TSTP Solution File: ITP027^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP027^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 04:01:34 EDT 2023
% Result : Theorem 20.28s 20.53s
% Output : Proof 20.28s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_carrie1948989069_d_a_e,type,
carrie1948989069_d_a_e: $tType ).
thf(ty_set_c_d_c_d_c_d,type,
set_c_d_c_d_c_d: $tType ).
thf(ty_set_c_d_c_d,type,
set_c_d_c_d: $tType ).
thf(ty_set_c,type,
set_c: $tType ).
thf(ty_d,type,
d: $tType ).
thf(ty_set_c_d,type,
set_c_d: $tType ).
thf(ty_c,type,
c: $tType ).
thf(ty_prod_z1214987823_d_a_e,type,
prod_z1214987823_d_a_e: set_c > ( c > carrie1948989069_d_a_e ) > c > d ).
thf(ty_carr_p1636662547_d_a_e,type,
carr_p1636662547_d_a_e: set_c > ( c > carrie1948989069_d_a_e ) > set_c_d ).
thf(ty_eigen__0,type,
eigen__0: c > d ).
thf(ty_member_c_d,type,
member_c_d: ( c > d ) > set_c_d > $o ).
thf(ty_pi_c_d_c_d,type,
pi_c_d_c_d: set_c_d > ( ( c > d ) > set_c_d ) > set_c_d_c_d ).
thf(ty_prod_p131511076_d_a_e,type,
prod_p131511076_d_a_e: set_c > ( c > carrie1948989069_d_a_e ) > ( c > d ) > ( c > d ) > c > d ).
thf(ty_pi_c_d_c_d_c_d,type,
pi_c_d_c_d_c_d: set_c_d > ( ( c > d ) > set_c_d_c_d ) > set_c_d_c_d_c_d ).
thf(ty_member_c_d_c_d_c_d,type,
member_c_d_c_d_c_d: ( ( c > d ) > ( c > d ) > c > d ) > set_c_d_c_d_c_d > $o ).
thf(ty_m,type,
m: c > carrie1948989069_d_a_e ).
thf(ty_i,type,
i: set_c ).
thf(ty_eigen__1,type,
eigen__1: c ).
thf(ty_prod_m854557927_d_a_e,type,
prod_m854557927_d_a_e: set_c > ( c > carrie1948989069_d_a_e ) > ( c > d ) > c > d ).
thf(ty_member_c_d_c_d,type,
member_c_d_c_d: ( ( c > d ) > c > d ) > set_c_d_c_d > $o ).
thf(sP1,plain,
( sP1
<=> ( ( member_c_d @ ( prod_z1214987823_d_a_e @ i @ m ) @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ X1 )
= ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_z1214987823_d_a_e @ i @ m ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( member_c_d @ eigen__0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ eigen__0 )
= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 )
= ( prod_p131511076_d_a_e @ i @ m @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( prod_p131511076_d_a_e @ i @ m @ eigen__0 @ ( prod_z1214987823_d_a_e @ i @ m ) @ eigen__1 )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ X1 )
= ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_z1214987823_d_a_e @ i @ m ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( member_c_d @ ( prod_z1214987823_d_a_e @ i @ m ) @ ( carr_p1636662547_d_a_e @ i @ m ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ eigen__0 @ eigen__1 )
= ( prod_p131511076_d_a_e @ i @ m @ eigen__0 @ ( prod_z1214987823_d_a_e @ i @ m ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( member_c_d @ eigen__0 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ eigen__0 )
= ( prod_p131511076_d_a_e @ i @ m @ eigen__0 @ ( prod_z1214987823_d_a_e @ i @ m ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ eigen__0 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: c] :
( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ eigen__0 @ X1 )
= ( prod_p131511076_d_a_e @ i @ m @ eigen__0 @ ( prod_z1214987823_d_a_e @ i @ m ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ X1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ eigen__0 )
= ( prod_p131511076_d_a_e @ i @ m @ eigen__0 @ ( prod_z1214987823_d_a_e @ i @ m ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ eigen__0 @ eigen__1 )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( member_c_d @ eigen__0 @ ( carr_p1636662547_d_a_e @ i @ m ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: c] :
( ( prod_p131511076_d_a_e @ i @ m @ ( prod_z1214987823_d_a_e @ i @ m ) @ eigen__0 @ X1 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(conj_2,conjecture,
! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_z1214987823_d_a_e @ i @ m ) )
= X1 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_z1214987823_d_a_e @ i @ m ) )
= X1 ) ),
inference(assume_negation,[status(cth)],[conj_2]) ).
thf(h1,assumption,
~ ( sP14
=> ( ( prod_p131511076_d_a_e @ i @ m @ eigen__0 @ ( prod_z1214987823_d_a_e @ i @ m ) )
= eigen__0 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP14,
introduced(assumption,[]) ).
thf(h3,assumption,
( ( prod_p131511076_d_a_e @ i @ m @ eigen__0 @ ( prod_z1214987823_d_a_e @ i @ m ) )
!= eigen__0 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: c] :
( ( prod_p131511076_d_a_e @ i @ m @ eigen__0 @ ( prod_z1214987823_d_a_e @ i @ m ) @ X1 )
= ( eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X2: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
=> ~ ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X3: c > d] :
( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) @ X3 )
= ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_p131511076_d_a_e @ i @ m @ X2 @ X3 ) ) ) ) ) ) )
=> ~ sP3 )
=> ~ ( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
=> ~ ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_m854557927_d_a_e @ i @ m @ X1 ) @ X1 )
= ( prod_z1214987823_d_a_e @ i @ m ) ) ) )
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP11,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ~ ( ~ ( ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X2: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
=> ~ ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X3: c > d] :
( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) @ X3 )
= ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_p131511076_d_a_e @ i @ m @ X2 @ X3 ) ) ) ) ) ) )
=> ~ sP3 )
=> ~ ( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
=> ~ ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_m854557927_d_a_e @ i @ m @ X1 ) @ X1 )
= ( prod_z1214987823_d_a_e @ i @ m ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP6,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ~ ( ~ ( ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X2: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
=> ~ ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X3: c > d] :
( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) @ X3 )
= ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_p131511076_d_a_e @ i @ m @ X2 @ X3 ) ) ) ) ) ) )
=> ~ sP3 )
=> ~ ( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_m854557927_d_a_e @ i @ m @ X1 ) @ X1 )
= ( prod_z1214987823_d_a_e @ i @ m ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ ( ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X2: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
=> ~ ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X3: c > d] :
( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) @ X3 )
= ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_p131511076_d_a_e @ i @ m @ X2 @ X3 ) ) ) ) ) ) )
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h13,assumption,
( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X2: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
=> ~ ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X3: c > d] :
( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) @ X3 )
= ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_p131511076_d_a_e @ i @ m @ X2 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP3,
introduced(assumption,[]) ).
thf(h16,assumption,
( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X2: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X3: c > d] :
( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) @ X3 )
= ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_p131511076_d_a_e @ i @ m @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP4
| ~ sP7
| ~ sP13 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP15
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| ~ sP14
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP2
| ~ sP14
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP1
| ~ sP6
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h2,h5,h15,h9,h7]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,12,h16,h17]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,13,h14,h15]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,14,h12,h13]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,15,h10,h11]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,16,h8,h9]) ).
thf(conj_1,axiom,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( member_c_d_c_d_c_d @ ( prod_p131511076_d_a_e @ i @ m )
@ ( pi_c_d_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] :
( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X2: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
=> ~ ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X2: c > d] :
( ( member_c_d @ X2 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ! [X3: c > d] :
( ( member_c_d @ X3 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_p131511076_d_a_e @ i @ m @ X1 @ X2 ) @ X3 )
= ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_p131511076_d_a_e @ i @ m @ X2 @ X3 ) ) ) ) ) ) )
=> ~ sP3 )
=> ~ ( member_c_d_c_d @ ( prod_m854557927_d_a_e @ i @ m )
@ ( pi_c_d_c_d @ ( carr_p1636662547_d_a_e @ i @ m )
@ ^ [X1: c > d] : ( carr_p1636662547_d_a_e @ i @ m ) ) ) )
=> ~ ! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ ( prod_m854557927_d_a_e @ i @ m @ X1 ) @ X1 )
= ( prod_z1214987823_d_a_e @ i @ m ) ) ) )
=> ~ sP6 )
=> ~ sP11 ) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[conj_1,17,h6,h7]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,18,h5]) ).
thf(20,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h2,h3,h1,h0]),tab_fe(discharge,[h4])],[h3,19,h4]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,20,h2,h3]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,21,h1]) ).
thf(0,theorem,
! [X1: c > d] :
( ( member_c_d @ X1 @ ( carr_p1636662547_d_a_e @ i @ m ) )
=> ( ( prod_p131511076_d_a_e @ i @ m @ X1 @ ( prod_z1214987823_d_a_e @ i @ m ) )
= X1 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[22,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ITP027^1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 11:10:12 EDT 2023
% 0.13/0.33 % CPUTime :
% 20.28/20.53 % SZS status Theorem
% 20.28/20.53 % Mode: cade22sinegrackle2xfaf3
% 20.28/20.53 % Steps: 1056
% 20.28/20.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------