%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA129^1 : 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 : n016.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 07:45:49 AM UTC 2026
% Result : Theorem 70.01s 23.52s
% Output : Refutation 70.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 21 unt; 0 typ; 3 def)
% Number of atoms : 117 ( 23 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 510 ( 51 ~; 41 |; 6 &; 400 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 143 ( 75 ^; 65 !; 0 ?; 143 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% 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/SUC_decl',type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
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/polynomial_function_decl',type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(sk1_decl,type,
sk1: 'type/realax/real' > 'type/realax/real' ).
thf(sk2_decl,type,
sk2: 'type/nums/num' ).
thf(sk3_decl,type,
sk3: ( 'type/nums/num' > $o ) > 'type/nums/num' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real' > 'type/realax/real'] :
~ ( ( 'const/iterate/polynomial_function' @ A )
=> ! [B: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( A @ C ) @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/nums/num'] :
~ ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: 'type/nums/num' > $o] :
@+[B: 'type/nums/num'] :
~ ( ( A @ B )
=> ( A @ ( 'const/nums/SUC' @ B ) ) ) ) ) ).
thf(6,axiom,
! [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(28,plain,
! [A: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,plain,
! [A: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : A ),
inference(cnf,[status(esa)],[28]) ).
thf(3,axiom,
! [A: 'type/nums/num' > $o] :
( ( ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
& ! [B: 'type/nums/num'] :
( ( A @ B )
=> ( A @ ( 'const/nums/SUC' @ B ) ) ) )
=> ! [B: 'type/nums/num'] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/nums/num_INDUCTION_') ).
thf(13,plain,
! [A: 'type/nums/num' > $o] :
( ( ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
& ! [B: 'type/nums/num'] :
( ( A @ B )
=> ( A @ ( 'const/nums/SUC' @ B ) ) ) )
=> ! [B: 'type/nums/num'] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [B: 'type/nums/num',A: 'type/nums/num' > $o] :
( ( ~ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
| ( A @ ( sk3 @ A ) )
| ( A @ B ) )
& ( ~ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
| ~ ( A @ ( 'const/nums/SUC' @ ( sk3 @ A ) ) )
| ( A @ B ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [B: 'type/nums/num',A: 'type/nums/num' > $o] :
( ~ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
| ( A @ ( sk3 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(1,conjecture,
! [A: 'type/realax/real' > 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_POW_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/realax/real' > 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( A @ C ) @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: 'type/realax/real' > 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
~ ! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ! [B: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( A @ C ) @ B ) ) ),
inference(miniscope,[status(thm)],[8]) ).
thf(10,plain,
( ( 'const/iterate/polynomial_function' @ sk1 )
& ~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ A ) @ sk2 ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(12,plain,
~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ A ) @ sk2 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(52,plain,
! [B: 'type/nums/num',A: 'type/nums/num' > $o] :
( ~ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
| ( A @ ( sk3 @ A ) )
| ~ $true
| ( ( A @ B )
!= ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ C ) @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,12]) ).
thf(53,plain,
! [B: 'type/nums/num',A: 'type/nums/num' > $o] :
( ~ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
| ( A @ ( sk3 @ A ) )
| ( ( A @ B )
!= ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ C ) @ sk2 ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(88,plain,
( ~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ A ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] :
( 'const/realax/real_pow' @ ( sk1 @ A )
@ ( sk3
@ ^ [B: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ C ) @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[53:[bind(A,$thf( ^ [C: 'type/nums/num'] : ( 'const/iterate/polynomial_function' @ ^ [D: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ D ) @ C ) ) )),bind(B,$thf( sk2 ))]]) ).
thf(7,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(30,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)],[7]) ).
thf(31,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)],[30]) ).
thf(32,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)],[31]) ).
thf(2131,plain,
( ~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] :
( 'const/realax/real_pow' @ ( sk1 @ A )
@ ( sk3
@ ^ [B: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ C ) @ B ) ) ) ) ) ),
inference(rewrite,[status(thm)],[88,32]) ).
thf(2134,plain,
! [A: 'type/realax/real'] :
( ~ $true
| ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] :
( 'const/realax/real_pow' @ ( sk1 @ B )
@ ( sk3
@ ^ [C: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [D: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ D ) @ C ) ) ) ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : A )
!= ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,2131]) ).
thf(2135,plain,
! [A: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] :
( 'const/realax/real_pow' @ ( sk1 @ B )
@ ( sk3
@ ^ [C: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [D: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ D ) @ C ) ) ) ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : A )
!= ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(simp,[status(thm)],[2134]) ).
thf(2136,plain,
( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] :
( 'const/realax/real_pow' @ ( sk1 @ A )
@ ( sk3
@ ^ [B: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ C ) @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2135:[bind(A,$thf( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ))]]) ).
thf(11,plain,
'const/iterate/polynomial_function' @ sk1,
inference(cnfConj,[status(thm)],[10]) ).
thf(4,axiom,
! [A: 'type/realax/real' > 'type/realax/real',B: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ A )
& ( 'const/iterate/polynomial_function' @ B ) )
=> ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_MUL_') ).
thf(23,plain,
! [A: 'type/realax/real' > 'type/realax/real',B: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ A )
& ( 'const/iterate/polynomial_function' @ B ) )
=> ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,plain,
! [B: 'type/realax/real' > 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ A )
| ~ ( 'const/iterate/polynomial_function' @ B )
| ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(160,plain,
! [B: 'type/realax/real' > 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ $true
| ~ ( 'const/iterate/polynomial_function' @ B )
| ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) )
| ( ( 'const/iterate/polynomial_function' @ sk1 )
!= ( 'const/iterate/polynomial_function' @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,24]) ).
thf(161,plain,
! [B: 'type/realax/real' > 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ B )
| ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) )
| ( ( 'const/iterate/polynomial_function' @ sk1 )
!= ( 'const/iterate/polynomial_function' @ A ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(162,plain,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ A )
| ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ B ) @ ( A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(190,plain,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ A )
| ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ B ) @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(2321,plain,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ~ $true
| ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ B ) @ ( A @ B ) ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] :
( 'const/realax/real_pow' @ ( sk1 @ B )
@ ( sk3
@ ^ [C: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [D: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ D ) @ C ) ) ) ) )
!= ( 'const/iterate/polynomial_function' @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2136,190]) ).
thf(2322,plain,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ B ) @ ( A @ B ) ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] :
( 'const/realax/real_pow' @ ( sk1 @ B )
@ ( sk3
@ ^ [C: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [D: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ D ) @ C ) ) ) ) )
!= ( 'const/iterate/polynomial_function' @ A ) ) ),
inference(simp,[status(thm)],[2321]) ).
thf(2323,plain,
( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] :
( 'const/realax/real_mul' @ ( sk1 @ A )
@ ( 'const/realax/real_pow' @ ( sk1 @ A )
@ ( sk3
@ ^ [B: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ C ) @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2322:[bind(A,$thf( ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ ( sk3 @ ^ [C: 'type/nums/num'] : ( 'const/iterate/polynomial_function' @ ^ [D: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ D ) @ C ) ) ) ) ))]]) ).
thf(5,axiom,
! [A: 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/realax/real_pow' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_pow' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/real_pow_1') ).
thf(25,plain,
! [A: 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/realax/real_pow' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_pow' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,plain,
! [B: 'type/nums/num',A: 'type/realax/real'] :
( ( 'const/realax/real_pow' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_pow' @ A @ B ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [B: 'type/nums/num',A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_pow' @ A @ B ) )
= ( 'const/realax/real_pow' @ A @ ( 'const/nums/SUC' @ B ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(2388,plain,
( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] :
( 'const/realax/real_pow' @ ( sk1 @ A )
@ ( 'const/nums/SUC'
@ ( sk3
@ ^ [B: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ C ) @ B ) ) ) ) ) ),
inference(rewrite,[status(thm)],[2323,27]) ).
thf(16,plain,
! [B: 'type/nums/num',A: 'type/nums/num' > $o] :
( ~ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
| ~ ( A @ ( 'const/nums/SUC' @ ( sk3 @ A ) ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(2412,plain,
! [B: 'type/nums/num',A: 'type/nums/num' > $o] :
( ~ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
| ~ $true
| ( A @ B )
| ( ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] :
( 'const/realax/real_pow' @ ( sk1 @ C )
@ ( 'const/nums/SUC'
@ ( sk3
@ ^ [D: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [E: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ E ) @ D ) ) ) ) ) )
!= ( A @ ( 'const/nums/SUC' @ ( sk3 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2388,16]) ).
thf(2413,plain,
! [B: 'type/nums/num',A: 'type/nums/num' > $o] :
( ~ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
| ( A @ B )
| ( ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] :
( 'const/realax/real_pow' @ ( sk1 @ C )
@ ( 'const/nums/SUC'
@ ( sk3
@ ^ [D: 'type/nums/num'] :
( 'const/iterate/polynomial_function'
@ ^ [E: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ E ) @ D ) ) ) ) ) )
!= ( A @ ( 'const/nums/SUC' @ ( sk3 @ A ) ) ) ) ),
inference(simp,[status(thm)],[2412]) ).
thf(2430,plain,
! [A: 'type/nums/num'] :
( ~ ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ A ) ) ),
inference(pre_uni,[status(thm)],[2413:[bind(A,$thf( ^ [C: 'type/nums/num'] : ( 'const/iterate/polynomial_function' @ ^ [D: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ D ) @ C ) ) )),bind(B,$thf( B ))]]) ).
thf(2436,plain,
! [A: 'type/nums/num'] :
( ~ ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ A ) ) ),
inference(simp,[status(thm)],[2430]) ).
thf(12598,plain,
! [A: 'type/nums/num'] :
( ~ ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ A ) ) ),
inference(rewrite,[status(thm)],[2436,32]) ).
thf(12738,plain,
! [A: 'type/nums/num'] :
( ~ ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ~ $true
| ( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ A ) )
!= ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12598,12]) ).
thf(12739,plain,
! [A: 'type/nums/num'] :
( ~ ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ A ) )
!= ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( sk1 @ B ) @ sk2 ) ) ) ),
inference(simp,[status(thm)],[12738]) ).
thf(12740,plain,
~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ),
inference(pattern_uni,[status(thm)],[12739:[bind(A,$thf( sk2 ))]]) ).
thf(13173,plain,
~ $true,
inference(rewrite,[status(thm)],[12740,29]) ).
thf(13174,plain,
$false,
inference(simp,[status(thm)],[13173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA129^1 : 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
% 0.10/0.20 % Computer : n016.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 17:50:04 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.99 % [INFO] Parsing done (203ms).
% 1.18/1.01 % [INFO] Running in sequential loop mode.
% 2.02/1.40 % [INFO] eprover registered as external prover.
% 2.02/1.41 % [INFO] Scanning for conjecture ...
% 2.20/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.20/1.55 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.20/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.57 % [INFO] Type checking passed.
% 2.20/1.57 % [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 ...
% 70.01/23.52 % [INFO] Killing All external provers ...
% 70.01/23.52 % Time passed: 23172ms (effective reasoning time: 22506ms)
% 70.01/23.52 % 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)>
% 70.01/23.52 % Axioms used in derivation (5): thm/iterate/POLYNOMIAL_FUNCTION_MUL_, thm/iterate/POLYNOMIAL_FUNCTION_CONST_, thm/realax/real_pow_0, thm/realax/real_pow_1, thm/nums/num_INDUCTION_
% 70.01/23.52 % No. of inferences in proof: 51
% 70.01/23.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23172 ms resp. 22506 ms w/o parsing
% 70.01/23.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 70.01/23.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------