%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV302^5 : TPTP v8.1.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n032.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 18:05:48 EDT 2022
% Result : Theorem 0.13s 0.32s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: ( ( $i > $o ) > $o ) > $o ).
thf(ty_eigen__1,type,
eigen__1: ( $i > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: ( ( $i > $o ) > $o ) > $o ).
thf(ty_eigen__4,type,
eigen__4: ( ( $i > $o ) > $o ) > $o ).
thf(ty_eigen__3,type,
eigen__3: ( $i > $o ) > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__2
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: ( $i > $o ) > $o] :
( ( eigen__4 @ X1 )
=> ( eigen__4
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: ( $i > $o ) > $o] :
( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ( ( eigen__0 @ X1 )
=> ( eigen__0
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__4 @ eigen__3 )
=> ( eigen__4
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( eigen__3
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__4
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( eigen__3
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__3 )
=> ( eigen__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( eigen__3
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( eigen__3
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__4
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( sP12
=> ~ sP2 )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP12
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP3
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(def_cZERO,definition,
( cZERO
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_cSUCC,definition,
( cSUCC
= ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ).
thf(def_cNAT,definition,
( cNAT
= ( ^ [X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ cZERO )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2 @ ( cSUCC @ X3 ) ) ) )
=> ( X2 @ X1 ) ) ) ) ).
thf(cX6102_B,conjecture,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( ~ ( ~ ( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) ) )
=> ~ ( X1
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ~ ( ! [X4: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: $i > $o] :
! [X6: $i] :
~ ( X5 @ X6 ) )
=> ~ ! [X5: ( $i > $o ) > $o] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: $i > $o] :
~ ! [X7: $i] :
( ( X6 @ X7 )
=> ~ ( X5
@ ^ [X8: $i] :
~ ( ( X8 != X7 )
=> ~ ( X6 @ X8 ) ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ( X1 @ X3 ) )
=> ~ ( ! [X4: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: $i > $o] :
! [X6: $i] :
~ ( X5 @ X6 ) )
=> ~ ! [X5: ( $i > $o ) > $o] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: $i > $o] :
~ ! [X7: $i] :
( ( X6 @ X7 )
=> ~ ( X5
@ ^ [X8: $i] :
~ ( ( X8 != X7 )
=> ~ ( X6 @ X8 ) ) ) ) ) ) )
=> ( X4
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X3
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) )
=> ~ ( X1
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) ) )
=> ~ ( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ( X1 @ X2 ) ) )
=> ( X1 @ X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( ~ ( ~ ( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) ) )
=> ~ ( X1
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ~ ( ! [X4: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: $i > $o] :
! [X6: $i] :
~ ( X5 @ X6 ) )
=> ~ ! [X5: ( $i > $o ) > $o] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: $i > $o] :
~ ! [X7: $i] :
( ( X6 @ X7 )
=> ~ ( X5
@ ^ [X8: $i] :
~ ( ( X8 != X7 )
=> ~ ( X6 @ X8 ) ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ( X1 @ X3 ) )
=> ~ ( ! [X4: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: $i > $o] :
! [X6: $i] :
~ ( X5 @ X6 ) )
=> ~ ! [X5: ( $i > $o ) > $o] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: $i > $o] :
~ ! [X7: $i] :
( ( X6 @ X7 )
=> ~ ( X5
@ ^ [X8: $i] :
~ ( ( X8 != X7 )
=> ~ ( X6 @ X8 ) ) ) ) ) ) )
=> ( X4
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X3
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) )
=> ~ ( X1
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) ) )
=> ~ ( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ( X1 @ X2 ) ) )
=> ( X1 @ X2 ) ) ),
inference(assume_negation,[status(cth)],[cX6102_B]) ).
thf(h1,assumption,
~ ( ~ ( sP15
=> ~ sP4 )
=> ! [X1: ( $i > $o ) > $o] :
( ( ~ ( ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) ) )
=> ~ sP15 )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ~ ( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ~ ( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X2
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) )
=> ~ ( eigen__0
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) ) )
=> ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ( eigen__0 @ X1 ) ) )
=> ( eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP15
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: ( $i > $o ) > $o] :
( ( ~ ( ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) ) )
=> ~ sP15 )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ~ ( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ~ ( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X2
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) )
=> ~ ( eigen__0
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) ) )
=> ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ( eigen__0 @ X1 ) ) )
=> ( eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP15,
introduced(assumption,[]) ).
thf(h5,assumption,
sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( ~ ( ~ ( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) ) )
=> ~ sP15 )
=> ~ ! [X1: ( $i > $o ) > $o] :
( ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) )
=> ~ ( eigen__0
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ) )
=> ~ ( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1 @ eigen__1 ) )
=> ~ sP11 ) )
=> sP11 ),
introduced(assumption,[]) ).
thf(h7,assumption,
( ~ ( ~ ( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) ) )
=> ~ sP15 )
=> ~ ! [X1: ( $i > $o ) > $o] :
( ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) )
=> ~ ( eigen__0
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ) )
=> ~ ( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1 @ eigen__1 ) )
=> ~ sP11 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h9,assumption,
( ~ ( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) ) )
=> ~ sP15 )
=> ~ ! [X1: ( $i > $o ) > $o] :
( ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) )
=> ~ ( eigen__0
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1 @ eigen__1 ) )
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h11,assumption,
( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) ) )
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: ( $i > $o ) > $o] :
( ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) )
=> ~ ( eigen__0
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( sP1
=> ~ ! [X1: ( $i > $o ) > $o] :
( ( eigen__2 @ X1 )
=> ( eigen__2
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) )
=> sP1 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP1
=> ~ ! [X1: ( $i > $o ) > $o] :
( ( eigen__2 @ X1 )
=> ( eigen__2
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
! [X1: ( $i > $o ) > $o] :
( ( eigen__2 @ X1 )
=> ( eigen__2
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h19,h16,h17,h15,h13,h11,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0])],[h18,h17]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h15,h13,h11,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h16,1,h18,h19]) ).
thf(3,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h11,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,2,h16,h17]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h11,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__2)],[h13,3,h15]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h14,h11,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0])],[h4,h14]) ).
thf(6,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[h11,4,5,h13,h14]) ).
thf(h20,assumption,
~ ( ~ ( sP3
=> ~ sP9 )
=> ~ ( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( eigen__3
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) )
=> ~ sP10 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( sP3
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h22,assumption,
( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( eigen__3
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h23,assumption,
sP3,
introduced(assumption,[]) ).
thf(h24,assumption,
sP9,
introduced(assumption,[]) ).
thf(h25,assumption,
~ ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( eigen__3
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( ~ sP14
=> sP6 ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h29,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h30,assumption,
sP12,
introduced(assumption,[]) ).
thf(h31,assumption,
sP2,
introduced(assumption,[]) ).
thf(7,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| ~ sP8
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP14
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP14
| ~ sP12
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h30,h31,h28,h29,h27,h25,h23,h24,h21,h22,h20,h12,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0])],[7,8,9,10,11,h23,h30,h31,h29]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h29,h27,h25,h23,h24,h21,h22,h20,h12,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h30,h31])],[h28,12,h30,h31]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h25,h23,h24,h21,h22,h20,h12,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,13,h28,h29]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h23,h24,h21,h22,h20,h12,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__4)],[h25,14,h27]) ).
thf(16,plain,
( ~ sP4
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP16
| ~ sP3
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP7
| ~ sP9
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h23,h24,h21,h22,h20,h12,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0])],[16,17,18,h5,h23,h24,h26]) ).
thf(20,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h23,h24,h21,h22,h20,h12,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h25]),tab_imp(discharge,[h26])],[h22,15,19,h25,h26]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h20,h12,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h23,h24])],[h21,20,h23,h24]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h12,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,21,h21,h22]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__3)],[h12,22,h20]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,6,23,h11,h12]) ).
thf(h32,assumption,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h33,assumption,
sP11,
introduced(assumption,[]) ).
thf(25,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h32,h33,h10,h7,h8,h6,h4,h5,h2,h3,h1,h0])],[h33,h8]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h32,h33])],[h10,25,h32,h33]) ).
thf(27,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h7,24,26,h9,h10]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,27,h7,h8]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h3,28,h6]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,29,h4,h5]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,30,h2,h3]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,31,h1]) ).
thf(0,theorem,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( ~ ( ~ ( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) ) )
=> ~ ( X1
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ~ ( ! [X4: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: $i > $o] :
! [X6: $i] :
~ ( X5 @ X6 ) )
=> ~ ! [X5: ( $i > $o ) > $o] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: $i > $o] :
~ ! [X7: $i] :
( ( X6 @ X7 )
=> ~ ( X5
@ ^ [X8: $i] :
~ ( ( X8 != X7 )
=> ~ ( X6 @ X8 ) ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ( X1 @ X3 ) )
=> ~ ( ! [X4: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: $i > $o] :
! [X6: $i] :
~ ( X5 @ X6 ) )
=> ~ ! [X5: ( $i > $o ) > $o] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: $i > $o] :
~ ! [X7: $i] :
( ( X6 @ X7 )
=> ~ ( X5
@ ^ [X8: $i] :
~ ( ( X8 != X7 )
=> ~ ( X6 @ X8 ) ) ) ) ) ) )
=> ( X4
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X3
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) )
=> ~ ( X1
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) ) )
=> ~ ( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ( X1 @ X2 ) ) )
=> ( X1 @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[32,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SEV302^5 : TPTP v8.1.0. Bugfixed v6.2.0.
% 0.02/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Tue Jun 28 14:47:57 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.13/0.32 % SZS status Theorem
% 0.13/0.32 % Mode: mode213
% 0.13/0.32 % Inferences: 16
% 0.13/0.32 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------