%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA127^1 : 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 : 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 07:45:49 AM UTC 2026
% Result : Theorem 35.95s 9.48s
% Output : Refutation 36.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 79 ( 13 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 228 ( 28 ~; 18 |; 9 &; 166 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 23 ^; 38 !; 0 ?; 63 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('const/realax/real_sub_decl',type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/realax/real_neg_decl',type,
'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
thf('const/realax/real_add_decl',type,
'const/realax/real_add': 'type/realax/real' > '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(sk1_decl,type,
sk1: 'type/realax/real' > 'type/realax/real' ).
thf(sk2_decl,type,
sk2: 'type/realax/real' > 'type/realax/real' ).
thf(sk1_def,definition,
( sk1
= ( @+[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_sub' @ ( A @ C ) @ ( B @ C ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/realax/real' > 'type/realax/real'] :
~ ( ( ( 'const/iterate/polynomial_function' @ sk1 )
& ( 'const/iterate/polynomial_function' @ A ) )
=> ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( A @ B ) ) ) ) ) ) ).
thf(4,axiom,
! [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(13,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)],[4]) ).
thf(14,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(cnf,[status(esa)],[13]) ).
thf(15,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(lifteq,[status(thm)],[14]) ).
thf(3,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_add' @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_ADD_') ).
thf(11,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_add' @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,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_add' @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(78,plain,
! [C: 'type/realax/real' > 'type/realax/real',B: 'type/realax/real' > 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ B )
| ~ ( 'const/iterate/polynomial_function' @ A )
| ( 'const/iterate/polynomial_function'
@ ^ [D: 'type/realax/real'] : ( 'const/realax/real_add' @ ( B @ D ) @ ( C @ D ) ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [D: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( A @ D ) ) )
!= ( 'const/iterate/polynomial_function' @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,12]) ).
thf(79,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_add' @ ( A @ C ) @ ( 'const/realax/real_neg' @ ( B @ C ) ) ) ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( ^ [E: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( D @ E ) ) ))]]) ).
thf(87,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_add' @ ( A @ C ) @ ( 'const/realax/real_neg' @ ( B @ C ) ) ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(5,axiom,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ A @ B )
= ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/real_sub_') ).
thf(16,plain,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ A @ B )
= ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ A @ B )
= ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ B ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ B ) )
= ( 'const/realax/real_sub' @ A @ B ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(3439,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_sub' @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(rewrite,[status(thm)],[87,18]) ).
thf(1,conjecture,
! [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_sub' @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_SUB_') ).
thf(2,negated_conjecture,
~ ! [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_sub' @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,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_sub' @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ( 'const/iterate/polynomial_function' @ sk1 )
& ( 'const/iterate/polynomial_function' @ sk2 )
& ~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(10,plain,
~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(3467,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 )
| ~ $true
| ( ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( A @ C ) @ ( B @ C ) ) )
!= ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3439,10]) ).
thf(3468,plain,
! [B: 'type/realax/real' > 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ A )
| ~ ( 'const/iterate/polynomial_function' @ B )
| ( ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( A @ C ) @ ( B @ C ) ) )
!= ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(simp,[status(thm)],[3467]) ).
thf(3469,plain,
( ~ ( 'const/iterate/polynomial_function' @ sk1 )
| ~ ( 'const/iterate/polynomial_function' @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3468:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(8,plain,
'const/iterate/polynomial_function' @ sk1,
inference(cnfConj,[status(thm)],[7]) ).
thf(9,plain,
'const/iterate/polynomial_function' @ sk2,
inference(cnfConj,[status(thm)],[7]) ).
thf(4100,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[3469,8,9]) ).
thf(4101,plain,
$false,
inference(simp,[status(thm)],[4100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA127^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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
% 0.12/0.23 % Computer : n007.cluster.edu
% 0.12/0.23 % Model : x86_64 x86_64
% 0.12/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.23 % Memory : 8046.5625MB
% 0.12/0.23 % OS : Linux 6.8.0-71-generic
% 0.12/0.23 % CPULimit : 300
% 0.12/0.23 % WCLimit : 300
% 0.12/0.23 % DateTime : Tue Sep 29 17:42:56 UTC 2026
% 0.12/0.24 % CPUTime :
% 0.12/0.24 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
% 1.04/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.48/1.03 % [INFO] Parsing done (194ms).
% 1.48/1.04 % [INFO] Running in sequential loop mode.
% 2.05/1.45 % [INFO] eprover registered as external prover.
% 2.05/1.45 % [INFO] Scanning for conjecture ...
% 2.25/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.25/1.58 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.25/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.43/1.60 % [INFO] Type checking passed.
% 2.43/1.60 % [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 ...
% 35.95/9.47 % [INFO] Killing All external provers ...
% 35.95/9.47 % Time passed: 9083ms (effective reasoning time: 8419ms)
% 35.95/9.47 % 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)>
% 35.95/9.48 % Axioms used in derivation (3): thm/iterate/POLYNOMIAL_FUNCTION_NEG_, thm/iterate/POLYNOMIAL_FUNCTION_ADD_, thm/realax/real_sub_
% 35.95/9.48 % No. of inferences in proof: 27
% 35.95/9.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9083 ms resp. 8419 ms w/o parsing
% 36.19/9.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 36.19/9.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------