TSTP Solution File: SET764^4 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET764^4 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -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 : 600s
% DateTime : Tue Jul 19 04:55:29 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i ).
thf(def_in,definition,
( in
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_is_a,definition,
( is_a
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_emptyset,definition,
( emptyset
= ( ^ [X1: $i] : $false ) ) ).
thf(def_unord_pair,definition,
( unord_pair
= ( ^ [X1: $i,X2: $i,X3: $i] :
( ( X3 != X1 )
=> ( X3 = X2 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).
thf(def_union,definition,
( union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_excl_union,definition,
( excl_union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ~ ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ) ).
thf(def_intersection,definition,
( intersection
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_setminus,definition,
( setminus
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_complement,definition,
( complement
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_disjoint,definition,
( disjoint
= ( ^ [X1: $i > $o,X2: $i > $o] :
( ( intersection @ X1 @ X2 )
= emptyset ) ) ) ).
thf(def_subset,definition,
( subset
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_meets,definition,
( meets
= ( ^ [X1: $i > $o,X2: $i > $o] :
~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_misses,definition,
( misses
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_fun_image,definition,
( fun_image
= ( ^ [X1: $i > $i,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3
!= ( X1 @ X4 ) ) ) ) ) ).
thf(def_fun_composition,definition,
( fun_composition
= ( ^ [X1: $i > $i,X2: $i > $i,X3: $i] : ( X2 @ ( X1 @ X3 ) ) ) ) ).
thf(def_fun_inv_image,definition,
( fun_inv_image
= ( ^ [X1: $i > $i,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X4
!= ( X1 @ X3 ) ) ) ) ) ).
thf(def_fun_injective,definition,
( fun_injective
= ( ^ [X1: $i > $i] :
! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) ) ) ).
thf(def_fun_surjective,definition,
( fun_surjective
= ( ^ [X1: $i > $i] :
! [X2: $i] :
~ ! [X3: $i] :
( X2
!= ( X1 @ X3 ) ) ) ) ).
thf(def_fun_bijective,definition,
( fun_bijective
= ( ^ [X1: $i > $i] :
~ ( ( fun_injective @ X1 )
=> ~ ( fun_surjective @ X1 ) ) ) ) ).
thf(def_fun_decreasing,definition,
( fun_decreasing
= ( ^ [X1: $i > $i,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( X1 @ X4 ) @ ( X1 @ X3 ) ) ) ) ) ).
thf(def_fun_increasing,definition,
( fun_increasing
= ( ^ [X1: $i > $i,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) ) ) ) ).
thf(thm,conjecture,
! [X1: $i > $i] :
( ( ^ [X2: $i] :
~ ! [X3: $i] :
( $false
=> ( X3
!= ( X1 @ X2 ) ) ) )
= ( ^ [X2: $i] : $false ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i] :
( ( ^ [X2: $i] :
~ ! [X3: $i] :
( $false
=> ( X3
!= ( X1 @ X2 ) ) ) )
= ( ^ [X2: $i] : $false ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
( ^ [X1: $i] :
~ ! [X2: $i] :
( $false
=> ( X2
!= ( eigen__0 @ X1 ) ) ) )
!= ( ^ [X1: $i] : $false ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( ~ ! [X2: $i] :
( $false
=> ( X2
!= ( eigen__0 @ X1 ) ) ) )
= $false ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ~ ! [X1: $i] :
( $false
=> ( X1
!= ( eigen__0 @ eigen__1 ) ) ) )
!= $false,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( $false
=> ( X1
!= ( eigen__0 @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
$false,
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: $i] :
( $false
=> ( X1
!= ( eigen__0 @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ $false,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( $false
=> ( eigen__2
!= ( eigen__0 @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
( eigen__2
= ( eigen__0 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_false,[status(thm),assumptions([h5,h9,h8,h4,h5,h3,h2,h1,h0])],[h5]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h9])],[h8,1,h5,h9]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h4,2,h8]) ).
thf(4,plain,
$false,
inference(tab_false,[status(thm),assumptions([h6,h7,h3,h2,h1,h0])],[h7]) ).
thf(5,plain,
$false,
inference(tab_be,[status(thm),assumptions([h3,h2,h1,h0]),tab_be(discharge,[h4,h5]),tab_be(discharge,[h6,h7])],[h3,3,4,h4,h5,h6,h7]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,5,h3]) ).
thf(7,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h1,h0]),tab_fe(discharge,[h2])],[h1,6,h2]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,7,h1]) ).
thf(0,theorem,
! [X1: $i > $i] :
( ( ^ [X2: $i] :
~ ! [X3: $i] :
( $false
=> ( X3
!= ( X1 @ X2 ) ) ) )
= ( ^ [X2: $i] : $false ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET764^4 : TPTP v8.1.0. Released v3.6.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 15:57:27 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.35 % SZS status Theorem
% 0.13/0.35 % Mode: mode213
% 0.13/0.35 % Inferences: 0
% 0.13/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------