TSTP Solution File: SYO171^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO171^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 : Fri Sep 1 04:45:43 EDT 2023
% Result : Theorem 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_g,type,
g: $i > $i > $o ).
thf(ty_f,type,
f: $i > $i ).
thf(ty_a,type,
a: $i ).
thf(sP1,plain,
( sP1
<=> ( ~ ( g @ a @ a )
=> ( g @ a @ ( f @ a ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( g @ a @ X1 )
=> ~ ( g @ X1 @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ~ ( g @ X1 @ a )
=> ( g @ ( f @ X1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( g @ a @ a )
=> ( g @ ( f @ a ) @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( g @ a @ ( f @ a ) )
=> ~ ( g @ ( f @ a ) @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( g @ a @ ( f @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( g @ a @ a ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP7
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ~ ( g @ X2 @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( g @ ( f @ a ) @ a ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ~ ( g @ X1 @ a )
=> ( g @ X1 @ ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cSYN031_1,conjecture,
( ~ ( ~ ( ~ ( sP3
=> ~ sP11 )
=> ~ ! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ ( f @ X2 ) @ X2 ) ) )
=> ~ ! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ X2 @ ( f @ X2 ) ) ) )
=> ~ sP9 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( sP3
=> ~ sP11 )
=> ~ ! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ ( f @ X2 ) @ X2 ) ) )
=> ~ ! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ X2 @ ( f @ X2 ) ) ) )
=> ~ sP9 ),
inference(assume_negation,[status(cth)],[cSYN031_1]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( sP3
=> ~ sP11 )
=> ~ ! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ ( f @ X2 ) @ X2 ) ) )
=> ~ ! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ X2 @ ( f @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP9,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP3
=> ~ sP11 )
=> ~ ! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ ( f @ X2 ) @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ X2 @ ( f @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP3
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ ( f @ X2 ) @ X2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP3,
introduced(assumption,[]) ).
thf(h8,assumption,
sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP6
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| ~ sP7
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP7
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP7
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,h7,h8,h2]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,10,h7,h8]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,11,h5,h6]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,12,h3,h4]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,13,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( sP3
=> ~ sP11 )
=> ~ ! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ ( f @ X2 ) @ X2 ) ) )
=> ~ ! [X1: $i,X2: $i] :
( ( g @ X1 @ X2 )
=> ( g @ X2 @ ( f @ X2 ) ) ) )
=> ~ sP9 ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SYO171^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.36 % Computer : n026.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Aug 26 06:30:18 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % Mode: cade22grackle2xfee4
% 0.21/0.38 % Steps: 33
% 0.21/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------