TSTP Solution File: ANA119^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ANA119^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% 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 : 300s
% DateTime : Tue May 7 07:27:55 EDT 2024
% Result : Theorem 3.17s 1.75s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 18
% Syntax : Number of formulae : 24 ( 5 unt; 14 typ; 0 def)
% Number of atoms : 20 ( 9 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 174 ( 2 ~; 0 |; 0 &; 167 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 19 ( 0 ^ 18 !; 0 ?; 19 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
'\'type/realax/real\'': $tType ).
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
thf('\'const/realax/real_sub\'_type',type,
'\'const/realax/real_sub\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_pow\'_type',type,
'\'const/realax/real_pow\'': '\'type/realax/real\'' > '\'type/nums/num\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_of_num\'_type',type,
'\'const/realax/real_of_num\'': '\'type/nums/num\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_neg\'_type',type,
'\'const/realax/real_neg\'': '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_mul\'_type',type,
'\'const/realax/real_mul\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).
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/sum\'_type',type,
'\'const/iterate/sum\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > '\'type/realax/real\'' ) > '\'type/realax/real\'' ) ).
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(1,conjecture,
! [A: '\'type/realax/real\'',B: '\'type/nums/num\''] :
( ( '\'const/arith/<=\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) @ B )
=> ( ( '\'const/realax/real_sub\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_pow\'' @ A @ B ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_sub\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) @ ( '\'const/arith/-\'' @ B @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_pow\'' @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/REAL_SUB_POW_L1_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/realax/real\'',B: '\'type/nums/num\''] :
( ( '\'const/arith/<=\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) @ B )
=> ( ( '\'const/realax/real_sub\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_pow\'' @ A @ B ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_sub\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) @ ( '\'const/arith/-\'' @ B @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_pow\'' @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: '\'type/realax/real\'',B: '\'type/nums/num\''] :
( ( '\'const/arith/<=\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) @ B )
=> ( ( '\'const/realax/real_sub\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_pow\'' @ A @ B ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_sub\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) @ ( '\'const/arith/-\'' @ B @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_pow\'' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/calc_int/REAL_MUL_LNEG_') ).
thf(10,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: '\'type/realax/real\'',B: '\'type/nums/num\''] :
( ( '\'const/arith/<=\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) @ B )
=> ( ( '\'const/realax/real_sub\'' @ ( '\'const/realax/real_pow\'' @ A @ B ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_sub\'' @ A @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) @ ( '\'const/arith/-\'' @ B @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_pow\'' @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/REAL_SUB_POW_R1_') ).
thf(13,plain,
! [A: '\'type/realax/real\'',B: '\'type/nums/num\''] :
( ( '\'const/arith/<=\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) @ B )
=> ( ( '\'const/realax/real_sub\'' @ ( '\'const/realax/real_pow\'' @ A @ B ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_sub\'' @ A @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) @ ( '\'const/arith/-\'' @ B @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_pow\'' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_sub\'' @ A @ B ) )
= ( '\'const/realax/real_sub\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realarith/REAL_NEG_SUB_') ).
thf(16,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_sub\'' @ A @ B ) )
= ( '\'const/realax/real_sub\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[6,10,13,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA119^1 : TPTP v8.1.2. Released v7.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 12:46:39 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.99 % [INFO] Parsing done (127ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 1.66/1.22 % [INFO] eprover registered as external prover.
% 1.66/1.22 % [INFO] cvc4 registered as external prover.
% 1.66/1.22 % [INFO] Scanning for conjecture ...
% 1.90/1.29 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.90/1.32 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.06/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.33 % [INFO] Type checking passed.
% 2.06/1.33 % [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 ...
% 3.17/1.75 % External prover 'e' found a proof!
% 3.17/1.75 % [INFO] Killing All external provers ...
% 3.17/1.75 % Time passed: 1213ms (effective reasoning time: 743ms)
% 3.17/1.75 % 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)>
% 3.17/1.75 % Axioms used in derivation (3): thm/calc_int/REAL_MUL_LNEG_, thm/iterate/REAL_SUB_POW_R1_, thm/realarith/REAL_NEG_SUB_
% 3.17/1.75 % No. of inferences in proof: 10
% 3.17/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1213 ms resp. 743 ms w/o parsing
% 3.49/1.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.49/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------