%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP033^1 : 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 : n006.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 01:44:51 PM UTC 2025
% Result : Theorem 0.19s 0.54s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_binary1439146945Tree_a,type,
binary1439146945Tree_a: $tType ).
thf(ty_int,type,
int: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_t2,type,
t2: binary1439146945Tree_a ).
thf(ty_binary476621312_Tip_a,type,
binary476621312_Tip_a: binary1439146945Tree_a ).
thf(ty_h,type,
h: a > int ).
thf(ty_t1,type,
t1: binary1439146945Tree_a ).
thf(ty_binary717961607le_T_a,type,
binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(ty_binary1721989714Tree_a,type,
binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
thf(ty_x,type,
x: a ).
thf(ty_binary1217730267_wrm_a,type,
binary1217730267_wrm_a: ( a > int ) > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(sP1,plain,
( sP1
<=> ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ( binary1721989714Tree_a @ h @ t1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a,X2: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ X1 @ X2 ) )
=> ( binary1721989714Tree_a @ h @ t1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( t2 = binary476621312_Tip_a ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: binary1439146945Tree_a,X2: a,X3: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ X1 @ X2 @ X3 ) )
=> ( binary1721989714Tree_a @ h @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a > int,X2: binary1439146945Tree_a,X3: a,X4: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ X1 @ ( binary717961607le_T_a @ X2 @ X3 @ X4 ) )
=> ( binary1721989714Tree_a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ X1 ) )
=> ( binary1721989714Tree_a @ h @ t1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( binary1721989714Tree_a @ h @ t1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(conj_0,conjecture,
sP8 ).
thf(h0,negated_conjecture,
~ sP8,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
( ~ sP4
=> ~ ( binary1721989714Tree_a @ h @ t2 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t2 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP4,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( binary1721989714Tree_a @ h @ t2 ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ( t1 != binary476621312_Tip_a )
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h6,assumption,
binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t1 ),
introduced(assumption,[]) ).
thf(fact_0_t2nTip,axiom,
~ sP4 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h3,h1,h0])],[h3,fact_0_t2nTip]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h3,h1,h0])],[h3,fact_0_t2nTip]) ).
thf(fact_7_h1,axiom,
( ~ ( ( t1 != binary476621312_Tip_a )
=> ~ sP8 )
=> ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t1 ) ) ) ).
thf(3,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_7_h1,1,2,h5,h6]) ).
thf(h7,assumption,
t1 = binary476621312_Tip_a,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(4,plain,
( ~ sP2
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_3_sortLemmaL,axiom,
sP6 ).
thf(fact_1_s,axiom,
sP1 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h5,h4,h1,h0])],[4,5,6,7,8,h0,fact_3_sortLemmaL,fact_1_s]) ).
thf(10,plain,
( ~ sP2
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h5,h4,h1,h0])],[10,11,12,13,14,h8,fact_3_sortLemmaL,fact_1_s]) ).
thf(16,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h4,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,9,15,h7,h8]) ).
thf(17,plain,
( ~ sP2
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h4,h1,h0])],[17,18,19,20,21,h0,fact_3_sortLemmaL,fact_1_s]) ).
thf(23,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_7_h1,16,22,h5,h6]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h1,3,23,h3,h4]) ).
thf(25,plain,
( ~ sP2
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h5,h2,h0])],[25,26,27,28,29,h0,fact_3_sortLemmaL,fact_1_s]) ).
thf(31,plain,
( ~ sP2
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(36,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h5,h2,h0])],[31,32,33,34,35,h8,fact_3_sortLemmaL,fact_1_s]) ).
thf(37,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,30,36,h7,h8]) ).
thf(38,plain,
( ~ sP2
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h2,h0])],[38,39,40,41,42,h0,fact_3_sortLemmaL,fact_1_s]) ).
thf(44,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_7_h1,37,43,h5,h6]) ).
thf(fact_11_h2,axiom,
( ~ ( ~ sP4
=> ~ ( binary1721989714Tree_a @ h @ t2 ) )
=> ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t2 ) ) ) ).
thf(45,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_11_h2,24,44,h1,h2]) ).
thf(0,theorem,
sP8,
inference(contra,[status(thm),contra(discharge,[h0])],[45,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP033^1 : TPTP v9.2.0. Released v7.5.0.
% 0.11/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Oct 8 17:56:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54 % Mode: cade22sinegrackle2x6978
% 0.19/0.54 % Steps: 740
% 0.19/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------