TSTP Solution File: NUM021^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM021^1 : 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 : n008.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 : Mon Jul 18 13:49:53 EDT 2022
% Result : Theorem 221.26s 203.13s
% Output : Proof 221.26s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(sP1,plain,
( sP1
<=> ( ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) )
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) )
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X1
@ ^ [X2: $i > $i,X3: $i] : ( X2 @ ( X2 @ X3 ) )
@ ^ [X2: $i > $i,X3: $i] : ( X2 @ ( X2 @ ( X2 @ X3 ) ) ) )
= ( ^ [X2: $i > $i,X3: $i] : ( X2 @ ( X2 @ ( X2 @ ( X2 @ ( X2 @ X3 ) ) ) ) ) ) )
=> ( ( X1
@ ^ [X2: $i > $i] : X2
@ ^ [X2: $i > $i,X3: $i] : ( X2 @ ( X2 @ X3 ) ) )
!= ( ^ [X2: $i > $i,X3: $i] : ( X2 @ ( X2 @ ( X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) )
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(def_zero,definition,
( zero
= ( ^ [X1: $i > $i,X2: $i] : X2 ) ) ).
thf(def_one,definition,
( one
= ( ^ [X1: $i > $i] : X1 ) ) ).
thf(def_two,definition,
( two
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ) ).
thf(def_three,definition,
( three
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ).
thf(def_four,definition,
( four
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_five,definition,
( five
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ).
thf(def_six,definition,
( six
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ).
thf(def_seven,definition,
( seven
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ).
thf(def_eight,definition,
( eight
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ).
thf(def_nine,definition,
( nine
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ).
thf(def_ten,definition,
( ten
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(def_succ,definition,
( succ
= ( ^ [X1: ( $i > $i ) > $i > $i,X2: $i > $i,X3: $i] : ( X2 @ ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_plus,definition,
( plus
= ( ^ [X1: ( $i > $i ) > $i > $i,X2: ( $i > $i ) > $i > $i,X3: $i > $i,X4: $i] : ( X1 @ X3 @ ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_mult,definition,
( mult
= ( ^ [X1: ( $i > $i ) > $i > $i,X2: ( $i > $i ) > $i > $i,X3: $i > $i] : ( X1 @ ( X2 @ X3 ) ) ) ) ).
thf(thm,conjecture,
~ sP3 ).
thf(h0,negated_conjecture,
sP3,
inference(assume_negation,[status(cth)],[thm]) ).
thf(1,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
sP1,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| ~ sP4
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,h0]) ).
thf(0,theorem,
~ sP3,
inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM021^1 : TPTP v8.1.0. Released v3.6.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n008.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 : Thu Jul 7 22:42:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 221.26/203.13 % SZS status Theorem
% 221.26/203.13 % Mode: mode492
% 221.26/203.13 % Inferences: 310917
% 221.26/203.13 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------