TSTP Solution File: SWV443^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWV443^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 : 300s
% DateTime : Thu Aug 31 22:49:15 EDT 2023
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(def_mfalse,definition,
( mfalse
= ( ^ [X1: $i] : sP1 ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimpl,definition,
( mimpl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_miff,definition,
( miff
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimpl @ X1 @ X2 ) @ ( mimpl @ X2 @ X1 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X3 @ X4 )
@ ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
? [X4: $i] :
( ( X1 @ X3 @ X4 )
& ( X2 @ X4 ) ) ) ) ).
thf(def_mall,definition,
( mall
= ( ^ [X1: individuals > $i > $o,X2: $i] :
! [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists,definition,
( mexists
= ( ^ [X1: individuals > $i > $o,X2: $i] :
? [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_cs4_atom,definition,
( cs4_atom
= ( ^ [X1: $i > $o] : ( mbox @ reli @ X1 ) ) ) ).
thf(def_cs4_and,definition,
( cs4_and
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
thf(def_cs4_or,definition,
( cs4_or
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ X1 @ X2 ) ) ) ).
thf(def_cs4_impl,definition,
( cs4_impl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ reli @ ( mimpl @ X1 @ X2 ) ) ) ) ).
thf(def_cs4_true,definition,
cs4_true = mtrue ).
thf(def_cs4_false,definition,
cs4_false = mfalse ).
thf(def_cs4_all,definition,
( cs4_all
= ( ^ [X1: individuals > $i > $o] : ( mbox @ reli @ ( mall @ X1 ) ) ) ) ).
thf(def_cs4_box,definition,
( cs4_box
= ( ^ [X1: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X1 ) ) ) ) ).
thf(def_cs4_valid,definition,
( cs4_valid
= ( ^ [X1: $i > $o] : ( mvalid @ X1 ) ) ) ).
thf(def_bl_atom,definition,
( bl_atom
= ( ^ [X1: $i > $o] : ( cs4_atom @ X1 ) ) ) ).
thf(def_bl_princ,definition,
( bl_princ
= ( ^ [X1: $i > $o] : ( cs4_atom @ X1 ) ) ) ).
thf(def_bl_and,definition,
( bl_and
= ( ^ [X1: $i > $o,X2: $i > $o] : ( cs4_and @ X1 @ X2 ) ) ) ).
thf(def_bl_or,definition,
( bl_or
= ( ^ [X1: $i > $o,X2: $i > $o] : ( cs4_or @ X1 @ X2 ) ) ) ).
thf(def_bl_impl,definition,
( bl_impl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( cs4_impl @ X1 @ X2 ) ) ) ).
thf(def_bl_all,definition,
( bl_all
= ( ^ [X1: individuals > $i > $o] : ( cs4_all @ X1 ) ) ) ).
thf(def_bl_true,definition,
bl_true = cs4_true ).
thf(def_bl_false,definition,
bl_false = cs4_false ).
thf(def_bl_says,definition,
( bl_says
= ( ^ [X1: individuals,X2: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ X1 ) ) @ X2 ) ) ) ) ).
thf(def_bl_valid,definition,
bl_valid = mvalid ).
thf(bl_id2,conjecture,
~ sP1 ).
thf(h0,negated_conjecture,
sP1,
inference(assume_negation,[status(cth)],[bl_id2]) ).
thf(1,plain,
~ sP1,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,h0]) ).
thf(0,theorem,
~ sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[2,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV443^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n025.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 : Tue Aug 29 10:29:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % Mode: cade22grackle2xfee4
% 0.19/0.40 % Steps: 1
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------