TSTP Solution File: SEV200^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV200^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 19:32:58 EDT 2023
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_x,type,
x: a ).
thf(ty_eigen__0,type,
eigen__0: a > a > a > $o ).
thf(ty_cZ,type,
cZ: a ).
thf(ty_cP,type,
cP: a > a > a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a,X3: a] :
( ( ~ ( ( ( X1 = cZ )
=> ( X2 != X3 ) )
=> ~ ( ( X2 = cZ )
=> ( X1 != X3 ) ) )
=> ~ ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ~ ( ~ ( ~ ( ( X1
= ( cP @ X4 @ X5 ) )
=> ( X2
!= ( cP @ X6 @ X7 ) ) )
=> ( X3
!= ( cP @ X8 @ X9 ) ) )
=> ~ ( eigen__0 @ X4 @ X6 @ X8 ) )
=> ~ ( eigen__0 @ X5 @ X7 @ X9 ) ) )
=> ( eigen__0 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: a] :
( ( ~ ( ( X1 != X2 )
=> ~ ( ( X1 = cZ )
=> ( cZ != X2 ) ) )
=> ~ ! [X3: a,X4: a,X5: a,X6: a,X7: a,X8: a] :
( ~ ( ~ ( ~ ( ( cZ
= ( cP @ X3 @ X4 ) )
=> ( X1
!= ( cP @ X5 @ X6 ) ) )
=> ( X2
!= ( cP @ X7 @ X8 ) ) )
=> ~ ( eigen__0 @ X3 @ X5 @ X7 ) )
=> ~ ( eigen__0 @ X4 @ X6 @ X8 ) ) )
=> ( eigen__0 @ cZ @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( ~ ( ( x != X1 )
=> ~ ( ( x = cZ )
=> ( cZ != X1 ) ) )
=> ~ ! [X2: a,X3: a,X4: a,X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ( cZ
= ( cP @ X2 @ X3 ) )
=> ( x
!= ( cP @ X4 @ X5 ) ) )
=> ( X1
!= ( cP @ X6 @ X7 ) ) )
=> ~ ( eigen__0 @ X2 @ X4 @ X6 ) )
=> ~ ( eigen__0 @ X3 @ X5 @ X7 ) ) )
=> ( eigen__0 @ cZ @ x @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ cZ @ x @ x ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(cS_LEM1C_pme,conjecture,
( ~ ( ~ ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
=> ~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( X1 @ cZ )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X2: a] : ( X1 @ X2 ) ) )
=> ! [X1: a > a > a > $o] :
( ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ cZ @ x @ x ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
=> ~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( X1 @ cZ )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X2: a] : ( X1 @ X2 ) ) )
=> ! [X1: a > a > a > $o] :
( ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ cZ @ x @ x ) ) ),
inference(assume_negation,[status(cth)],[cS_LEM1C_pme]) ).
thf(h1,assumption,
~ ( ~ ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
=> ~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( X1 @ cZ )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X2: a] : ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > a > a > $o] :
( ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ cZ @ x @ x ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
=> ~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: a > $o] :
( ~ ( ( X1 @ cZ )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X2: a] : ( X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP1
=> sP4 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,h8,h9]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,4,h8,h9]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h2,5,h7]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,6,h5,h6]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,7,h3,h4]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,8,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
=> ~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( X1 @ cZ )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X2: a] : ( X1 @ X2 ) ) )
=> ! [X1: a > a > a > $o] :
( ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ cZ @ x @ x ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV200^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 02:29:00 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % Mode: cade22grackle2xfee4
% 0.19/0.43 % Steps: 68
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------