%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM736^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n002.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 02:09:45 PM UTC 2025
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(def_is_of,definition,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_all_of,definition,
( all_of
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( is_of @ X3 @ X1 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_d_Sep,definition,
( d_Sep
= ( ^ [X1: $i,X2: $i > $o] :
( if
@ ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X2 @ X3 ) )
@ ( repl @ X1
@ ^ [X3: $i] :
( if @ ( X2 @ X3 ) @ X3
@ ( eps
@ ^ [X4: $i] :
( ( in @ X4 @ X1 )
& ( X2 @ X4 ) ) ) ) )
@ emptyset ) ) ) ).
thf(def_omega,definition,
( omega
= ( d_Sep @ ( univof @ emptyset ) @ nat_p ) ) ).
thf(def_ap,definition,
( ap
= ( ^ [X1: $i,X2: $i] :
( d_ReplSep @ X1
@ ^ [X3: $i] :
? [X4: $i] :
( X3
= ( pair @ X2 @ X4 ) )
@ proj1 ) ) ) ).
thf(def_d_Pi,definition,
( d_Pi
= ( ^ [X1: $i,X2: $i > $i] :
( d_Sep
@ ( power
@ ( d_Sigma @ X1
@ ^ [X3: $i] : ( union @ ( X2 @ X3 ) ) ) )
@ ^ [X3: $i] :
! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( in @ ( ap @ X3 @ X4 ) @ ( X2 @ X4 ) ) ) ) ) ) ).
thf(def_nat,definition,
( nat
= ( d_Sep @ omega
@ ^ [X1: $i] : ( (~) @ ( X1 = emptyset ) ) ) ) ).
thf(def_n_some,definition,
( n_some
= ( l_some @ nat ) ) ).
thf(def_diffprop,definition,
( diffprop
= ( ^ [X1: $i,X2: $i,X3: $i] : ( n_is @ X1 @ ( n_pl @ X2 @ X3 ) ) ) ) ).
thf(def_d_29_ii,definition,
( d_29_ii
= ( ^ [X1: $i,X2: $i] : ( n_some @ ( diffprop @ X1 @ X2 ) ) ) ) ).
thf(def_iii,definition,
( iii
= ( ^ [X1: $i,X2: $i] : ( n_some @ ( diffprop @ X2 @ X1 ) ) ) ) ).
thf(def_times,definition,
( times
= ( ^ [X1: $i] :
( ind
@ ( d_Pi @ nat
@ ^ [X2: $i] : nat )
@ ( d_428_prop2 @ X1 ) ) ) ) ).
thf(def_n_ts,definition,
( n_ts
= ( ^ [X1: $i] : ( ap @ ( times @ X1 ) ) ) ) ).
thf(def_d_1to,definition,
( d_1to
= ( ^ [X1: $i] :
( d_Sep @ nat
@ ^ [X2: $i] : ( lessis @ X2 @ X1 ) ) ) ) ).
thf(def_n_2,definition,
( n_2
= ( n_pl @ n_1 @ n_1 ) ) ).
thf(def_pair1type,definition,
( pair1type
= ( ^ [X1: $i] :
( d_Pi @ ( d_1to @ n_2 )
@ ^ [X2: $i] : X1 ) ) ) ).
thf(def_first1,definition,
( first1
= ( ^ [X1: $i,X2: $i] : ( ap @ X2 @ n_1t ) ) ) ).
thf(def_second1,definition,
( second1
= ( ^ [X1: $i,X2: $i] : ( ap @ X2 @ n_2t ) ) ) ).
thf(def_frac,definition,
( frac
= ( pair1type @ nat ) ) ).
thf(def_num,definition,
( num
= ( first1 @ nat ) ) ).
thf(def_den,definition,
( den
= ( second1 @ nat ) ) ).
thf(def_moref,definition,
( moref
= ( ^ [X1: $i,X2: $i] : ( d_29_ii @ ( n_ts @ ( num @ X1 ) @ ( den @ X2 ) ) @ ( n_ts @ ( num @ X2 ) @ ( den @ X1 ) ) ) ) ) ).
thf(def_lessf,definition,
( lessf
= ( ^ [X1: $i,X2: $i] : ( iii @ ( n_ts @ ( num @ X1 ) @ ( den @ X2 ) ) @ ( n_ts @ ( num @ X2 ) @ ( den @ X1 ) ) ) ) ) ).
thf(satz42,conjecture,
~ sP1 ).
thf(h0,negated_conjecture,
sP1,
inference(assume_negation,[status(cth)],[satz42]) ).
thf(1,plain,
~ sP1,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,h0]) ).
thf(0,theorem,
~ sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[2,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM736^4 : TPTP v9.2.0. Released v7.1.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n002.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 : Wed Oct 8 22:03:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % Mode: cade22sinegrackle2x6978
% 0.20/0.44 % Steps: 1
% 0.20/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------