%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM746^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n016.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 02:12:01 PM UTC 2025
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_frac,type,
frac: $tType ).
thf(ty_z,type,
z: frac ).
thf(ty_y,type,
y: frac ).
thf(ty_eq,type,
eq: frac > frac > $o ).
thf(ty_lessf,type,
lessf: frac > frac > $o ).
thf(ty_x,type,
x: frac ).
thf(sP1,plain,
( sP1
<=> ! [X1: frac] :
( ( eq @ x @ y )
=> ( ( eq @ y @ X1 )
=> ( eq @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( lessf @ x @ z ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: frac,X2: frac] :
( ( lessf @ x @ X1 )
=> ( ( ~ ( lessf @ X1 @ X2 )
=> ( eq @ X1 @ X2 ) )
=> ( lessf @ x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( lessf @ y @ z ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: frac] :
( ( lessf @ x @ y )
=> ( ( ~ ( lessf @ y @ X1 )
=> ( eq @ y @ X1 ) )
=> ( lessf @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( lessf @ x @ y )
=> ( ( ~ sP4
=> ( eq @ y @ z ) )
=> sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eq @ y @ z ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eq @ x @ y )
=> ( sP8
=> ( eq @ x @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) )
=> ( sP4
=> sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ~ sP4
=> sP8 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: frac,X2: frac] :
( ( eq @ x @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eq @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( ~ ( lessf @ X1 @ X2 )
=> ( eq @ X1 @ X2 ) )
=> ( ( lessf @ X2 @ X3 )
=> ( lessf @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eq @ x @ z ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( lessf @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP4
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: frac,X2: frac] :
( ( ~ ( lessf @ x @ X1 )
=> ( eq @ x @ X1 ) )
=> ( ( lessf @ X1 @ X2 )
=> ( lessf @ x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: frac] :
( sP11
=> ( ( lessf @ y @ X1 )
=> ( lessf @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( lessf @ X1 @ X2 )
=> ( ( ~ ( lessf @ X2 @ X3 )
=> ( eq @ X2 @ X3 ) )
=> ( lessf @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP4
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP8
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(satz52,conjecture,
( ~ sP2
=> sP16 ) ).
thf(h0,negated_conjecture,
~ ( ~ sP2
=> sP16 ),
inference(assume_negation,[status(cth)],[satz52]) ).
thf(h1,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h3,assumption,
sP17,
introduced(assumption,[]) ).
thf(h4,assumption,
sP14,
introduced(assumption,[]) ).
thf(h5,assumption,
sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
sP8,
introduced(assumption,[]) ).
thf(1,plain,
( sP11
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP15
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP19
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP20
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP10
| ~ sP11
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP18
| ~ sP4
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(satz51a,axiom,
sP15 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h3,h1,h2,h0])],[1,2,3,4,5,6,h3,h5,satz51a,h1]) ).
thf(8,plain,
( sP22
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP21
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP6
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP7
| ~ sP17
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP12
| ~ sP22
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(satz51b,axiom,
sP21 ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h3,h1,h2,h0])],[8,9,10,11,12,13,h3,h6,satz51b,h1]) ).
thf(k,axiom,
sP22 ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h1,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[k,7,14,h5,h6]) ).
thf(16,plain,
( sP11
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP15
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP19
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP20
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP10
| ~ sP11
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP18
| ~ sP4
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h4,h1,h2,h0])],[16,17,18,19,20,21,h4,h5,satz51a,h1]) ).
thf(23,plain,
( ~ sP5
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP13
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP9
| ~ sP14
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP23
| ~ sP8
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(satz39,axiom,
sP5 ).
thf(28,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h4,h1,h2,h0])],[23,24,25,26,27,h4,h6,satz39,h2]) ).
thf(29,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h1,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[k,22,28,h5,h6]) ).
thf(l,axiom,
sP11 ).
thf(30,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[l,15,29,h3,h4]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,30,h1,h2]) ).
thf(0,theorem,
( ~ sP2
=> sP16 ),
inference(contra,[status(thm),contra(discharge,[h0])],[31,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM746^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 22:28:23 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % Mode: mode213
% 0.14/0.40 % Inferences: 64
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------