%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO040^2 : 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 : n027.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 03:24:44 PM UTC 2025
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_h,type,
h: $o > $i ).
thf(ty_f,type,
f: $o > $o ).
thf(ty_x,type,
x: $o ).
thf(sP1,plain,
( sP1
<=> ( ( ( f @ x )
= x )
=> ( x
= ( f @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( f @ ( f @ x ) )
= ( f @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( f @ ( f @ x ) )
= x )
=> ( x
= ( f @ ( f @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( x
= ( f @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( x
= ( f @ ( f @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $o] :
( ( ( f @ x )
= X1 )
=> ( X1
= ( f @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( f @ x )
= ( f @ ( f @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $o] :
( ( ( f @ ( f @ x ) )
= X1 )
=> ( X1
= ( f @ ( f @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( f @ ( f @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( f @ x ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> x ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( h @ ( f @ sP10 ) )
= ( h @ sP11 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( f @ sP10 )
= sP11 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP8
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( f @ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP11 = sP12 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP10 = sP12 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(2,conjecture,
sP13 ).
thf(h0,negated_conjecture,
~ sP13,
inference(assume_negation,[status(cth)],[2]) ).
thf(1,plain,
( sP8
| ~ sP11
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf('2_001',plain,
( sP8
| sP11
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP15
| ~ sP8
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( sP17
| ~ sP11
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP17
| sP11
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP1
| ~ sP17
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP7
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP16
| sP10
| ~ sP3 ),
inference(mating_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP11
| sP10
| ~ sP5 ),
inference(mating_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP10
| sP16
| ~ sP8 ),
inference(mating_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP10
| sP11
| ~ sP17 ),
inference(mating_rule,[status(thm)],[]) ).
thf(13,plain,
( sP18
| ~ sP10
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP18
| sP10
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP4
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP2
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP16
| sP11
| ~ sP18 ),
inference(mating_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP11
| sP16
| ~ sP6 ),
inference(mating_rule,[status(thm)],[]) ).
thf(20,plain,
( sP14
| ~ sP16
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP14
| sP16
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
sP2,
inference(eq_sym,[status(thm)],[]) ).
thf(24,plain,
( sP13
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h0]) ).
thf(0,theorem,
sP13,
inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYO040^2 : TPTP v9.2.0. Released v4.1.0.
% 0.02/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Oct 9 01:34:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % Mode: mode213
% 0.18/0.36 % Inferences: 24
% 0.18/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------