%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA122^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:48 AM UTC 2026
% Result : Theorem 52.54s 19.19s
% Output : Refutation 52.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 63 ( 36 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 268 ( 18 ~; 3 |; 0 &; 247 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 18 ^; 44 !; 12 ?; 76 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% 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_pow_decl',type,
'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
thf('const/realax/real_of_num_decl',type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf('const/realax/real_mul_decl',type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/nums/NUMERAL_decl',type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/BIT1_decl',type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/_0_decl',type,
'const/nums/_0': 'type/nums/num' ).
thf('const/iterate/sum_decl',type,
'const/iterate/sum':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > 'type/realax/real' ) > 'type/realax/real' ) ).
thf('const/iterate/polynomial_function_decl',type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf('const/iterate/.._decl',type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(sk1_decl,type,
sk1: 'type/realax/real' ).
thf(sk5_decl,type,
sk5: ( 'type/nums/num' > 'type/realax/real' ) > 'type/nums/num' > 'type/realax/real' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real'] :
~ ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : A ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num'] :
@+[C: 'type/realax/real'] :
( sk1
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ B )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ D ) @ ( 'const/realax/real_pow' @ C @ D ) ) ) ) ) ) ).
thf(3,axiom,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realarith/REAL_MUL_RID_') ).
thf(9,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= A ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= A ),
inference(lifteq,[status(thm)],[10]) ).
thf(5,axiom,
! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ B ) @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SING_NUMSEG_') ).
thf(15,plain,
! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ B ) @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [B: 'type/nums/num',A: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ B ) @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [B: 'type/nums/num',A: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ B ) @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(6,axiom,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
= ( ? [B: 'type/nums/num',C: 'type/nums/num' > 'type/realax/real'] :
! [D: 'type/realax/real'] :
( ( A @ D )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ B )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( C @ E ) @ ( 'const/realax/real_pow' @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/polynomial_function_') ).
thf(18,plain,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
= ( ? [B: 'type/nums/num',C: 'type/nums/num' > 'type/realax/real'] :
! [D: 'type/realax/real'] :
( ( A @ D )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ B )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( C @ E ) @ ( 'const/realax/real_pow' @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,plain,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
= ( ? [B: 'type/nums/num',C: 'type/nums/num' > 'type/realax/real'] :
! [D: 'type/realax/real'] :
( ( A @ D )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ B )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( C @ E ) @ ( 'const/realax/real_pow' @ D @ E ) ) ) ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
= ( ? [B: 'type/nums/num',C: 'type/nums/num' > 'type/realax/real'] :
! [D: 'type/realax/real'] :
( ( A @ D )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ B )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( C @ E ) @ ( 'const/realax/real_pow' @ D @ E ) ) ) ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(1,conjecture,
! [A: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_CONST_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(23,plain,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ~ ? [B: 'type/nums/num',C: 'type/nums/num' > 'type/realax/real'] :
! [D: 'type/realax/real'] :
( ( A @ D )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ B )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( C @ E ) @ ( 'const/realax/real_pow' @ D @ E ) ) ) )
| ( ( 'const/iterate/polynomial_function' @ A )
!= ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[20,8]) ).
thf(24,plain,
~ ? [A: 'type/nums/num',B: 'type/nums/num' > 'type/realax/real'] :
! [C: 'type/realax/real'] :
( sk1
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ A )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ D ) @ ( 'const/realax/real_pow' @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( ^ [B: 'type/realax/real'] : sk1 ))]]) ).
thf(29,plain,
! [B: 'type/nums/num' > 'type/realax/real',A: 'type/nums/num'] :
( sk1
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ A )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ C ) @ ( 'const/realax/real_pow' @ ( sk5 @ B @ A ) @ C ) ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(30,plain,
! [B: 'type/nums/num' > 'type/realax/real',A: 'type/nums/num'] :
( sk1
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ A )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ C ) @ ( 'const/realax/real_pow' @ ( sk5 @ B @ A ) @ C ) ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(97,plain,
! [D: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',B: 'type/nums/num',A: 'type/nums/num' > 'type/realax/real'] :
( ( ( A @ B )
!= sk1 )
| ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ B ) @ A )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ C )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( D @ E ) @ ( 'const/realax/real_pow' @ ( sk5 @ D @ C ) @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,30]) ).
thf(98,plain,
! [A: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/realax/real_pow' @ ( sk5 @ A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( ^ [F: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( G @ F ) @ ( 'const/realax/real_pow' @ ( sk5 @ G @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ F ) ) )),bind(B,$thf( 'const/nums/NUMERAL' @ 'const/nums/_0' )),bind(C,$thf( 'const/nums/NUMERAL' @ 'const/nums/_0' )),bind(D,$thf( G ))]]) ).
thf(140,plain,
! [A: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/realax/real_pow' @ ( sk5 @ A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= sk1 ),
inference(simp,[status(thm)],[98]) ).
thf(4,axiom,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_pow' @ A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/real_pow_0') ).
thf(12,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_pow' @ A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_pow' @ A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_pow' @ A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(4020,plain,
! [A: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= sk1 ),
inference(rewrite,[status(thm)],[140,14]) ).
thf(4028,plain,
! [B: 'type/nums/num' > 'type/realax/real',A: 'type/realax/real'] :
( ( A != sk1 )
| ( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_mul' @ ( B @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,4020]) ).
thf(4117,plain,
! [A: 'type/nums/num' > 'type/realax/real'] :
( ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[4028:[bind(A,$thf( B @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ))]]) ).
thf(4118,plain,
$false,
inference(pre_uni,[status(thm)],[4117:[bind(A,$thf( ^ [B: 'type/nums/num'] : sk1 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA122^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n007.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 17:42:56 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.03/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.02 % [INFO] Parsing done (209ms).
% 1.53/1.04 % [INFO] Running in sequential loop mode.
% 2.14/1.43 % [INFO] eprover registered as external prover.
% 2.14/1.44 % [INFO] Scanning for conjecture ...
% 2.32/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.32/1.56 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.32/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.32/1.60 % [INFO] Type checking passed.
% 2.51/1.60 % [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 ...
% 52.54/19.18 % [INFO] Killing All external provers ...
% 52.54/19.19 % Time passed: 18819ms (effective reasoning time: 18139ms)
% 52.54/19.19 % 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)>
% 52.54/19.19 % Axioms used in derivation (4): thm/realarith/REAL_MUL_RID_, thm/iterate/SUM_SING_NUMSEG_, thm/iterate/polynomial_function_, thm/realax/real_pow_0
% 52.54/19.19 % No. of inferences in proof: 31
% 52.54/19.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18819 ms resp. 18139 ms w/o parsing
% 52.73/19.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.73/19.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------