%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA123^1 : 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 : n019.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 4.01s 2.44s
% Output : Refutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 5 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 6 ~; 1 |; 0 &; 16 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 8 ^; 4 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('const/trivia/I_decl',type,
'const/trivia/I':
!>[TA: $tType] : ( TA > TA ) ).
thf('const/iterate/polynomial_function_decl',type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(3,axiom,
! [TA: $tType] :
( ( 'const/trivia/I' @ TA )
= ( ^ [A: TA] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/trivia/I_DEF_') ).
thf(6,plain,
! [TA: $tType] :
( ( 'const/trivia/I' @ TA )
= ( ^ [A: TA] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,plain,
! [TA: $tType] :
( ( 'const/trivia/I' @ TA )
= ( ^ [A: TA] : A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
! [TA: $tType] :
( ( 'const/trivia/I' @ TA )
= ( ^ [A: TA] : A ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(1,conjecture,
'const/iterate/polynomial_function' @ ( 'const/trivia/I' @ 'type/realax/real' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_I_') ).
thf(2,negated_conjecture,
~ ( 'const/iterate/polynomial_function' @ ( 'const/trivia/I' @ 'type/realax/real' ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( 'const/iterate/polynomial_function' @ ( 'const/trivia/I' @ 'type/realax/real' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
( ~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : A )
| ( ( 'const/trivia/I' @ 'type/realax/real' )
!= ( 'const/trivia/I' @ 'type/realax/real' ) ) ),
inference(paramod_ordered,[status(thm)],[8,5]) ).
thf(12,plain,
~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : A ),
inference(pattern_uni,[status(thm)],[11:[]]) ).
thf(4,axiom,
( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_ID_') ).
thf(9,plain,
( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
~ $true,
inference(rewrite,[status(thm)],[12,9]) ).
thf(17,plain,
$false,
inference(simp,[status(thm)],[16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA123^1 : 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
% 0.08/0.21 % Computer : n019.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 17:45:02 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 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
% 0.85/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (189ms).
% 1.18/0.99 % [INFO] Running in sequential loop mode.
% 1.97/1.46 % [INFO] eprover registered as external prover.
% 1.97/1.47 % [INFO] Scanning for conjecture ...
% 2.19/1.55 % [INFO] No direction of definition thm/trivia/I_DEF_ detected. Treating as axiom ...
% 2.19/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.36/1.64 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.36/1.64 % [INFO] No direction of definition thm/trivia/I_DEF_ detected. Treating as axiom ...
% 2.36/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.36/1.65 % [INFO] Type checking passed.
% 2.36/1.66 % [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 ...
% 4.01/2.43 % [INFO] Killing All external provers ...
% 4.01/2.44 % Time passed: 2087ms (effective reasoning time: 1440ms)
% 4.01/2.44 % 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)>
% 4.01/2.44 % Axioms used in derivation (2): thm/trivia/I_DEF_, thm/iterate/POLYNOMIAL_FUNCTION_ID_
% 4.01/2.44 % No. of inferences in proof: 13
% 4.01/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2087 ms resp. 1440 ms w/o parsing
% 4.01/2.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.01/2.49 % [INFO] Killing All external provers ...
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