%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV290^5 : TPTP v9.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 Oct 9 02:55:24 PM UTC 2025
% Result : Theorem 22.49s 22.69s
% Output : Proof 22.49s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_c0,type,
c0: ( $i > $o ) > $o ).
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3 @ X2 )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(def_cSUCC,definition,
( cSUCC
= ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
? [X3: $i] :
( ( X2 @ X3 )
& ( X1
@ ^ [X4: $i] :
( ( (~) @ ( X4 = X3 ) )
& ( X2 @ X4 ) ) ) ) ) ) ).
thf(def_c_less__eq_,definition,
( c_less__eq_
= ( ^ [X1: ( $i > $o ) > $o,X2: ( $i > $o ) > $o] :
! [X3: ( ( $i > $o ) > $o ) > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( ( X3 @ X1 )
& ! [X4: ( $i > $o ) > $o] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X3 @ X4 )
@ ( X3 @ ( cSUCC @ X4 ) ) ) )
@ ( X3 @ X2 ) ) ) ) ).
thf(cBLEDSOE1,conjecture,
~ sP2 ).
thf(h0,negated_conjecture,
sP2,
inference(assume_negation,[status(cth)],[cBLEDSOE1]) ).
thf(1,plain,
~ sP1,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,h0]) ).
thf(0,theorem,
~ sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.13 % Problem : SEV290^5 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 19:10:53 EDT 2025
% 0.20/0.35 % CPUTime :
% 22.49/22.69 % SZS status Theorem
% 22.49/22.69 % Mode: cade22grackle2x798d
% 22.49/22.69 % Steps: 11
% 22.49/22.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------