TSTP Solution File: QUA005^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : QUA005^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n032.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 13:31:54 EDT 2023
% Result : Theorem 82.40s 82.71s
% Output : Proof 82.40s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_multiplication,type,
multiplication: $i > $i > $i ).
thf(ty_sup,type,
sup: ( $i > $o ) > $i ).
thf(ty_zero,type,
zero: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( sup
@ ^ [X2: $i] : ( X2 = X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( sup
@ ^ [X1: $i] : $false )
= ( multiplication
@ @+[X1: $i] :
( ( multiplication @ X1 @ zero )
!= zero )
@ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( sup
@ ^ [X1: $i] :
( X1
= ( @+[X2: $i] :
( ( multiplication @ X2 @ zero )
!= zero ) ) ) )
= ( @+[X1: $i] :
( ( multiplication @ X1 @ zero )
!= zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( multiplication @ ( sup @ X1 ) @ ( sup @ X2 ) )
= ( sup
@ ^ [X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( X1 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X3
!= ( multiplication @ X4 @ X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $o] :
( ( multiplication
@ ( sup
@ ^ [X2: $i] :
( X2
= ( @+[X3: $i] :
( ( multiplication @ X3 @ zero )
!= zero ) ) ) )
@ ( sup @ X1 ) )
= ( sup
@ ^ [X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( X3
= ( @+[X5: $i] :
( ( multiplication @ X5 @ zero )
!= zero ) ) )
=> ~ ( X1 @ X4 ) )
=> ( X2
!= ( multiplication @ X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( sup
@ ^ [X1: $i] : $false )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( multiplication
@ @+[X1: $i] :
( ( multiplication @ X1 @ zero )
!= zero )
@ zero )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( sup
@ ^ [X1: $i] :
( X1
= ( sup
@ ^ [X2: $i] : $false ) ) )
= ( sup
@ ^ [X1: $i] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( multiplication
@ @+[X1: $i] :
( ( multiplication @ X1 @ zero )
!= zero )
@ zero )
= ( sup
@ ^ [X1: $i] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( multiplication
@ ( sup
@ ^ [X1: $i] :
( X1
= ( @+[X2: $i] :
( ( multiplication @ X2 @ zero )
!= zero ) ) ) )
@ ( sup
@ ^ [X1: $i] : $false ) )
= ( multiplication
@ @+[X1: $i] :
( ( multiplication @ X1 @ zero )
!= zero )
@ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( multiplication
@ ( sup
@ ^ [X1: $i] :
( X1
= ( @+[X2: $i] :
( ( multiplication @ X2 @ zero )
!= zero ) ) ) )
@ ( sup
@ ^ [X1: $i] : $false ) )
= ( sup
@ ^ [X1: $i] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(def_emptyset,definition,
( emptyset
= ( ^ [X1: $i] : $false ) ) ).
thf(def_union,definition,
( union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).
thf(def_supset,definition,
( supset
= ( ^ [X1: ( $i > $o ) > $o,X2: $i] :
? [X3: $i > $o] :
( ( X1 @ X3 )
& ( ( sup @ X3 )
= X2 ) ) ) ) ).
thf(def_unionset,definition,
( unionset
= ( ^ [X1: ( $i > $o ) > $o,X2: $i] :
? [X3: $i > $o] :
( ( X1 @ X3 )
& ( X3 @ X2 ) ) ) ) ).
thf(def_addition,definition,
( addition
= ( ^ [X1: $i,X2: $i] : ( sup @ ( union @ ( singleton @ X1 ) @ ( singleton @ X2 ) ) ) ) ) ).
thf(def_crossmult,definition,
( crossmult
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
? [X4: $i,X5: $i] :
( ( X1 @ X4 )
& ( X2 @ X5 )
& ( X3
= ( multiplication @ X4 @ X5 ) ) ) ) ) ).
thf(multiplication_anni,conjecture,
! [X1: $i] :
( ( multiplication @ X1 @ zero )
= zero ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ( multiplication @ X1 @ zero )
= zero ),
inference(assume_negation,[status(cth)],[multiplication_anni]) ).
thf(1,plain,
( sP10
| ~ sP6
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP11
| sP9
| ~ sP10
| ~ sP11 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| sP7
| ~ sP2
| ~ sP6 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP2 ),
inference(symeq,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(multiplication_def,axiom,
sP4 ).
thf(sup_singleset,axiom,
sP1 ).
thf(sup_es,axiom,
sP6 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0,h0])],[1,2,3,4,5,6,7,8,h0,multiplication_def,sup_singleset,sup_es]) ).
thf(0,theorem,
! [X1: $i] :
( ( multiplication @ X1 @ zero )
= zero ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : QUA005^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.09/0.31 % Computer : n032.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Sat Aug 26 16:44:14 EDT 2023
% 0.09/0.31 % CPUTime :
% 82.40/82.71 % SZS status Theorem
% 82.40/82.71 % Mode: cade22grackle2x4fb9
% 82.40/82.71 % Steps: 27199
% 82.40/82.71 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------