TSTP Solution File: ANA125^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ANA125^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 May 20 18:39:21 EDT 2024
% Result : Theorem 7.64s 2.95s
% Output : Refutation 7.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 12 unt; 6 typ; 0 def)
% Number of atoms : 40 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 163 ( 18 ~; 5 |; 0 &; 133 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 19 ^ 38 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
'\'type/realax/real\'': $tType ).
thf('\'const/realax/real_mul\'_type',type,
'\'const/realax/real_mul\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/iterate/polynomial_function\'_type',type,
'\'const/iterate/polynomial_function\'': ( '\'type/realax/real\'' > '\'type/realax/real\'' ) > $o ).
thf(sk1_type,type,
sk1: '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf(sk2_type,type,
sk2: '\'type/realax/real\'' ).
thf(sk9_type,type,
sk9: '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf(4,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ A @ B )
= ( '\'const/realax/real_mul\'' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_MUL_SYM_') ).
thf(12,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ A @ B )
= ( '\'const/realax/real_mul\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ A @ B )
= ( '\'const/realax/real_mul\'' @ B @ A ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ A @ B )
= ( '\'const/realax/real_mul\'' @ B @ A ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(1,conjecture,
! [A: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ A )
=> ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ ( A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_RMUL_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ A )
=> ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ ( A @ C ) @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ A )
=> ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ ( A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ! [A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ A )
=> ! [B: '\'type/realax/real\''] :
( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ ( A @ C ) @ B ) ) ),
inference(miniscope,[status(thm)],[5]) ).
thf(8,plain,
'\'const/iterate/polynomial_function\'' @ sk1,
inference(cnf,[status(esa)],[6]) ).
thf(3,axiom,
! [A: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ A )
=> ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_') ).
thf(9,plain,
! [A: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ A )
=> ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ A )
=> ! [B: '\'type/realax/real\''] :
( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) ) ),
inference(miniscope,[status(thm)],[9]) ).
thf(11,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(7,plain,
~ ( '\'const/iterate/polynomial_function\''
@ ^ [A: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ ( sk1 @ A ) @ sk2 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(18,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ ( sk1 @ C ) @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,7]) ).
thf(23,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ ( sk1 @ C ) @ sk2 ) ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(30,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ ( sk1 @ C ) @ sk2 ) ) )
| ( ( '\'const/iterate/polynomial_function\'' @ sk1 )
!= ( '\'const/iterate/polynomial_function\'' @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,23]) ).
thf(31,plain,
! [A: '\'type/realax/real\''] :
( ( ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ B ) ) )
!= ( ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ ( sk1 @ B ) @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(34,plain,
! [A: '\'type/realax/real\''] :
( ( ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ B ) ) )
!= ( ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ ( sk1 @ B ) @ sk2 ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(61,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( sk1 @ ( sk9 @ A ) ) @ sk2 )
!= ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ ( sk9 @ A ) ) ) ),
inference(func_ext,[status(esa)],[34]) ).
thf(168,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( '\'const/realax/real_mul\'' @ C @ ( sk1 @ ( sk9 @ C ) ) ) )
| ( ( '\'const/realax/real_mul\'' @ A @ B )
!= ( '\'const/realax/real_mul\'' @ ( sk1 @ ( sk9 @ C ) ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[14,61]) ).
thf(169,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ sk2 @ ( sk1 @ ( sk9 @ A ) ) )
!= ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ ( sk9 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( sk1 @ ( sk9 @ E ) )),bind(B,$thf( sk2 )),bind(C,$thf( E ))]]) ).
thf(172,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ sk2 @ ( sk1 @ ( sk9 @ A ) ) )
!= ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ ( sk9 @ A ) ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(177,plain,
$false,
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( sk2 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : ANA125^1 : TPTP v8.2.0. Released v7.0.0.
% 0.09/0.11 % Command : run_Leo-III %s %d
% 0.10/0.31 % Computer : n002.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 08:00:08 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.89/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.07 % [INFO] Parsing done (165ms).
% 1.30/1.09 % [INFO] Running in sequential loop mode.
% 1.79/1.43 % [INFO] eprover registered as external prover.
% 1.79/1.43 % [INFO] cvc4 registered as external prover.
% 1.79/1.44 % [INFO] Scanning for conjecture ...
% 1.89/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.00/1.55 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.00/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.00/1.56 % [INFO] Type checking passed.
% 2.00/1.56 % [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 ...
% 7.64/2.94 % [INFO] Killing All external provers ...
% 7.64/2.95 % Time passed: 2482ms (effective reasoning time: 1855ms)
% 7.64/2.95 % 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)>
% 7.64/2.95 % Axioms used in derivation (2): thm/realax/REAL_MUL_SYM_, thm/iterate/POLYNOMIAL_FUNCTION_LMUL_
% 7.64/2.95 % No. of inferences in proof: 24
% 7.64/2.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2482 ms resp. 1855 ms w/o parsing
% 7.64/2.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.64/2.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------