%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO500^1.002 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 03:25:52 PM UTC 2025
% Result : Theorem 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_f0,type,
f0: $o > $o ).
thf(ty_f1,type,
f1: $o > $o ).
thf(ty_x,type,
x: $o ).
thf(sP1,plain,
( sP1
<=> ( f0 @ ( f0 @ ( f0 @ ( f1 @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( f1 @ ( f1 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( f1 @ x ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( x = sP2 )
=> ( sP2 = x ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( x = sP3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( f0 @ ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> x ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP2 = sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP3 = sP7 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP2 = sP3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP3
= ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP10
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $o] :
( ( sP7 = X1 )
=> ( X1 = sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( f0 @ sP3 )
= sP6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP6
= ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( f1 @ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $o] :
( ( sP3 = X1 )
=> ( X1 = sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP7 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( f0 @ sP3 )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP6 = sP17 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP3 = sP17 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( f0 @ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP3 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( f0 @ sP3 )
= sP17 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP17
= ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP17 = sP3 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP17 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP24
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( f0 @ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(kaminski2,conjecture,
sP1 = sP23 ).
thf(h0,negated_conjecture,
sP1 != sP23,
inference(assume_negation,[status(cth)],[kaminski2]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
sP23,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(1,plain,
( sP24
| ~ sP3
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP24
| sP3
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP29
| ~ sP24
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP18
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( sP10
| ~ sP3
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP10
| sP3
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP13
| ~ sP10
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP18
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP17
| sP2
| ~ sP11 ),
inference(mating_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP3
| sP2
| ~ sP5 ),
inference(mating_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP2
| sP17
| ~ sP24 ),
inference(mating_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP2
| sP3
| ~ sP10 ),
inference(mating_rule,[status(thm)],[]) ).
thf(13,plain,
( sP19
| ~ sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP19
| sP7
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP4
| ~ sP19
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP14
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP17
| sP3
| ~ sP8 ),
inference(mating_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP3
| sP17
| ~ sP19 ),
inference(mating_rule,[status(thm)],[]) ).
thf(20,plain,
( sP22
| sP3
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP12
| ~ sP3
| ~ sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP9
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP30
| sP23
| ~ sP22 ),
inference(mating_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP30
| sP6
| ~ sP12 ),
inference(mating_rule,[status(thm)],[]) ).
thf(25,plain,
( sP16
| sP6
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( sP25
| sP30
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP1
| sP6
| ~ sP16 ),
inference(mating_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP6
| sP23
| ~ sP25 ),
inference(mating_rule,[status(thm)],[]) ).
thf(29,plain,
( sP21
| ~ sP6
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
sP9,
inference(eq_sym,[status(thm)],[]) ).
thf(31,plain,
( ~ sP1
| sP23
| ~ sP21 ),
inference(mating_rule,[status(thm)],[]) ).
thf(32,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,h1,h2]) ).
thf(33,plain,
( sP24
| ~ sP3
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP24
| sP3
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP29
| ~ sP24
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP18
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( sP10
| ~ sP3
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP10
| sP3
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP13
| ~ sP10
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP18
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP17
| sP2
| ~ sP11 ),
inference(mating_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP3
| sP2
| ~ sP5 ),
inference(mating_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP2
| sP17
| ~ sP24 ),
inference(mating_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP2
| sP3
| ~ sP10 ),
inference(mating_rule,[status(thm)],[]) ).
thf(45,plain,
( sP19
| ~ sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( sP19
| sP7
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP4
| ~ sP19
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP14
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP17
| sP3
| ~ sP8 ),
inference(mating_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP3
| sP17
| ~ sP19 ),
inference(mating_rule,[status(thm)],[]) ).
thf(52,plain,
( sP27
| ~ sP17
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( sP20
| sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP9
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP23
| sP30
| ~ sP27 ),
inference(mating_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP6
| sP30
| ~ sP20 ),
inference(mating_rule,[status(thm)],[]) ).
thf(57,plain,
( sP26
| ~ sP17
| ~ sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( sP15
| ~ sP30
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP23
| sP6
| ~ sP26 ),
inference(mating_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP6
| sP1
| ~ sP15 ),
inference(mating_rule,[status(thm)],[]) ).
thf(61,plain,
( sP28
| sP17
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
sP9,
inference(eq_sym,[status(thm)],[]) ).
thf(63,plain,
( ~ sP23
| sP1
| ~ sP28 ),
inference(mating_rule,[status(thm)],[]) ).
thf(64,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h0])],[33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,h3,h4]) ).
thf(65,plain,
$false,
inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,32,64,h1,h2,h3,h4]) ).
thf(0,theorem,
sP1 = sP23,
inference(contra,[status(thm),contra(discharge,[h0])],[65,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO500^1.002 : TPTP v9.2.0. Released v4.1.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Oct 9 00:38:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % Mode: mode213
% 0.18/0.39 % Inferences: 124
% 0.18/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------