TSTP Solution File: ITP117^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP117^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 00:29:10 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 20
% Syntax : Number of formulae : 34 ( 16 unt; 12 typ; 0 def)
% Number of atoms : 108 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 139 ( 11 ~; 4 |; 0 &; 122 @)
% ( 0 <=>; 1 =>; 1 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 5 ( 5 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 11 ( 6 ^ 5 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_finite964658038_int_n,type,
finite964658038_int_n: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_sigma_1466784463real_n,type,
sigma_1466784463real_n: $tType ).
thf(ty_extend1728876344nnreal,type,
extend1728876344nnreal: $tType ).
thf(ty_set_Fi1058188332real_n,type,
set_Fi1058188332real_n: $tType ).
thf(ty_sigma_1536574303real_n,type,
sigma_1536574303real_n: sigma_1466784463real_n > set_Fi1058188332real_n > extend1728876344nnreal ).
thf(ty_comple230862828real_n,type,
comple230862828real_n: sigma_1466784463real_n > sigma_1466784463real_n ).
thf(ty_eigen__0,type,
eigen__0: nat ).
thf(ty_t2,type,
t2: finite964658038_int_n > set_Fi1058188332real_n ).
thf(ty_t,type,
t: finite964658038_int_n > set_Fi1058188332real_n ).
thf(ty_lebesg260170249real_n,type,
lebesg260170249real_n: sigma_1466784463real_n ).
thf(ty_f,type,
f: nat > finite964658038_int_n ).
thf(conj_0,conjecture,
( ( ^ [X1: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ X1 ) ) ) )
= ( ^ [X1: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ X1 ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ^ [X1: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ X1 ) ) ) )
!= ( ^ [X1: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ ! [X1: nat] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ X1 ) ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ eigen__0 ) ) )
!= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(nax22,axiom,
( p22
<= ( ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft2 @ ( ff @ f__0 ) ) )
= ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft @ ( ff @ f__0 ) ) ) ) ),
file('<stdin>',nax22) ).
thf(ax4,axiom,
~ p22,
file('<stdin>',ax4) ).
thf(pax1,axiom,
( p1
=> ! [X8: finite964658038_int_n] :
( ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft @ X8 ) )
= ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft2 @ X8 ) ) ) ),
file('<stdin>',pax1) ).
thf(ax25,axiom,
p1,
file('<stdin>',ax25) ).
thf(c_0_4,plain,
( ( ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft2 @ ( ff @ f__0 ) ) )
!= ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft @ ( ff @ f__0 ) ) ) )
| p22 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax22])]) ).
thf(c_0_5,plain,
~ p22,
inference(fof_simplification,[status(thm)],[ax4]) ).
thf(c_0_6,plain,
! [X46: finite964658038_int_n] :
( ~ p1
| ( ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft @ X46 ) )
= ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft2 @ X46 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1])])]) ).
thf(c_0_7,plain,
( p22
| ( ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft2 @ ( ff @ f__0 ) ) )
!= ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft @ ( ff @ f__0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_8,plain,
~ p22,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X8: finite964658038_int_n] :
( ( ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft @ X8 ) )
= ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft2 @ X8 ) ) )
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
p1,
inference(split_conjunct,[status(thm)],[ax25]) ).
thf(c_0_11,plain,
( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft @ ( ff @ f__0 ) ) )
!= ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft2 @ ( ff @ f__0 ) ) ),
inference(sr,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_12,plain,
! [X8: finite964658038_int_n] :
( ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft @ X8 ) )
= ( fsigma_1536574303real_n @ ( fcomple230862828real_n @ flebesg260170249real_n ) @ ( ft2 @ X8 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]) ).
thf(c_0_13,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h2,h1,h0])],]) ).
thf(2,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,1,h2]) ).
thf(3,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,2,h1]) ).
thf(0,theorem,
( ( ^ [X1: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ X1 ) ) ) )
= ( ^ [X1: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP117^1 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 3 18:38:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.19/0.45 % Inferences: 1
% 0.19/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------