%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM674^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 02:09:34 PM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_x,type,
x: nat ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(ty_y,type,
y: nat ).
thf(ty_z,type,
z: nat ).
thf(sP1,plain,
( sP1
<=> ( ( pl @ z @ x )
= ( pl @ z @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(satz19e,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[satz19e]) ).
thf(1,plain,
~ sP2,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP1
| ~ sP3
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(i,axiom,
sP3 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,h0,i]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM674^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n017.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 22:26:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: cade22grackle2xfee4
% 0.13/0.37 % Steps: 3
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------