TSTP Solution File: SEV212^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV212^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n016.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 : 600s
% DateTime : Tue Jul 19 18:05:23 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_iS,type,
iS: $tType ).
thf(ty_eigen__2,type,
eigen__2: iS ).
thf(ty_cP,type,
cP: iS > iS > iS ).
thf(ty_eigen__1,type,
eigen__1: iS ).
thf(ty_eigen__0,type,
eigen__0: iS ).
thf(ty_eigen__4,type,
eigen__4: iS > iS > iS > $o ).
thf(ty_eigen__3,type,
eigen__3: iS ).
thf(ty_c0,type,
c0: iS ).
thf(sP1,plain,
( sP1
<=> ! [X1: iS,X2: iS,X3: iS] :
( ( ~ ( ( ( X1 = c0 )
=> ( X2 != X3 ) )
=> ~ ( ( X2 = c0 )
=> ( X1 != X3 ) ) )
=> ~ ! [X4: iS,X5: iS,X6: iS,X7: iS,X8: iS,X9: iS] :
( ~ ( ~ ( ~ ( ( X1
= ( cP @ X4 @ X5 ) )
=> ( X2
!= ( cP @ X6 @ X7 ) ) )
=> ( X3
!= ( cP @ X8 @ X9 ) ) )
=> ~ ( eigen__4 @ X4 @ X6 @ X8 ) )
=> ~ ( eigen__4 @ X5 @ X7 @ X9 ) ) )
=> ( eigen__4 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( cP @ eigen__0 @ eigen__2 )
= ( cP @ eigen__0 @ eigen__2 ) )
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: iS] :
( ( ~ ( ( ( ( cP @ eigen__0 @ eigen__2 )
= c0 )
=> ( ( cP @ eigen__1 @ eigen__3 )
!= X1 ) )
=> ~ ( ( ( cP @ eigen__1 @ eigen__3 )
= c0 )
=> ( ( cP @ eigen__0 @ eigen__2 )
!= X1 ) ) )
=> ~ ! [X2: iS,X3: iS,X4: iS,X5: iS,X6: iS,X7: iS] :
( ~ ( ~ ( ~ ( ( ( cP @ eigen__0 @ eigen__2 )
= ( cP @ X2 @ X3 ) )
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ X4 @ X5 ) ) )
=> ( X1
!= ( cP @ X6 @ X7 ) ) )
=> ~ ( eigen__4 @ X2 @ X4 @ X6 ) )
=> ~ ( eigen__4 @ X3 @ X5 @ X7 ) ) )
=> ( eigen__4 @ ( cP @ eigen__0 @ eigen__2 ) @ ( cP @ eigen__1 @ eigen__3 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cP @ eigen__0 @ eigen__2 )
= ( cP @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP2
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ~ ( ~ ( ~ ( sP4
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ X1 @ X2 ) ) )
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ X3 @ X4 ) ) )
=> ~ ( eigen__4 @ eigen__0 @ X1 @ X3 ) )
=> ~ ( eigen__4 @ eigen__2 @ X2 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP5
=> ~ ( eigen__4 @ eigen__0 @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ~ $false
=> ~ sP1 )
=> ( eigen__4 @ eigen__0 @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: iS,X2: iS,X3: iS,X4: iS,X5: iS,X6: iS] :
( ~ ( ~ ( ~ ( ( ( cP @ eigen__0 @ eigen__2 )
= ( cP @ X1 @ X2 ) )
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ X3 @ X4 ) ) )
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ X5 @ X6 ) ) )
=> ~ ( eigen__4 @ X1 @ X3 @ X5 ) )
=> ~ ( eigen__4 @ X2 @ X4 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: iS,X2: iS,X3: iS,X4: iS,X5: iS] :
( ~ ( ~ ( ~ ( ( ( cP @ eigen__0 @ eigen__2 )
= ( cP @ eigen__0 @ X1 ) )
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ X2 @ X3 ) ) )
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ X4 @ X5 ) ) )
=> ~ ( eigen__4 @ eigen__0 @ X2 @ X4 ) )
=> ~ ( eigen__4 @ X1 @ X3 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: iS,X2: iS] :
( ~ ( ~ ( ~ sP2
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ X1 @ X2 ) ) )
=> ~ ( eigen__4 @ eigen__0 @ eigen__1 @ X1 ) )
=> ~ ( eigen__4 @ eigen__2 @ eigen__3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> $false ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( ~ ( ( ( ( cP @ eigen__0 @ eigen__2 )
= c0 )
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ eigen__1 @ eigen__3 ) ) )
=> ~ ( ( ( cP @ eigen__1 @ eigen__3 )
= c0 )
=> ( ( cP @ eigen__0 @ eigen__2 )
!= ( cP @ eigen__1 @ eigen__3 ) ) ) )
=> ~ sP9 )
=> ( eigen__4 @ ( cP @ eigen__0 @ eigen__2 ) @ ( cP @ eigen__1 @ eigen__3 ) @ ( cP @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: iS,X2: iS] :
( ( ~ ( ( ( ( cP @ eigen__0 @ eigen__2 )
= c0 )
=> ( X1 != X2 ) )
=> ~ ( ( X1 = c0 )
=> ( ( cP @ eigen__0 @ eigen__2 )
!= X2 ) ) )
=> ~ ! [X3: iS,X4: iS,X5: iS,X6: iS,X7: iS,X8: iS] :
( ~ ( ~ ( ~ ( ( ( cP @ eigen__0 @ eigen__2 )
= ( cP @ X3 @ X4 ) )
=> ( X1
!= ( cP @ X5 @ X6 ) ) )
=> ( X2
!= ( cP @ X7 @ X8 ) ) )
=> ~ ( eigen__4 @ X3 @ X5 @ X7 ) )
=> ~ ( eigen__4 @ X4 @ X6 @ X8 ) ) )
=> ( eigen__4 @ ( cP @ eigen__0 @ eigen__2 ) @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__4 @ eigen__0 @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: iS,X3: iS,X4: iS] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: iS,X6: iS,X7: iS,X8: iS,X9: iS,X10: iS] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ( X1 @ eigen__2 @ eigen__3 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__4 @ ( cP @ eigen__0 @ eigen__2 ) @ ( cP @ eigen__1 @ eigen__3 ) @ ( cP @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( cP @ eigen__1 @ eigen__3 )
= ( cP @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( ( ( ( cP @ eigen__0 @ eigen__2 )
= c0 )
=> ~ sP18 )
=> ~ ( ( ( cP @ eigen__1 @ eigen__3 )
= c0 )
=> ( ( cP @ eigen__0 @ eigen__2 )
!= ( cP @ eigen__1 @ eigen__3 ) ) ) )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__4 @ eigen__2 @ eigen__3 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ~ sP12
=> ~ sP1 )
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP12
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: iS,X3: iS,X4: iS] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: iS,X6: iS,X7: iS,X8: iS,X9: iS,X10: iS] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ( X1 @ eigen__0 @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP7
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: iS,X2: iS,X3: iS] :
( ~ ( ~ ( ~ ( sP4
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ eigen__1 @ X1 ) ) )
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ X2 @ X3 ) ) )
=> ~ ( eigen__4 @ eigen__0 @ eigen__1 @ X2 ) )
=> ~ ( eigen__4 @ eigen__2 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: iS] :
( ~ ( ~ ( ~ sP2
=> ( ( cP @ eigen__1 @ eigen__3 )
!= ( cP @ eigen__1 @ X1 ) ) )
=> ~ sP15 )
=> ~ ( eigen__4 @ eigen__2 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(cS_LEM2_pme,conjecture,
( ~ ( ~ ( ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 )
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ~ ( ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ X1 @ X2 @ X2 ) )
=> ~ ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 @ X4 ) ) )
=> ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ ( cP @ X1 @ X3 ) @ ( cP @ X2 @ X4 ) @ ( cP @ X2 @ X4 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 )
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ~ ( ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ X1 @ X2 @ X2 ) )
=> ~ ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 @ X4 ) ) )
=> ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ ( cP @ X1 @ X3 ) @ ( cP @ X2 @ X4 ) @ ( cP @ X2 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cS_LEM2_pme]) ).
thf(h1,assumption,
~ ( ~ ( ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 )
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ~ ( ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ X1 @ X2 @ X2 ) )
=> ~ ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 @ X4 ) ) )
=> ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ ( cP @ X1 @ X3 ) @ ( cP @ X2 @ X4 ) @ ( cP @ X2 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 )
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: iS,X2: iS,X3: iS] :
( ~ ( ! [X4: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X5: iS,X6: iS,X7: iS] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: iS,X9: iS,X10: iS,X11: iS,X12: iS,X13: iS] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) ) )
=> ( X4 @ eigen__0 @ X1 @ X1 ) )
=> ~ ! [X4: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X5: iS,X6: iS,X7: iS] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: iS,X9: iS,X10: iS,X11: iS,X12: iS,X13: iS] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) ) )
=> ( X4 @ X2 @ X3 @ X3 ) ) )
=> ! [X4: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X5: iS,X6: iS,X7: iS] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: iS,X9: iS,X10: iS,X11: iS,X12: iS,X13: iS] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) ) )
=> ( X4 @ ( cP @ eigen__0 @ X2 ) @ ( cP @ X1 @ X3 ) @ ( cP @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: iS,X2: iS] :
( ~ ( sP23
=> ~ ! [X3: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X4: iS,X5: iS,X6: iS] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: iS,X8: iS,X9: iS,X10: iS,X11: iS,X12: iS] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) ) )
=> ( X3 @ X1 @ X2 @ X2 ) ) )
=> ! [X3: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X4: iS,X5: iS,X6: iS] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: iS,X8: iS,X9: iS,X10: iS,X11: iS,X12: iS] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) ) )
=> ( X3 @ ( cP @ eigen__0 @ X1 ) @ ( cP @ eigen__1 @ X2 ) @ ( cP @ eigen__1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: iS] :
( ~ ( sP23
=> ~ ! [X2: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X3: iS,X4: iS,X5: iS] :
( ( ~ ( ( ( X3 = c0 )
=> ( X4 != X5 ) )
=> ~ ( ( X4 = c0 )
=> ( X3 != X5 ) ) )
=> ~ ! [X6: iS,X7: iS,X8: iS,X9: iS,X10: iS,X11: iS] :
( ~ ( ~ ( ~ ( ( X3
= ( cP @ X6 @ X7 ) )
=> ( X4
!= ( cP @ X8 @ X9 ) ) )
=> ( X5
!= ( cP @ X10 @ X11 ) ) )
=> ~ ( X2 @ X6 @ X8 @ X10 ) )
=> ~ ( X2 @ X7 @ X9 @ X11 ) ) )
=> ( X2 @ X3 @ X4 @ X5 ) ) )
=> ( X2 @ eigen__2 @ X1 @ X1 ) ) )
=> ! [X2: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X3: iS,X4: iS,X5: iS] :
( ( ~ ( ( ( X3 = c0 )
=> ( X4 != X5 ) )
=> ~ ( ( X4 = c0 )
=> ( X3 != X5 ) ) )
=> ~ ! [X6: iS,X7: iS,X8: iS,X9: iS,X10: iS,X11: iS] :
( ~ ( ~ ( ~ ( ( X3
= ( cP @ X6 @ X7 ) )
=> ( X4
!= ( cP @ X8 @ X9 ) ) )
=> ( X5
!= ( cP @ X10 @ X11 ) ) )
=> ~ ( X2 @ X6 @ X8 @ X10 ) )
=> ~ ( X2 @ X7 @ X9 @ X11 ) ) )
=> ( X2 @ X3 @ X4 @ X5 ) ) )
=> ( X2 @ ( cP @ eigen__0 @ eigen__2 ) @ ( cP @ eigen__1 @ X1 ) @ ( cP @ eigen__1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ~ ( sP23
=> ~ sP16 )
=> ! [X1: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: iS,X3: iS,X4: iS] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: iS,X6: iS,X7: iS,X8: iS,X9: iS,X10: iS] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ( X1 @ ( cP @ eigen__0 @ eigen__2 ) @ ( cP @ eigen__1 @ eigen__3 ) @ ( cP @ eigen__1 @ eigen__3 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP23
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: iS,X3: iS,X4: iS] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: iS,X6: iS,X7: iS,X8: iS,X9: iS,X10: iS] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ( X1 @ ( cP @ eigen__0 @ eigen__2 ) @ ( cP @ eigen__1 @ eigen__3 ) @ ( cP @ eigen__1 @ eigen__3 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP23,
introduced(assumption,[]) ).
thf(h14,assumption,
sP16,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ sP22
=> sP17 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h19,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
sP18,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP25
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP11
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP26
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP24
| sP7
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP7
| sP5
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP5
| sP2
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| ~ sP4
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP19
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP23
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP8
| sP22
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP21
| sP22
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP22
| sP12
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
~ sP12,
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP1
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP14
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP3
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP13
| ~ sP19
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h16,h17,h15,h13,h14,h11,h12,h10,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,h13,h14,h19,h17]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h15,h13,h14,h11,h12,h10,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h16,24,h18,h19]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h11,h12,h10,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,25,h16,h17]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h11,h12,h10,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[h12,26,h15]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h11,27,h13,h14]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,28,h11,h12]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,29,h10]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,30,h9]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,31,h8]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h2,32,h7]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,33,h5,h6]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,34,h3,h4]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,35,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 )
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ~ ( ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ X1 @ X2 @ X2 ) )
=> ~ ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 @ X4 ) ) )
=> ! [X5: iS > iS > iS > $o] :
( ~ ( ~ sP12
=> ~ ! [X6: iS,X7: iS,X8: iS] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: iS,X10: iS,X11: iS,X12: iS,X13: iS,X14: iS] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) ) )
=> ( X5 @ ( cP @ X1 @ X3 ) @ ( cP @ X2 @ X4 ) @ ( cP @ X2 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[36,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV212^5 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 03:36:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % Mode: mode213
% 0.19/0.38 % Inferences: 31
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------