%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO250^5 : 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 : n031.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 : Fri Sep 1 04:46:02 EDT 2023
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__0 != X1 )
=> ( eigen__0 = X2 ) )
=> ( eigen__0 = X3 ) )
=> ( eigen__0 = X4 ) )
=> ( eigen__0 = X5 ) )
=> ( eigen__0 = X6 ) )
=> ( eigen__0 = X7 ) )
=> ( eigen__0 = X8 ) )
=> ( eigen__0 = X9 ) )
=> ( eigen__0 = X10 ) )
=> ( eigen__0 = X11 ) )
=> ( X1 = X2 ) )
=> ( X1 = X3 ) )
=> ( X1 = X4 ) )
=> ( X1 = X5 ) )
=> ( X1 = X6 ) )
=> ( X1 = X7 ) )
=> ( X1 = X8 ) )
=> ( X1 = X9 ) )
=> ( X1 = X10 ) )
=> ( X1 = X11 ) )
=> ( X2 = X3 ) )
=> ( X2 = X4 ) )
=> ( X2 = X5 ) )
=> ( X2 = X6 ) )
=> ( X2 = X7 ) )
=> ( X2 = X8 ) )
=> ( X2 = X9 ) )
=> ( X2 = X10 ) )
=> ( X2 = X11 ) )
=> ( X4 = X5 ) )
=> ( X4 = X6 ) )
=> ( X4 = X7 ) )
=> ( X4 = X8 ) )
=> ( X4 = X9 ) )
=> ( X4 = X10 ) )
=> ( X4 = X11 ) )
=> ( X5 = X6 ) )
=> ( X5 = X7 ) )
=> ( X5 = X8 ) )
=> ( X5 = X9 ) )
=> ( X5 = X10 ) )
=> ( X5 = X11 ) )
=> ( X6 = X7 ) )
=> ( X6 = X8 ) )
=> ( X6 = X9 ) )
=> ( X6 = X10 ) )
=> ( X6 = X11 ) )
=> ( X7 = X8 ) )
=> ( X7 = X9 ) )
=> ( X7 = X10 ) )
=> ( X7 = X11 ) )
=> ( X8 = X9 ) )
=> ( X8 = X10 ) )
=> ( X8 = X11 ) )
=> ( X9 = X10 ) )
=> ( X9 = X11 ) )
=> ( X10 = X11 ) )
=> ! [X12: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X12 @ eigen__0 )
= ( X12 @ X1 ) )
=> ( ( X12 @ X2 )
!= ( X12 @ X3 ) ) )
=> ( ( X12 @ X8 )
!= ( X12 @ X11 ) ) )
=> ( ( X12 @ X4 )
= ( X12 @ X7 ) ) )
=> ~ ( ~ ( ~ ( ( ( X12 @ eigen__0 )
= ( X12 @ X1 ) )
=> ( ( X12 @ X10 )
!= ( X12 @ X11 ) ) )
=> ( ( X12 @ X2 )
!= ( X12 @ X5 ) ) )
=> ( ( X12 @ X6 )
!= ( X12 @ X9 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X12 @ X4 )
= ( X12 @ X5 ) )
=> ( ( X12 @ X5 )
!= ( X12 @ X6 ) ) )
=> ( ( X12 @ X6 )
!= ( X12 @ X7 ) ) )
=> ( ( X12 @ eigen__0 )
= ( X12 @ X3 ) ) )
=> ( ( X12 @ X8 )
!= ( X12 @ X11 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X12 @ eigen__0 )
= ( X12 @ X1 ) )
=> ( ( X12 @ X6 )
!= ( X12 @ X7 ) ) )
=> ( ( X12 @ X2 )
= ( X12 @ X5 ) ) )
=> ( ( X12 @ X8 )
= ( X12 @ X11 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X12 @ X8 )
= ( X12 @ X9 ) )
=> ( ( X12 @ X10 )
!= ( X12 @ X11 ) ) )
=> ( ( X12 @ X4 )
!= ( X12 @ X7 ) ) )
=> ( ( X12 @ eigen__0 )
!= ( X12 @ X3 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X12 @ X2 )
= ( X12 @ X3 ) )
=> ( ( X12 @ X3 )
!= ( X12 @ X4 ) ) )
=> ( ( X12 @ X4 )
!= ( X12 @ X5 ) ) )
=> ( ( X12 @ X8 )
= ( X12 @ X11 ) ) )
=> ( ( X12 @ X6 )
= ( X12 @ X9 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X12 @ eigen__0 )
= ( X12 @ X1 ) )
=> ( ( X12 @ X2 )
!= ( X12 @ X3 ) ) )
=> ( ( X12 @ X4 )
!= ( X12 @ X5 ) ) )
=> ( ( X12 @ X6 )
!= ( X12 @ X7 ) ) )
=> ( ( X12 @ X8 )
!= ( X12 @ X9 ) ) )
=> ( ( X12 @ X10 )
!= ( X12 @ X11 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i,X12: $i] :
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 != X2 )
=> ( X1 = X3 ) )
=> ( X1 = X4 ) )
=> ( X1 = X5 ) )
=> ( X1 = X6 ) )
=> ( X1 = X7 ) )
=> ( X1 = X8 ) )
=> ( X1 = X9 ) )
=> ( X1 = X10 ) )
=> ( X1 = X11 ) )
=> ( X1 = X12 ) )
=> ( X2 = X3 ) )
=> ( X2 = X4 ) )
=> ( X2 = X5 ) )
=> ( X2 = X6 ) )
=> ( X2 = X7 ) )
=> ( X2 = X8 ) )
=> ( X2 = X9 ) )
=> ( X2 = X10 ) )
=> ( X2 = X11 ) )
=> ( X2 = X12 ) )
=> ( X3 = X4 ) )
=> ( X3 = X5 ) )
=> ( X3 = X6 ) )
=> ( X3 = X7 ) )
=> ( X3 = X8 ) )
=> ( X3 = X9 ) )
=> ( X3 = X10 ) )
=> ( X3 = X11 ) )
=> ( X3 = X12 ) )
=> ( X5 = X6 ) )
=> ( X5 = X7 ) )
=> ( X5 = X8 ) )
=> ( X5 = X9 ) )
=> ( X5 = X10 ) )
=> ( X5 = X11 ) )
=> ( X5 = X12 ) )
=> ( X6 = X7 ) )
=> ( X6 = X8 ) )
=> ( X6 = X9 ) )
=> ( X6 = X10 ) )
=> ( X6 = X11 ) )
=> ( X6 = X12 ) )
=> ( X7 = X8 ) )
=> ( X7 = X9 ) )
=> ( X7 = X10 ) )
=> ( X7 = X11 ) )
=> ( X7 = X12 ) )
=> ( X8 = X9 ) )
=> ( X8 = X10 ) )
=> ( X8 = X11 ) )
=> ( X8 = X12 ) )
=> ( X9 = X10 ) )
=> ( X9 = X11 ) )
=> ( X9 = X12 ) )
=> ( X10 = X11 ) )
=> ( X10 = X12 ) )
=> ( X11 = X12 ) )
=> ! [X13: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X13 @ X1 )
= ( X13 @ X2 ) )
=> ( ( X13 @ X3 )
!= ( X13 @ X4 ) ) )
=> ( ( X13 @ X9 )
!= ( X13 @ X12 ) ) )
=> ( ( X13 @ X5 )
= ( X13 @ X8 ) ) )
=> ~ ( ~ ( ~ ( ( ( X13 @ X1 )
= ( X13 @ X2 ) )
=> ( ( X13 @ X11 )
!= ( X13 @ X12 ) ) )
=> ( ( X13 @ X3 )
!= ( X13 @ X6 ) ) )
=> ( ( X13 @ X7 )
!= ( X13 @ X10 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X13 @ X5 )
= ( X13 @ X6 ) )
=> ( ( X13 @ X6 )
!= ( X13 @ X7 ) ) )
=> ( ( X13 @ X7 )
!= ( X13 @ X8 ) ) )
=> ( ( X13 @ X1 )
= ( X13 @ X4 ) ) )
=> ( ( X13 @ X9 )
!= ( X13 @ X12 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X13 @ X1 )
= ( X13 @ X2 ) )
=> ( ( X13 @ X7 )
!= ( X13 @ X8 ) ) )
=> ( ( X13 @ X3 )
= ( X13 @ X6 ) ) )
=> ( ( X13 @ X9 )
= ( X13 @ X12 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X13 @ X9 )
= ( X13 @ X10 ) )
=> ( ( X13 @ X11 )
!= ( X13 @ X12 ) ) )
=> ( ( X13 @ X5 )
!= ( X13 @ X8 ) ) )
=> ( ( X13 @ X1 )
!= ( X13 @ X4 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X13 @ X3 )
= ( X13 @ X4 ) )
=> ( ( X13 @ X4 )
!= ( X13 @ X5 ) ) )
=> ( ( X13 @ X5 )
!= ( X13 @ X6 ) ) )
=> ( ( X13 @ X9 )
= ( X13 @ X12 ) ) )
=> ( ( X13 @ X7 )
= ( X13 @ X10 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X13 @ X1 )
= ( X13 @ X2 ) )
=> ( ( X13 @ X3 )
!= ( X13 @ X4 ) ) )
=> ( ( X13 @ X5 )
!= ( X13 @ X6 ) ) )
=> ( ( X13 @ X7 )
!= ( X13 @ X8 ) ) )
=> ( ( X13 @ X9 )
!= ( X13 @ X10 ) ) )
=> ( ( X13 @ X11 )
!= ( X13 @ X12 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(cSIXFRIENDS,conjecture,
~ sP3 ).
thf(h0,negated_conjecture,
sP3,
inference(assume_negation,[status(cth)],[cSIXFRIENDS]) ).
thf(1,plain,
~ sP2,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,h0]) ).
thf(0,theorem,
~ sP3,
inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO250^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 06:49:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % Mode: cade22grackle2xfee4
% 0.19/0.41 % Steps: 5
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------