TSTP Solution File: SEV059^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV059^5 : TPTP v8.1.0. Released v4.0.0.
% 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 : 600s
% DateTime : Tue Jul 19 18:04:40 EDT 2022
% Result : Theorem 26.00s 26.06s
% Output : Proof 26.00s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_cG,type,
cG: b > b ).
thf(ty_eigen__0,type,
eigen__0: b ).
thf(ty_c_less_,type,
c_less_: a > a > $o ).
thf(ty_cA,type,
cA: b > a ).
thf(ty_cF,type,
cF: b > b ).
thf(sP1,plain,
( sP1
<=> ( cG
= ( ^ [X1: b] : ( cF @ ( cF @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cG @ eigen__0 )
= ( cF @ ( cF @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( cA @ ( cG @ eigen__0 ) )
= ( cA @ ( cF @ ( cF @ eigen__0 ) ) ) )
=> ( ( cA @ ( cF @ ( cF @ eigen__0 ) ) )
= ( cA @ ( cG @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ( c_less_ @ ( cA @ eigen__0 ) @ ( cA @ ( cF @ eigen__0 ) ) )
=> ~ ( c_less_ @ ( cA @ ( cF @ eigen__0 ) ) @ ( cA @ ( cG @ eigen__0 ) ) ) )
=> ( c_less_ @ ( cA @ eigen__0 ) @ ( cA @ ( cG @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( ( cA @ ( cG @ eigen__0 ) )
= X1 )
=> ( X1
= ( cA @ ( cG @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( c_less_ @ ( cA @ ( cF @ eigen__0 ) ) @ ( cA @ ( cF @ ( cF @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cA @ ( cG @ eigen__0 ) )
= ( cA @ ( cF @ ( cF @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( cA @ ( cF @ eigen__0 ) )
= ( cA @ ( cF @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: b] :
( ( cG @ X1 )
= ( cF @ ( cF @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a,X2: a] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: b] : ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cF @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( c_less_ @ ( cA @ eigen__0 ) @ ( cA @ ( cG @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( c_less_ @ ( cA @ eigen__0 ) @ ( cA @ ( cF @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ~ ( sP13
=> ~ ( c_less_ @ ( cA @ ( cF @ eigen__0 ) ) @ X1 ) )
=> ( c_less_ @ ( cA @ eigen__0 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( c_less_ @ ( cA @ ( cF @ eigen__0 ) ) @ ( cA @ ( cG @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP13
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( cA @ ( cF @ ( cF @ eigen__0 ) ) )
= ( cA @ ( cG @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( c_less_ @ X1 @ X2 )
=> ~ ( c_less_ @ X2 @ X3 ) )
=> ( c_less_ @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a,X2: a] :
( ~ ( ( c_less_ @ ( cA @ eigen__0 ) @ X1 )
=> ~ ( c_less_ @ X1 @ X2 ) )
=> ( c_less_ @ ( cA @ eigen__0 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(cTHM89A_pme,conjecture,
( ~ ( ~ ( sP18
=> ~ sP11 )
=> ~ sP1 )
=> ! [X1: b] : ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cG @ X1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( sP18
=> ~ sP11 )
=> ~ sP1 )
=> ! [X1: b] : ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cG @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM89A_pme]) ).
thf(h1,assumption,
~ ( ~ ( sP18
=> ~ sP11 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: b] : ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cG @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP18
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
sP18,
introduced(assumption,[]) ).
thf(h6,assumption,
sP11,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
sP8,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| ~ sP7
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP15
| ~ sP8
| ~ sP17 ),
inference(mating_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP11
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP14
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP4
| sP16
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP16
| ~ sP13
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP19
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
sP10,
inference(eq_sym,[status(thm)],]) ).
thf(14,plain,
( ~ sP18
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP11
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP1
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h5,h6,h4,h7]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h2,17,h7]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,18,h5,h6]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,19,h3,h4]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,20,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( sP18
=> ~ sP11 )
=> ~ sP1 )
=> ! [X1: b] : ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cG @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEV059^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 28 15:20:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 26.00/26.06 % SZS status Theorem
% 26.00/26.06 % Mode: mode461
% 26.00/26.06 % Inferences: 1886
% 26.00/26.06 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------