TSTP Solution File: SEV214^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV214^5 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 18:05:23 EDT 2022
% Result : Theorem 25.81s 26.12s
% Output : Proof 25.81s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_iS,type,
iS: $tType ).
thf(ty_eigen__2,type,
eigen__2: iS ).
thf(ty_cP,type,
cP: iS > iS > iS ).
thf(ty_eigen__1,type,
eigen__1: iS ).
thf(ty_eigen__0,type,
eigen__0: iS ).
thf(ty_eigen__3,type,
eigen__3: iS ).
thf(ty_c0,type,
c0: iS ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 = c0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: iS] :
( ( eigen__0 = X1 )
=> ( X1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__2 = c0 )
=> ( c0 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: iS] :
( ( cP @ eigen__3 @ X1 )
!= c0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( c0
= ( cP @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: iS,X2: iS] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( c0 = eigen__2 )
=> ( eigen__2 = c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: iS] :
( ( c0 = X1 )
=> ( X1 = c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: iS] :
( ( eigen__2 = X1 )
=> ( X1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( c0
= ( cP @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( c0 = eigen__0 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__2 = c0 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( c0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( cP @ eigen__3 @ eigen__2 )
= c0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP1
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP6
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( cP @ eigen__0 @ eigen__1 )
= c0 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( c0 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP11
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: iS] :
( ( cP @ eigen__0 @ X1 )
!= c0 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(cS_T_LR_LEM2_pme,conjecture,
( ~ ( ~ ( sP4
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ~ ( ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) ) )
= ( (=) @ c0 ) )
=> ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) ) )
!= ( (=) @ c0 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( sP4
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ~ ( ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) ) )
= ( (=) @ c0 ) )
=> ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) ) )
!= ( (=) @ c0 ) ) ) ),
inference(assume_negation,[status(cth)],[cS_T_LR_LEM2_pme]) ).
thf(h1,assumption,
~ ( ~ ( sP4
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) ) )
= ( (=) @ c0 ) )
=> ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) ) )
!= ( (=) @ c0 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP4
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) ) )
!= ( (=) @ c0 ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) ) )
!= ( (=) @ c0 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: iS] :
( ( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) )
= ( c0 = X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
( ~ sP1
=> ~ ! [X1: iS] :
( c0
!= ( cP @ eigen__0 @ X1 ) ) )
!= sP14,
introduced(assumption,[]) ).
thf(h11,assumption,
( ~ sP1
=> ~ ! [X1: iS] :
( c0
!= ( cP @ eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP14,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ sP1
=> ~ ! [X1: iS] :
( c0
!= ( cP @ eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: iS] :
( c0
!= ( cP @ eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP16
| ~ sP1
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
sP7,
inference(eq_sym,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h11,h12,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,h15,h12]) ).
thf(h17,assumption,
sP11,
introduced(assumption,[]) ).
thf(6,plain,
( ~ sP21
| ~ sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP4
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP20
| ~ sP11
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
sP7,
inference(eq_sym,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h16,h11,h12,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[6,7,8,9,10,11,h5,h17]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h11,h12,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__1)],[h16,12,h17]) ).
thf(14,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h12,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h11,5,13,h15,h16]) ).
thf(h18,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
! [X1: iS] :
( c0
!= ( cP @ eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(15,plain,
( ~ sP12
| ~ sP14
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP9
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
sP7,
inference(eq_sym,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h13,h14,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[15,16,17,18,h18,h14]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h13,19,h18,h19]) ).
thf(21,plain,
$false,
inference(tab_be,[status(thm),assumptions([h10,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h11,h12]),tab_be(discharge,[h13,h14])],[h10,14,20,h11,h12,h13,h14]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__0)],[h9,21,h10]) ).
thf(23,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_fe(discharge,[h9])],[h7,22,h9]) ).
thf(h20,assumption,
~ ! [X1: iS] :
( ( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) )
= ( c0 = X1 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
( ~ sP13
=> ~ ! [X1: iS] :
( c0
!= ( cP @ X1 @ eigen__2 ) ) )
!= sP19,
introduced(assumption,[]) ).
thf(h22,assumption,
( ~ sP13
=> ~ ! [X1: iS] :
( c0
!= ( cP @ X1 @ eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
sP19,
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( ~ sP13
=> ~ ! [X1: iS] :
( c0
!= ( cP @ X1 @ eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h26,assumption,
sP13,
introduced(assumption,[]) ).
thf(h27,assumption,
~ ! [X1: iS] :
( c0
!= ( cP @ X1 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(24,plain,
( ~ sP3
| ~ sP13
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP7
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
sP7,
inference(eq_sym,[status(thm)],]) ).
thf(28,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h22,h23,h21,h20,h8,h5,h6,h3,h4,h1,h2,h0])],[24,25,26,27,h26,h23]) ).
thf(h28,assumption,
sP6,
introduced(assumption,[]) ).
thf(29,plain,
( ~ sP5
| ~ sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP17
| ~ sP6
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP9
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
sP7,
inference(eq_sym,[status(thm)],]) ).
thf(34,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h28,h27,h22,h23,h21,h20,h8,h5,h6,h3,h4,h1,h2,h0])],[29,30,31,32,33,34,h5,h28]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h27,h22,h23,h21,h20,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__3)],[h27,35,h28]) ).
thf(37,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h22,h23,h21,h20,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h26]),tab_imp(discharge,[h27])],[h22,28,36,h26,h27]) ).
thf(h29,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h30,assumption,
! [X1: iS] :
( c0
!= ( cP @ X1 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(38,plain,
( ~ sP8
| ~ sP19
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP9
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
sP7,
inference(eq_sym,[status(thm)],]) ).
thf(42,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h29,h30,h24,h25,h21,h20,h8,h5,h6,h3,h4,h1,h2,h0])],[38,39,40,41,h29,h25]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h21,h20,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h29,h30])],[h24,42,h29,h30]) ).
thf(44,plain,
$false,
inference(tab_be,[status(thm),assumptions([h21,h20,h8,h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h22,h23]),tab_be(discharge,[h24,h25])],[h21,37,43,h22,h23,h24,h25]) ).
thf(45,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h20,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__2)],[h20,44,h21]) ).
thf(46,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h8,h5,h6,h3,h4,h1,h2,h0]),tab_fe(discharge,[h20])],[h8,45,h20]) ).
thf(47,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h2,23,46,h7,h8]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,47,h5,h6]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,48,h3,h4]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,49,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( sP4
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ~ ( ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) ) )
= ( (=) @ c0 ) )
=> ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) ) )
!= ( (=) @ c0 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[50,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV214^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 16:59:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 25.81/26.12 % SZS status Theorem
% 25.81/26.12 % Mode: mode461
% 25.81/26.12 % Inferences: 416
% 25.81/26.12 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------