TSTP Solution File: ITP117^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP117^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 04:02:12 EDT 2023
% Result : Theorem 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_finite964658038_int_n,type,
finite964658038_int_n: $tType ).
thf(ty_sigma_1466784463real_n,type,
sigma_1466784463real_n: $tType ).
thf(ty_set_Fi1058188332real_n,type,
set_Fi1058188332real_n: $tType ).
thf(ty_extend1728876344nnreal,type,
extend1728876344nnreal: $tType ).
thf(ty_nat,type,
nat: $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_t2,type,
t2: finite964658038_int_n > set_Fi1058188332real_n ).
thf(ty_t,type,
t: finite964658038_int_n > set_Fi1058188332real_n ).
thf(ty_eigen__0,type,
eigen__0: nat ).
thf(ty_lebesg260170249real_n,type,
lebesg260170249real_n: sigma_1466784463real_n ).
thf(ty_f,type,
f: nat > finite964658038_int_n ).
thf(sP1,plain,
( sP1
<=> ( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ eigen__0 ) ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ eigen__0 ) ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ X1 ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
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,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP1 ),
inference(symeq,[status(thm)],]) ).
thf(fact_0_emeasure__T_H,axiom,
sP3 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,h2,fact_0_emeasure__T_H]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,3,h2]) ).
thf(5,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,4,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])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP117^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n028.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 : 300
% 0.13/0.34 % DateTime : Sun Aug 27 15:50:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % Mode: cade22sinegrackle2x6978
% 0.21/0.47 % Steps: 718
% 0.21/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------