TSTP Solution File: ALG290^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG290^5 : 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 : n029.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 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cG,type,
cG: a > $o ).
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_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_cF,type,
cF: a > $o ).
thf(ty_cX,type,
cX: a > $o ).
thf(sP1,plain,
( sP1
<=> ( ~ ( cF @ ( cP @ eigen__2 @ eigen__0 ) )
=> ( cG @ ( cP @ eigen__2 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
=> ( cX @ X2 ) )
=> ~ ( cF @ ( cP @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__4 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) )
=> ~ ( ~ ( cF @ ( cP @ eigen__4 @ eigen__0 ) )
=> ( cG @ ( cP @ eigen__4 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cG @ ( cP @ eigen__4 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__4 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) )
=> ~ ( cG @ ( cP @ eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) )
=> ~ ( cF @ ( cP @ eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( cF @ ( cP @ eigen__4 @ eigen__0 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__2 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
=> ( cX @ X2 ) )
=> ~ ( ~ ( cF @ ( cP @ X1 @ eigen__0 ) )
=> ( cG @ ( cP @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cF @ ( cP @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
=> ( cX @ X2 ) )
=> ~ ( cG @ ( cP @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cG @ ( cP @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__2 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cF @ ( cP @ eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(cPU_X2310A_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] :
~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( ~ ( cF @ ( cP @ X2 @ X1 ) )
=> ( cG @ ( cP @ X2 @ X1 ) ) ) ) )
= ( ^ [X1: a] :
( ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cF @ ( cP @ X2 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cG @ ( cP @ X2 @ X1 ) ) ) ) ) ) ) ).
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] :
~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( ~ ( cF @ ( cP @ X2 @ X1 ) )
=> ( cG @ ( cP @ X2 @ X1 ) ) ) ) )
= ( ^ [X1: a] :
( ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cF @ ( cP @ X2 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cG @ ( cP @ X2 @ X1 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cPU_X2310A_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 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ^ [X1: a] :
~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( ~ ( cF @ ( cP @ X2 @ X1 ) )
=> ( cG @ ( cP @ X2 @ X1 ) ) ) ) )
!= ( ^ [X1: a] :
( ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cF @ ( cP @ X2 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cG @ ( cP @ X2 @ X1 ) ) ) ) ),
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 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ),
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 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: a] :
( ( ( X1 != cZ ) )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
( ( cL @ cZ )
= cZ ),
introduced(assumption,[]) ).
thf(h12,assumption,
( ( cR @ cZ )
= cZ ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( ~ ( cF @ ( cP @ X2 @ X1 ) )
=> ( cG @ ( cP @ X2 @ X1 ) ) ) ) )
= ( ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cF @ ( cP @ X2 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cG @ ( cP @ X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
( ~ sP10 )
!= ( sP2
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h16,assumption,
( sP2
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP10,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP2
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP16
=> ~ ( ~ sP11
=> sP13 ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP16,
introduced(assumption,[]) ).
thf(h21,assumption,
( ~ sP11
=> sP13 ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP11,
introduced(assumption,[]) ).
thf(h23,assumption,
sP13,
introduced(assumption,[]) ).
thf(h24,assumption,
sP2,
introduced(assumption,[]) ).
thf(h25,assumption,
sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| ~ sP16
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h25,h22,h20,h21,h19,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,h20,h22,h24]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h20,h21,h19,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h24,h25])],[h16,3,h24,h25]) ).
thf(5,plain,
( ~ sP12
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| ~ sP16
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h25,h23,h20,h21,h19,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[5,6,h20,h23,h25]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h20,h21,h19,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h24,h25])],[h16,7,h24,h25]) ).
thf(9,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h20,h21,h19,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h22]),tab_imp(discharge,[h23])],[h21,4,8,h22,h23]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h20,h21])],[h19,9,h20,h21]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__1)],[h15,10,h19]) ).
thf(h26,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h28,assumption,
~ ( sP14
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h29,assumption,
sP14,
introduced(assumption,[]) ).
thf(h30,assumption,
sP15,
introduced(assumption,[]) ).
thf(12,plain,
( sP1
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP10
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP9
| ~ sP14
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h29,h30,h28,h26,h17,h18,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[12,13,14,h17,h29,h30]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h26,h17,h18,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h29,h30])],[h28,15,h29,h30]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h17,h18,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__2)],[h26,16,h28]) ).
thf(h31,assumption,
~ ( sP5
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h32,assumption,
sP5,
introduced(assumption,[]) ).
thf(h33,assumption,
sP4,
introduced(assumption,[]) ).
thf(18,plain,
( sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP3
| ~ sP5
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h32,h33,h31,h27,h17,h18,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[18,19,20,h17,h32,h33]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h27,h17,h18,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h32,h33])],[h31,21,h32,h33]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h27,h17,h18,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__4)],[h27,22,h31]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h18,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h26]),tab_imp(discharge,[h27])],[h18,17,23,h26,h27]) ).
thf(25,plain,
$false,
inference(tab_be,[status(thm),assumptions([h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h15,h16]),tab_be(discharge,[h17,h18])],[h14,11,24,h15,h16,h17,h18]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__0)],[h13,25,h14]) ).
thf(27,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_fe(discharge,[h13])],[h2,26,h13]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,27,h11,h12]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,28,h9,h10]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,29,h7,h8]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,30,h5,h6]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,31,h3,h4]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,32,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] :
~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( ~ ( cF @ ( cP @ X2 @ X1 ) )
=> ( cG @ ( cP @ X2 @ X1 ) ) ) ) )
= ( ^ [X1: a] :
( ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cF @ ( cP @ X2 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cG @ ( cP @ X2 @ X1 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[33,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG290^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.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 : Thu Jun 9 02:56:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % Mode: mode213
% 0.12/0.38 % Inferences: 36
% 0.12/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------