TSTP Solution File: ITP010^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP010^5 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n025.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 : Sun Jul 17 00:28:26 EDT 2022
% Result : Theorem 1.49s 1.65s
% Output : Proof 1.49s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_del,type,
del: $tType ).
thf(ty_p,type,
p: $i > $o ).
thf(ty_mem,type,
mem: $i > del > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_c_2Ecardinal_2Ecardleq,type,
c_2Ecardinal_2Ecardleq: del > del > $i ).
thf(ty_eigen__1,type,
eigen__1: del ).
thf(ty_eigen__0,type,
eigen__0: del ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_ap,type,
ap: $i > $i > $i ).
thf(ty_bool,type,
bool: del ).
thf(ty_arr,type,
arr: del > del > del ).
thf(conj_thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
! [X1: del,X2: del,X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ X2 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: del,X2: del,X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ X2 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Ecardinal_2ECARD__NOT__LE]) ).
thf(h1,assumption,
~ ! [X1: del,X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__0 @ bool ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ X1 ) @ X2 ) @ X3 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ X1 ) @ X2 ) @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__0 @ bool ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__1 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ X1 ) @ X2 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ X1 ) @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ( mem @ eigen__2 @ ( arr @ eigen__0 @ bool ) )
=> ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__1 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
mem @ eigen__2 @ ( arr @ eigen__0 @ bool ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__1 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( mem @ eigen__3 @ ( arr @ eigen__1 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
mem @ eigen__3 @ ( arr @ eigen__1 @ bool ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 ) ) )
!= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_negrefl,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0])],[h8]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,1,h7,h8]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,2,h6]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,3,h4,h5]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,4,h3]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,5,h2]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).
thf(0,theorem,
! [X1: del,X2: del,X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ X2 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ITP010^5 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n025.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 : 600
% 0.12/0.33 % DateTime : Thu Jun 2 22:27:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.49/1.65 % SZS status Theorem
% 1.49/1.65 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 1.49/1.65 % Inferences: 0
% 1.49/1.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------