TSTP Solution File: SEV166^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV166^5 : 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 : n005.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 Aug 31 19:32:49 EDT 2023
% Result : Theorem 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__4,type,
eigen__4: a > a > a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(sP1,plain,
( sP1
<=> ( ( ^ [X1: a > a > a] : ( X1 @ eigen__0 @ eigen__1 ) )
= ( ^ [X1: a > a > a] : ( X1 @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > a > a] :
( ( X1 @ eigen__0 @ eigen__1 )
= ( X1 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> ( eigen__1 != eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__4 @ eigen__0 @ eigen__1 )
= ( eigen__4 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(cTHM182_pme,conjecture,
! [X1: a,X2: a,X3: a,X4: a] :
( ( ( ^ [X5: a > a > a] : ( X5 @ X1 @ X2 ) )
= ( ^ [X5: a > a > a] : ( X5 @ X3 @ X4 ) ) )
= ( ~ ( ( X1 = X3 )
=> ( X2 != X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( ^ [X5: a > a > a] : ( X5 @ X1 @ X2 ) )
= ( ^ [X5: a > a > a] : ( X5 @ X3 @ X4 ) ) )
= ( ~ ( ( X1 = X3 )
=> ( X2 != X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM182_pme]) ).
thf(h1,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ( ( ^ [X4: a > a > a] : ( X4 @ eigen__0 @ X1 ) )
= ( ^ [X4: a > a > a] : ( X4 @ X2 @ X3 ) ) )
= ( ~ ( ( eigen__0 = X2 )
=> ( X1 != X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a,X2: a] :
( ( ( ^ [X3: a > a > a] : ( X3 @ eigen__0 @ eigen__1 ) )
= ( ^ [X3: a > a > a] : ( X3 @ X1 @ X2 ) ) )
= ( ~ ( ( eigen__0 = X1 )
=> ( eigen__1 != X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a] :
( ( ( ^ [X2: a > a > a] : ( X2 @ eigen__0 @ eigen__1 ) )
= ( ^ [X2: a > a > a] : ( X2 @ eigen__2 @ X1 ) ) )
= ( ~ ( sP3
=> ( eigen__1 != X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( sP1 != ~ sP4 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| ~ sP3
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,h5,h6]) ).
thf(h9,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h11,assumption,
sP3,
introduced(assumption,[]) ).
thf(h12,assumption,
sP6,
introduced(assumption,[]) ).
thf(6,plain,
( sP5
| ~ sP6
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h9,h7,h8,h4,h3,h2,h1,h0])],[6,h10,h11,h12]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h9,h7,h8,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h8,7,h11,h12]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h4,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__4)],[h9,8,h10]) ).
thf(10,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h7,h8,h4,h3,h2,h1,h0]),tab_fe(discharge,[h9])],[h7,9,h9]) ).
thf(11,plain,
$false,
inference(tab_be,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h4,5,10,h5,h6,h7,h8]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,11,h4]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,12,h3]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,13,h2]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,14,h1]) ).
thf(0,theorem,
! [X1: a,X2: a,X3: a,X4: a] :
( ( ( ^ [X5: a > a > a] : ( X5 @ X1 @ X2 ) )
= ( ^ [X5: a > a > a] : ( X5 @ X3 @ X4 ) ) )
= ( ~ ( ( X1 = X3 )
=> ( X2 != X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEV166^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 03:11:09 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.43 % SZS status Theorem
% 0.22/0.43 % Mode: cade22grackle2xfee4
% 0.22/0.43 % Steps: 42
% 0.22/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------