@ ^ [X5: $i,X6: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X2
@ ^ [X5: $i,X6: ( $i > $i ) > $i] :
( X6
@ ^ [X7: $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( ! [X5: $i,X6: $i,X7: $i,X8: $i] :
( ( c_In @ ( c_Inj0 @ X7 ) @ ( c_setsum @ ( c_setsum @ X5 @ ( c_setsum @ X6 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_Inj1 @ ( c_setsum @ X6 @ c_Empty ) ) ) )
=> ( ( X2
@ ^ [X9: $i,X10: ( $i > $i ) > $i] : X8
@ c_Empty )
=> ( X3
@ ^ [X9: $i] : c_Empty
@ ^ [X9: ( ( $i > $i ) > $i ) > $i,X10: $i > $i > $i,X11: $i,X12: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ X6 ) ) )
=> ( ! [X5: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i,X6: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ X6 )
=> ( ( X2
@ ^ [X7: $i,X8: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X1
@ ^ [X7: $i,X8: $i,X9: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( X5
@ ^ [X7: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) ) ) )
=> ( ! [X5: $i > $i,X6: $i] :
( ( X1
@ ^ [X7: $i,X8: $i,X9: ( $i > $i ) > $i > $i] : c_Empty
@ ( X5 @ c_Empty )
@ X6 )
=> c_False )
=> c_False ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o] : X1 ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( ! [X3: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i,X4: $i,X5: $i] :
( ( c_In @ ( c_Inj0 @ X5 ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ X5 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X1
@ ^ [X6: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ ^ [X6: ( ( $i > $i ) > $i ) > $i,X7: $i > $i > $i,X8: $i,X9: $i] : X8
@ ( c_setsum
@ ( X3
@ ^ [X6: $i > $i > $i,X7: $i > $i,X8: $i] : ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( X2
@ ^ [X6: $i,X7: $i > $i > $i] : ( c_Inj0 @ X6 )
@ X4
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( ! [X3: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i,X4: $i,X5: $i] :
( ( X2
@ ^ [X6: $i,X7: $i > $i > $i] : c_Empty
@ X5
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X2
@ ^ [X6: $i,X7: $i > $i > $i] : X5
@ ( c_setsum
@ ( X3
@ ^ [X6: ( $i > $i ) > $i > $i] : X5 )
@ X4 )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ! [X3: $i > $i > $i,X4: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( X3 @ c_Empty @ c_Empty ) ) ) ) )
=> ~ ( X1
@ ^ [X5: $i] : c_Empty
@ ^ [X5: ( ( $i > $i ) > $i ) > $i,X6: $i > $i > $i,X7: $i,X8: $i] : c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_Inj1 @ X4 ) ) ) )
=> ( ~ ( X2
@ ^ [X3: $i,X4: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> c_False ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( c_not @ $false ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o,X2: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X3: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( ! [X4: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: $i] :
( ( c_In @ ( c_Inj0 @ X6 ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ X6 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X2
@ ^ [X7: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ ^ [X7: ( ( $i > $i ) > $i ) > $i,X8: $i > $i > $i,X9: $i,X10: $i] : X9
@ ( c_setsum
@ ( X4
@ ^ [X7: $i > $i > $i,X8: $i > $i,X9: $i] : ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( X3
@ ^ [X7: $i,X8: $i > $i > $i] : ( c_Inj0 @ X7 )
@ X5
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( ! [X4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i,X5: $i,X6: $i] :
( ( X3
@ ^ [X7: $i,X8: $i > $i > $i] : c_Empty
@ X6
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X3
@ ^ [X7: $i,X8: $i > $i > $i] : X6
@ ( c_setsum
@ ( X4
@ ^ [X7: ( $i > $i ) > $i > $i] : X6 )
@ X5 )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ! [X4: $i > $i > $i,X5: $i > $i,X6: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( X4 @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X2
@ ^ [X7: $i] : c_Empty
@ ^ [X7: ( ( $i > $i ) > $i ) > $i,X8: $i > $i > $i,X9: $i,X10: $i] : c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_Inj1 @ X6 ) ) )
=> ( X1
@ ^ [X7: $i,X8: ( $i > $i ) > $i] : ( c_Inj0 @ c_Empty )
@ ( X4 @ c_Empty @ ( X5 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ( ( X3
@ ^ [X4: $i,X5: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X1
@ ^ [X4: $i,X5: ( $i > $i ) > $i] :
( X5
@ ^ [X6: $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( c_In @ ( c_Inj0 @ X6 ) @ ( c_setsum @ ( c_setsum @ X4 @ ( c_setsum @ X5 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_Inj1 @ ( c_setsum @ X5 @ c_Empty ) ) ) )
=> ( ( X1
@ ^ [X8: $i,X9: ( $i > $i ) > $i] : X7
@ c_Empty )
=> ( X2
@ ^ [X8: $i] : c_Empty
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ X5 ) ) )
=> ( ! [X4: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ X4 )
=> ~ ( X1
@ ^ [X5: $i,X6: ( $i > $i ) > $i] : c_Empty
@ c_Empty ) )
=> c_False ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> c_False ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> $false ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP6 = ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP8 = sP4 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X2: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o,X3: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( ! [X5: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i,X6: $i,X7: $i] :
( ( c_In @ ( c_Inj0 @ X7 ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ X7 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X3
@ ^ [X8: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : X10
@ ( c_setsum
@ ( X5
@ ^ [X8: $i > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( X4
@ ^ [X8: $i,X9: $i > $i > $i] : ( c_Inj0 @ X8 )
@ X6
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( ! [X5: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i,X6: $i,X7: $i] :
( ( X4
@ ^ [X8: $i,X9: $i > $i > $i] : c_Empty
@ X7
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X4
@ ^ [X8: $i,X9: $i > $i > $i] : X7
@ ( c_setsum
@ ( X5
@ ^ [X8: ( $i > $i ) > $i > $i] : X7 )
@ X6 )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ! [X5: $i > ( ( $i > $i ) > $i > $i ) > $i,X6: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i,X7: $i] :
( ( c_In @ ( c_Inj0 @ c_Empty )
@ ( c_setsum @ c_Empty
@ ( X5 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj0 @ c_Empty ) ) ) )
=> ( ( X1
@ ^ [X8: $i,X9: $i,X10: ( $i > $i ) > $i > $i] : X8
@ X7
@ ( X6
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj1 @ c_Empty )
@ ^ [X8: $i,X9: $i] : c_Empty ) )
=> ( X3
@ ^ [X8: $i] : X8
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : X10
@ ( c_setsum @ ( c_Inj0 @ c_Empty )
@ ( X6
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj0 @ c_Empty )
@ ^ [X8: $i,X9: $i] : X9 ) ) ) ) )
=> ( ! [X5: $i > $i > $i,X6: $i > $i,X7: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( X5 @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X3
@ ^ [X8: $i] : c_Empty
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_Inj1 @ X7 ) ) )
=> ( X2
@ ^ [X8: $i,X9: ( $i > $i ) > $i] : ( c_Inj0 @ c_Empty )
@ ( X5 @ c_Empty @ ( X6 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ( ( X4
@ ^ [X5: $i,X6: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X2
@ ^ [X5: $i,X6: ( $i > $i ) > $i] :
( X6
@ ^ [X7: $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( ! [X5: $i,X6: $i,X7: $i,X8: $i] :
( ( c_In @ ( c_Inj0 @ X7 ) @ ( c_setsum @ ( c_setsum @ X5 @ ( c_setsum @ X6 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_Inj1 @ ( c_setsum @ X6 @ c_Empty ) ) ) )
=> ( ( X2
@ ^ [X9: $i,X10: ( $i > $i ) > $i] : X8
@ c_Empty )
=> ( X3
@ ^ [X9: $i] : c_Empty
@ ^ [X9: ( ( $i > $i ) > $i ) > $i,X10: $i > $i > $i,X11: $i,X12: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ X6 ) ) )
=> ( ! [X5: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i,X6: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ X6 )
=> ( ( X2
@ ^ [X7: $i,X8: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X1
@ ^ [X7: $i,X8: $i,X9: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( X5
@ ^ [X7: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) ) ) )
=> ( ! [X5: $i > $i,X6: $i] :
( ( X1
@ ^ [X7: $i,X8: $i,X9: ( $i > $i ) > $i > $i] : c_Empty
@ ( X5 @ c_Empty )
@ X6 )
=> sP8 )
=> sP8 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $o] :
( ( c_not @ X1 )
= ( X1
=> sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(conj,conjecture,
sP3 ).
thf(h0,negated_conjecture,
~ sP3,
inference(assume_negation,[status(cth)],[conj]) ).
thf(1,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP12
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP6
| sP3
| sP12 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP6
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
~ sP9,
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP13
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP4
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP1
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP11
| ~ sP8
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(ax13,axiom,
sP1 ).
thf(ax11,axiom,
sP11 ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,h0,ax13,ax11]) ).
thf(0,theorem,
sP3,
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV524^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 01:55:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 20.25/20.57 % SZS status Theorem
% 20.25/20.57 % Mode: cade22sinegrackle2xfaf3
% 20.25/20.57 % Steps: 2012
% 20.25/20.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------