%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA126^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n003.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 45.81s 11.87s
% Output : Refutation 46.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 72 ( 35 unt; 0 typ; 1 def)
% Number of atoms : 149 ( 86 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 666 ( 70 ~; 51 |; 0 &; 542 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 129 ( 23 ^; 105 !; 0 ?; 129 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% 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_of_num_decl',type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf('const/realax/real_neg_decl',type,
'const/realax/real_neg': 'type/realax/real' > '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/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(sk3_decl,type,
sk3: 'type/realax/real' > ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(sk4_decl,type,
sk4: 'type/realax/real' > 'type/realax/real' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( A @ B ) ) )
!= ( 'const/iterate/polynomial_function' @ A ) ) ) ) ).
thf(6,axiom,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/calc_int/REAL_NEG_NEG_') ).
thf(19,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ A ) )
= A ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ A ) )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p','thm/calc_int/REAL_MUL_LNEG_') ).
thf(13,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)],[4]) ).
thf(14,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ B )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ B )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(3,axiom,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_MUL_LID_') ).
thf(10,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
= A ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
= A ),
inference(lifteq,[status(thm)],[11]) ).
thf(48,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) )
= C )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ B )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,12]) ).
thf(50,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) )
= C )
| ( ( 'const/realax/real_neg' @ A )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( B != C ) ),
inference(simp,[status(thm)],[48]) ).
thf(52,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) )
= B )
| ( ( 'const/realax/real_neg' @ A )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(274,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ B @ C ) )
= C )
| ( A
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ A ) )
!= ( 'const/realax/real_neg' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,52]) ).
thf(275,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ B ) @ A ) )
= A )
| ( B
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( D )),bind(B,$thf( 'const/realax/real_neg' @ D ))]]) ).
thf(317,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ A ) )
= A ),
inference(simp,[status(thm)],[275]) ).
thf(327,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A ) ) )
= A ),
inference(rewrite,[status(thm)],[317,15]) ).
thf(329,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ B @ C ) )
= C )
| ( A
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A ) ) )
!= ( 'const/realax/real_neg' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[327,52]) ).
thf(330,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ B ) ) @ A ) )
= A )
| ( B
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( F )),bind(B,$thf( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ F ) )),bind(C,$thf( C ))]]) ).
thf(384,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ A ) )
= A ),
inference(simp,[status(thm)],[330]) ).
thf(512,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ A ) ) )
= A ),
inference(rewrite,[status(thm)],[384,15]) ).
thf(521,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ A )
= B )
| ( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ A ) ) )
!= ( 'const/realax/real_neg' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[512,21]) ).
thf(522,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ A ) )
= ( 'const/realax/real_neg' @ A ) ),
inference(pattern_uni,[status(thm)],[521:[bind(A,$thf( E )),bind(B,$thf( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ E ) ))]]) ).
thf(597,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ A ) )
= ( 'const/realax/real_neg' @ A ) ),
inference(simp,[status(thm)],[522]) ).
thf(826,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A ) )
= ( 'const/realax/real_neg' @ A ) ),
inference(rewrite,[status(thm)],[597,12]) ).
thf(1,conjecture,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( A @ B ) ) )
= ( 'const/iterate/polynomial_function' @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_NEG_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( A @ B ) ) )
= ( 'const/iterate/polynomial_function' @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( A @ B ) ) )
= ( 'const/iterate/polynomial_function' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sk1 @ A ) ) )
!= ( 'const/iterate/polynomial_function' @ sk1 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sk1 @ A ) ) )
!= ( 'const/iterate/polynomial_function' @ sk1 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(24,plain,
( ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sk1 @ A ) ) )
| ( 'const/iterate/polynomial_function' @ sk1 ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(5,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(16,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)],[5]) ).
thf(17,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)],[16]) ).
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 ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(139,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ sk1 )
| ~ $true
| ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sk1 @ C ) ) )
!= ( 'const/iterate/polynomial_function' @ A ) ) ),
inference(paramod_ordered,[status(thm)],[24,18]) ).
thf(140,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ sk1 )
| ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sk1 @ C ) ) )
!= ( 'const/iterate/polynomial_function' @ A ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
! [A: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ sk1 )
| ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_neg' @ ( sk1 @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( ^ [C: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sk1 @ C ) ) )),bind(B,$thf( B ))]]) ).
thf(150,plain,
! [A: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ sk1 )
| ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_neg' @ ( sk1 @ B ) ) ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(250,plain,
! [A: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ sk1 )
| ( ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_neg' @ ( sk1 @ B ) ) ) )
!= ( 'const/iterate/polynomial_function' @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[150]) ).
thf(254,plain,
! [A: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ sk1 )
| ( ( ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_neg' @ ( sk1 @ B ) ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[250]) ).
thf(256,plain,
! [A: 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_neg' @ ( sk1 @ ( sk4 @ A ) ) ) )
!= ( sk1 @ ( sk4 @ A ) ) )
| ( 'const/iterate/polynomial_function' @ sk1 ) ),
inference(func_ext,[status(esa)],[254]) ).
thf(46,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ A @ C )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ B @ C ) ) )
| ( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ A ) )
!= ( 'const/realax/real_neg' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,15]) ).
thf(47,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ B @ A )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ B ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( D )),bind(B,$thf( 'const/realax/real_neg' @ D ))]]) ).
thf(54,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ B @ A )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ B ) @ A ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(55,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ B @ A ) ) )
= ( 'const/realax/real_mul' @ B @ A ) ),
inference(rewrite,[status(thm)],[54,15]) ).
thf(300,plain,
! [D: 'type/realax/real',C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ A )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( ( 'const/realax/real_neg' @ B )
= ( 'const/realax/real_mul' @ D @ C ) )
| ( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) )
!= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,55]) ).
thf(301,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ A )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( ( 'const/realax/real_mul' @ A @ B )
= ( 'const/realax/real_neg' @ B ) ) ),
inference(pattern_uni,[status(thm)],[300:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(135,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ A )
| ~ ( 'const/iterate/polynomial_function' @ sk1 )
| ( ( '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_neg' @ ( sk1 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,9]) ).
thf(146,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ A )
| ~ ( 'const/iterate/polynomial_function' @ sk1 )
| ( ( ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) )
!= ( ^ [C: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sk1 @ C ) ) ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(223,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ B @ ( A @ ( sk3 @ B @ A ) ) )
!= ( 'const/realax/real_neg' @ ( sk1 @ ( sk3 @ B @ A ) ) ) )
| ~ ( 'const/iterate/polynomial_function' @ A )
| ~ ( 'const/iterate/polynomial_function' @ sk1 ) ),
inference(func_ext,[status(esa)],[146]) ).
thf(6592,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ B @ ( A @ ( sk3 @ B @ A ) ) )
!= ( 'const/realax/real_neg' @ ( sk1 @ ( sk3 @ B @ A ) ) ) )
| ~ ( 'const/iterate/polynomial_function' @ sk1 )
| ( ( 'const/iterate/polynomial_function' @ A )
!= ( 'const/iterate/polynomial_function' @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[223]) ).
thf(6619,plain,
! [A: 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ A @ ( sk1 @ ( sk3 @ A @ sk1 ) ) )
!= ( 'const/realax/real_neg' @ ( sk1 @ ( sk3 @ A @ sk1 ) ) ) )
| ~ ( 'const/iterate/polynomial_function' @ sk1 ) ),
inference(pattern_uni,[status(thm)],[6592:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(6652,plain,
! [A: 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ A @ ( sk1 @ ( sk3 @ A @ sk1 ) ) )
!= ( 'const/realax/real_neg' @ ( sk1 @ ( sk3 @ A @ sk1 ) ) ) )
| ~ ( 'const/iterate/polynomial_function' @ sk1 ) ),
inference(simp,[status(thm)],[6619]) ).
thf(7540,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ A )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( ( 'const/realax/real_neg' @ B )
!= ( 'const/realax/real_neg' @ ( sk1 @ ( sk3 @ C @ sk1 ) ) ) )
| ~ ( 'const/iterate/polynomial_function' @ sk1 )
| ( ( 'const/realax/real_mul' @ A @ B )
!= ( 'const/realax/real_mul' @ C @ ( sk1 @ ( sk3 @ C @ sk1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,6652]) ).
thf(7541,plain,
! [A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ A )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( ( 'const/realax/real_neg' @ ( sk1 @ ( sk3 @ A @ sk1 ) ) )
!= ( 'const/realax/real_neg' @ ( sk1 @ ( sk3 @ A @ sk1 ) ) ) )
| ~ ( 'const/iterate/polynomial_function' @ sk1 ) ),
inference(pattern_uni,[status(thm)],[7540:[bind(A,$thf( E )),bind(B,$thf( sk1 @ ( sk3 @ E @ sk1 ) )),bind(C,$thf( E ))]]) ).
thf(7768,plain,
! [A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ A )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ~ ( 'const/iterate/polynomial_function' @ sk1 ) ),
inference(simp,[status(thm)],[7541]) ).
thf(8300,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( A
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ~ ( 'const/iterate/polynomial_function' @ sk1 )
| ( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ A ) )
!= ( 'const/realax/real_neg' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,7768]) ).
thf(8301,plain,
! [A: 'type/realax/real'] :
( ( A
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ~ ( 'const/iterate/polynomial_function' @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8300:[bind(A,$thf( C )),bind(B,$thf( 'const/realax/real_neg' @ C ))]]) ).
thf(8336,plain,
~ ( 'const/iterate/polynomial_function' @ sk1 ),
inference(simp,[status(thm)],[8301]) ).
thf(8357,plain,
! [A: 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_neg' @ ( sk1 @ ( sk4 @ A ) ) ) )
!= ( sk1 @ ( sk4 @ A ) ) )
| $false ),
inference(rewrite,[status(thm)],[256,8336]) ).
thf(8358,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_neg' @ ( sk1 @ ( sk4 @ A ) ) ) )
!= ( sk1 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[8357]) ).
thf(9008,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) )
!= ( sk1 @ ( sk4 @ C ) ) )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ B )
!= ( 'const/realax/real_mul' @ C @ ( 'const/realax/real_neg' @ ( sk1 @ ( sk4 @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,8358]) ).
thf(9009,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_neg' @ ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ A ) ) ) ) ) )
!= ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[9008:[bind(A,$thf( H )),bind(B,$thf( 'const/realax/real_neg' @ ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ H ) ) ) )),bind(C,$thf( 'const/realax/real_neg' @ H ))]]) ).
thf(9061,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_neg' @ ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ A ) ) ) ) ) )
!= ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ A ) ) ) ),
inference(simp,[status(thm)],[9009]) ).
thf(9603,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ A )
!= ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ B ) ) ) )
| ( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A ) )
!= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ B @ ( 'const/realax/real_neg' @ ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[826,9061]) ).
thf(9604,plain,
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) )
!= ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[9603:[bind(A,$thf( 'const/realax/real_neg' @ ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )),bind(B,$thf( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ))]]) ).
thf(9683,plain,
( ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
!= ( sk1 @ ( sk4 @ ( 'const/realax/real_neg' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[9604,21]) ).
thf(9684,plain,
$false,
inference(simp,[status(thm)],[9683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA126^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n003.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
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:46:43 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.98 % [INFO] Parsing done (199ms).
% 1.21/1.00 % [INFO] Running in sequential loop mode.
% 1.83/1.39 % [INFO] eprover registered as external prover.
% 1.99/1.40 % [INFO] Scanning for conjecture ...
% 1.99/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.16/1.53 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.16/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.54 % [INFO] Type checking passed.
% 2.16/1.55 % [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 ...
% 45.81/11.86 % [INFO] Killing All external provers ...
% 45.81/11.87 % Time passed: 11524ms (effective reasoning time: 10857ms)
% 45.81/11.87 % 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)>
% 45.81/11.87 % Axioms used in derivation (4): thm/calc_int/REAL_NEG_NEG_, thm/calc_int/REAL_MUL_LNEG_, thm/realax/REAL_MUL_LID_, thm/iterate/POLYNOMIAL_FUNCTION_LMUL_
% 45.81/11.87 % No. of inferences in proof: 71
% 45.81/11.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11524 ms resp. 10857 ms w/o parsing
% 46.30/11.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 46.30/11.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------