%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP181^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 01:45:22 PM UTC 2025
% Result : Theorem 23.85s 24.03s
% Output : Proof 23.85s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_product_prod_pi_pi,type,
product_prod_pi_pi: $tType ).
thf(ty_name,type,
name: $tType ).
thf(ty_x,type,
x: name ).
thf(ty_fresh_name_name,type,
fresh_name_name: name > name > $o ).
thf(ty_p,type,
p: pi ).
thf(ty_fresh_1376661020_pi_pi,type,
fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).
thf(ty_y,type,
y: name ).
thf(ty_q,type,
q: pi ).
thf(ty_produc235456326_pi_pi,type,
produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
thf(ty_product_Pair_pi_pi,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(sP1,plain,
( sP1
<=> ( ( fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) )
=> ( fresh_name_name @ y @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: name] :
( ( fresh_name_name @ X1 )
= ( ^ [X2: name] : ( X1 != X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: name,X2: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ X1 @ X2 ) )
=> ( fresh_name_name @ y @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: name] :
( ( fresh_name_name @ y @ X1 )
= ( y != X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( fresh_name_name @ y @ y ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ X1 ) )
=> ( fresh_name_name @ y @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( fresh_name_name @ y )
= ( ^ [X1: name] : ( y != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( fresh_name_name
= ( ^ [X1: name,X2: name] : ( X1 != X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( y = x ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: name,X2: name,X3: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ X1 @ ( produc235456326_pi_pi @ X2 @ X3 ) )
=> ( fresh_name_name @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> $false ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( fresh_name_name @ y @ x ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(conj_0,conjecture,
~ sP10 ).
thf(h0,negated_conjecture,
sP10,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP14
| sP5
| ~ sP12
| sP13 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
~ sP13,
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP1
| ~ sP8
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP7
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP6
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP10
| sP12 ),
inference(symeq,[status(thm)],[]) ).
thf(10,plain,
( ~ sP9
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP11
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_273_name__fresh,axiom,
sP9 ).
thf(fact_31_fresh__prodD_I1_J,axiom,
sP11 ).
thf(fact_1_Bound_Ohyps_I5_J,axiom,
sP8 ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,h0,fact_273_name__fresh,fact_31_fresh__prodD_I1_J,fact_1_Bound_Ohyps_I5_J]) ).
thf(0,theorem,
~ sP10,
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP181^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n022.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 17:58:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 23.85/24.03 % SZS status Theorem
% 23.85/24.03 % Mode: cade22sinegrackle2xfaf3
% 23.85/24.03 % Steps: 29095
% 23.85/24.03 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------