TSTP Solution File: ALG294^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG294^5 : 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 : n018.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 : Thu Jul 14 17:57:57 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_cP,type,
cP: a > a > a ).
thf(ty_cL,type,
cL: a > a ).
thf(ty_cPSI,type,
cPSI: ( a > $o ) > a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_cR,type,
cR: a > a ).
thf(ty_cZ,type,
cZ: a ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_cPHI,type,
cPHI: ( a > $o ) > a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 = cZ ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__3 @ X1 ) )
=> ~ ( ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__3 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 )
=> ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__3 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a,X2: a] :
( ( eigen__0
= ( cP @ X1 @ X2 ) )
=> ~ ( ~ ( cPHI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 )
=> ( cPSI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0
= ( cP @ eigen__3 @ eigen__4 ) )
=> ~ ( ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__4 )
=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__4 )
=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__5 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__5 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__6 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0
= ( cP @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__0
= ( cP @ eigen__5 @ eigen__6 ) )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0
= ( cP @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__1 @ X1 ) )
=> ~ ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__5 @ X1 ) )
=> ~ ( ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__5 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 )
=> ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__5 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP8
=> ~ ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP8
=> ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a,X2: a] :
( ( eigen__0
= ( cP @ X1 @ X2 ) )
=> ~ ( cPHI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a,X2: a] :
( ( eigen__0
= ( cP @ X1 @ X2 ) )
=> ~ ( cPSI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0
= ( cP @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__1 @ X1 ) )
=> ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(cPU_X2310B_pme,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( ( X1 != cZ ) )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPSI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ( ( ^ [X1: a] :
( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 )
=> ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) )
= ( ^ [X1: a] :
( ~ ( ~ ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) )
=> ( X1 = cZ ) )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( ( X1 != cZ ) )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPSI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ( ( ^ [X1: a] :
( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 )
=> ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) )
= ( ^ [X1: a] :
( ~ ( ~ ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) )
=> ( X1 = cZ ) )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cPU_X2310B_pme]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( ( X1 != cZ ) )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPSI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ^ [X1: a] :
( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 )
=> ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) )
!= ( ^ [X1: a] :
( ~ ( ~ ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) )
=> ( X1 = cZ ) )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( ( X1 != cZ ) )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: a > $o,X2: a] :
( ( cPSI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( ( X1 != cZ ) )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( ( X1 != cZ ) )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: a] :
( ( ( X1 != cZ ) )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ),
introduced(assumption,[]) ).
thf(h15,assumption,
( ( cL @ cZ )
= cZ ),
introduced(assumption,[]) ).
thf(h16,assumption,
( ( cR @ cZ )
= cZ ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: a] :
( ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 )
=> ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) )
= ( ~ ( ~ ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) )
=> ( X1 = cZ ) )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
( ~ sP1
=> ~ sP3 )
!= ( ~ ( ~ ( ~ sP1
=> ~ sP16 )
=> sP1 )
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h19,assumption,
( ~ sP1
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h20,assumption,
( ~ ( ~ ( ~ sP1
=> ~ sP16 )
=> sP1 )
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ sP1
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ ( ~ ( ~ ( ~ sP1
=> ~ sP16 )
=> sP1 )
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h23,assumption,
sP1,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( ~ ( ~ sP1
=> ~ sP16 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h26,assumption,
sP17,
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( ~ sP1
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h29,assumption,
sP16,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h28,h29,h27,h28,h25,h26,h23,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h23,h28]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h23,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h28,h29])],[h27,1,h28,h29]) ).
thf(3,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h23,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h27,h28])],[h25,2,h27,h28]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h25,h26])],[h20,3,h25,h26]) ).
thf(h30,assumption,
~ ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__1 @ X1 ) )
=> ~ ( ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 )
=> ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ),
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( sP8
=> ~ ( ~ sP20
=> sP14 ) ),
introduced(assumption,[]) ).
thf(h32,assumption,
sP8,
introduced(assumption,[]) ).
thf(h33,assumption,
( ~ sP20
=> sP14 ),
introduced(assumption,[]) ).
thf(h34,assumption,
sP20,
introduced(assumption,[]) ).
thf(h35,assumption,
sP14,
introduced(assumption,[]) ).
thf(5,plain,
( ~ sP16
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP21
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP15
| ~ sP8
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h28,h29,h27,h28,h25,h26,h34,h32,h33,h31,h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[5,6,7,h32,h34,h29]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h34,h32,h33,h31,h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h28,h29])],[h27,8,h28,h29]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h34,h32,h33,h31,h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h27,h28])],[h25,9,h27,h28]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h32,h33,h31,h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h25,h26])],[h20,10,h25,h26]) ).
thf(12,plain,
( ~ sP17
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP11
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP13
| ~ sP8
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h28,h29,h27,h28,h25,h26,h35,h32,h33,h31,h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[12,13,14,h32,h35,h26]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h35,h32,h33,h31,h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h28,h29])],[h27,15,h28,h29]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h35,h32,h33,h31,h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h27,h28])],[h25,16,h27,h28]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h32,h33,h31,h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h25,h26])],[h20,17,h25,h26]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h32,h33,h31,h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h34]),tab_imp(discharge,[h35])],[h33,11,18,h34,h35]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h32,h33])],[h31,19,h32,h33]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h30,h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__2)],[h30,20,h31]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__1)],[h24,21,h30]) ).
thf(23,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h19,h20,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h23]),tab_imp(discharge,[h24])],[h19,4,22,h23,h24]) ).
thf(h36,assumption,
sP3,
introduced(assumption,[]) ).
thf(h37,assumption,
( ~ ( ~ sP1
=> ~ sP16 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h38,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h39,assumption,
( ~ sP1
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h40,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(24,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h23,h39,h37,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h23,h28]) ).
thf(h41,assumption,
~ ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__3 @ X1 ) )
=> ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__3 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ),
introduced(assumption,[]) ).
thf(h42,assumption,
~ ( sP18
=> ~ sP19 ),
introduced(assumption,[]) ).
thf(h43,assumption,
sP18,
introduced(assumption,[]) ).
thf(h44,assumption,
sP19,
introduced(assumption,[]) ).
thf(25,plain,
( sP5
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP4
| ~ sP18
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h43,h44,h42,h41,h40,h39,h37,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[25,26,27,28,h36,h43,h44]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h42,h41,h40,h39,h37,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h43,h44])],[h42,29,h43,h44]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h41,h40,h39,h37,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h42]),tab_negall(eigenvar,eigen__4)],[h41,30,h42]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h40,h39,h37,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h41]),tab_negall(eigenvar,eigen__3)],[h40,31,h41]) ).
thf(33,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h39,h37,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h23]),tab_imp(discharge,[h40])],[h39,24,32,h23,h40]) ).
thf(34,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h23,h37,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h23,h28]) ).
thf(35,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h37,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h39]),tab_imp(discharge,[h23])],[h37,33,34,h39,h23]) ).
thf(h45,assumption,
~ ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__5 @ X1 ) )
=> ~ ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__5 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ),
introduced(assumption,[]) ).
thf(h46,assumption,
~ ( sP10
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h47,assumption,
sP10,
introduced(assumption,[]) ).
thf(h48,assumption,
sP6,
introduced(assumption,[]) ).
thf(36,plain,
( sP7
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP3
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP12
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP9
| ~ sP10
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h47,h48,h46,h45,h38,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[36,37,38,39,h36,h47,h48]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h46,h45,h38,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h47,h48])],[h46,40,h47,h48]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h45,h38,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h46]),tab_negall(eigenvar,eigen__6)],[h45,41,h46]) ).
thf(43,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h38,h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h45]),tab_negall(eigenvar,eigen__5)],[h38,42,h45]) ).
thf(44,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h28,h36,h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h37]),tab_imp(discharge,[h38])],[h22,35,43,h37,h38]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h28,h36])],[h21,44,h28,h36]) ).
thf(46,plain,
$false,
inference(tab_be,[status(thm),assumptions([h18,h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h19,h20]),tab_be(discharge,[h21,h22])],[h18,23,45,h19,h20,h21,h22]) ).
thf(47,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__0)],[h17,46,h18]) ).
thf(48,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_fe(discharge,[h17])],[h2,47,h17]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h13,48,h15,h16]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h11,49,h13,h14]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,50,h11,h12]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,51,h9,h10]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,52,h7,h8]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,53,h5,h6]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,54,h3,h4]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,55,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( ( X1 != cZ ) )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPSI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ( ( ^ [X1: a] :
( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 )
=> ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) )
= ( ^ [X1: a] :
( ~ ( ~ ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) )
=> ( X1 = cZ ) )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[56,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG294^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 8 09:30:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % Mode: mode213
% 0.14/0.40 % Inferences: 45
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------