TSTP Solution File: SEV494^1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV494^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n024.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 : Mon Jun 24 16:00:24 EDT 2024
% Result : Theorem 3.75s 1.92s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 183 ( 7 ~; 3 |; 0 &; 168 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 20 ( 0 ^ 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
thf('\'const/sets/INSERT\'_type',type,
'\'const/sets/INSERT\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > TA > $o ) ).
thf('\'const/nums/SUC\'_type',type,
'\'const/nums/SUC\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/NUMERAL\'_type',type,
'\'const/nums/NUMERAL\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/BIT1\'_type',type,
'\'const/nums/BIT1\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/_0\'_type',type,
'\'const/nums/_0\'': '\'type/nums/num\'' ).
thf('\'const/iterate/..\'_type',type,
'\'const/iterate/..\'': '\'type/nums/num\'' > '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).
thf('\'const/arith/-\'_type',type,
'\'const/arith/-\'': '\'type/nums/num\'' > '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/arith/<=\'_type',type,
'\'const/arith/<=\'': '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).
thf(sk1_type,type,
sk1: '\'type/nums/num\'' ).
thf(sk2_type,type,
sk2: '\'type/nums/num\'' ).
thf(1,conjecture,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] :
( ( '\'const/arith/<=\'' @ A @ ( '\'const/nums/SUC\'' @ B ) )
=> ( ( '\'const/iterate/..\'' @ A @ ( '\'const/nums/SUC\'' @ B ) )
= ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ ( '\'const/nums/SUC\'' @ B ) @ ( '\'const/iterate/..\'' @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NUMSEG_REC_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] :
( ( '\'const/arith/<=\'' @ A @ ( '\'const/nums/SUC\'' @ B ) )
=> ( ( '\'const/iterate/..\'' @ A @ ( '\'const/nums/SUC\'' @ B ) )
= ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ ( '\'const/nums/SUC\'' @ B ) @ ( '\'const/iterate/..\'' @ A @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] :
( ( '\'const/arith/<=\'' @ A @ ( '\'const/nums/SUC\'' @ B ) )
=> ( ( '\'const/iterate/..\'' @ A @ ( '\'const/nums/SUC\'' @ B ) )
= ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ ( '\'const/nums/SUC\'' @ B ) @ ( '\'const/iterate/..\'' @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
'\'const/arith/<=\'' @ sk1 @ ( '\'const/nums/SUC\'' @ sk2 ),
inference(cnf,[status(esa)],[5]) ).
thf(4,axiom,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] :
( ( '\'const/arith/<=\'' @ A @ B )
=> ( ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ B @ ( '\'const/iterate/..\'' @ A @ ( '\'const/arith/-\'' @ B @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) )
= ( '\'const/iterate/..\'' @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NUMSEG_RREC_') ).
thf(12,plain,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] :
( ( '\'const/arith/<=\'' @ A @ B )
=> ( ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ B @ ( '\'const/iterate/..\'' @ A @ ( '\'const/arith/-\'' @ B @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) )
= ( '\'const/iterate/..\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] :
( ~ ( '\'const/arith/<=\'' @ A @ B )
| ( ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ B @ ( '\'const/iterate/..\'' @ A @ ( '\'const/arith/-\'' @ B @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) )
= ( '\'const/iterate/..\'' @ A @ B ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] :
( ( ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ B @ ( '\'const/iterate/..\'' @ A @ ( '\'const/arith/-\'' @ B @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) )
= ( '\'const/iterate/..\'' @ A @ B ) )
| ~ ( '\'const/arith/<=\'' @ A @ B ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(21,plain,
! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] :
( ( ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ B @ ( '\'const/iterate/..\'' @ A @ ( '\'const/arith/-\'' @ B @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) )
= ( '\'const/iterate/..\'' @ A @ B ) )
| ( ( '\'const/arith/<=\'' @ sk1 @ ( '\'const/nums/SUC\'' @ sk2 ) )
!= ( '\'const/arith/<=\'' @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7,14]) ).
thf(22,plain,
( ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ ( '\'const/nums/SUC\'' @ sk2 ) @ ( '\'const/iterate/..\'' @ sk1 @ ( '\'const/arith/-\'' @ ( '\'const/nums/SUC\'' @ sk2 ) @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) )
= ( '\'const/iterate/..\'' @ sk1 @ ( '\'const/nums/SUC\'' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( sk1 )),bind(B,$thf( '\'const/nums/SUC\'' @ sk2 ))]]) ).
thf(3,axiom,
! [A: '\'type/nums/num\''] :
( ( '\'const/arith/-\'' @ ( '\'const/nums/SUC\'' @ A ) @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/SUC_SUB1_') ).
thf(9,plain,
! [A: '\'type/nums/num\''] :
( ( '\'const/arith/-\'' @ ( '\'const/nums/SUC\'' @ A ) @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [A: '\'type/nums/num\''] :
( ( '\'const/arith/-\'' @ ( '\'const/nums/SUC\'' @ A ) @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) )
= A ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [A: '\'type/nums/num\''] :
( ( '\'const/arith/-\'' @ ( '\'const/nums/SUC\'' @ A ) @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) )
= A ),
inference(lifteq,[status(thm)],[10]) ).
thf(35,plain,
( ( '\'const/iterate/..\'' @ sk1 @ ( '\'const/nums/SUC\'' @ sk2 ) )
= ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ ( '\'const/nums/SUC\'' @ sk2 ) @ ( '\'const/iterate/..\'' @ sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[22,11]) ).
thf(6,plain,
( ( '\'const/iterate/..\'' @ sk1 @ ( '\'const/nums/SUC\'' @ sk2 ) )
!= ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ ( '\'const/nums/SUC\'' @ sk2 ) @ ( '\'const/iterate/..\'' @ sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(8,plain,
( ( '\'const/iterate/..\'' @ sk1 @ ( '\'const/nums/SUC\'' @ sk2 ) )
!= ( '\'const/sets/INSERT\'' @ '\'type/nums/num\'' @ ( '\'const/nums/SUC\'' @ sk2 ) @ ( '\'const/iterate/..\'' @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(36,plain,
$false,
inference(simplifyReflect,[status(thm)],[35,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV494^1 : TPTP v8.2.0. Released v7.0.0.
% 0.00/0.10 % Command : run_Leo-III %s %d SAT
% 0.10/0.30 % Computer : n024.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Jun 21 19:04:55 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.83/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/0.93 % [INFO] Parsing done (132ms).
% 1.15/0.94 % [INFO] Running in sequential loop mode.
% 1.38/1.19 % [INFO] nitpick registered as external prover.
% 1.57/1.19 % [INFO] Scanning for conjecture ...
% 1.71/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.71/1.28 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.71/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.71/1.29 % [INFO] Type checking passed.
% 1.71/1.29 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.39/1.91 % [INFO] Killing All external provers ...
% 3.75/1.92 % Time passed: 1473ms (effective reasoning time: 967ms)
% 3.75/1.92 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.75/1.92 % Axioms used in derivation (2): thm/iterate/NUMSEG_RREC_, thm/arith/SUC_SUB1_
% 3.75/1.92 % No. of inferences in proof: 18
% 3.75/1.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1473 ms resp. 967 ms w/o parsing
% 3.75/1.97 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.75/1.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------