%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM830^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 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 : n010.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 08:18:15 AM UTC 2026
% Result : Theorem 3.24s 2.12s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 28 ( 15 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 84 ( 2 ~; 0 |; 9 &; 70 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(n_type,type,
n: $tType ).
thf(c0_decl,type,
c0: n ).
thf(cS_decl,type,
cS: n > n ).
thf(c_plus_decl,type,
c_plus: n > n > n ).
thf(c_star_decl,type,
c_star: n > n > n ).
thf(cPA_1_decl,type,
cPA_1: $o ).
thf(cPA_2_decl,type,
cPA_2: $o ).
thf(cPA_3_decl,type,
cPA_3: $o ).
thf(cPA_4_decl,type,
cPA_4: $o ).
thf(cPA_1_def,definition,
( cPA_1
= ( ! [A: n] :
( ( c_plus @ A @ c0 )
= A ) ) ) ).
thf(cPA_2_def,definition,
( cPA_2
= ( ! [A: n,B: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) ) ) ) ).
thf(cPA_3_def,definition,
( cPA_3
= ( ! [A: n] :
( ( c_star @ A @ c0 )
= c0 ) ) ) ).
thf(cPA_4_def,definition,
( cPA_4
= ( ! [A: n,B: n] :
( ( c_star @ A @ ( cS @ B ) )
= ( c_plus @ ( c_star @ A @ B ) @ A ) ) ) ) ).
thf(1,conjecture,
( ( cPA_1
& cPA_2
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_THM1) ).
thf(2,negated_conjecture,
~ ( ( cPA_1
& cPA_2
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: n] :
( ( c_plus @ A @ c0 )
= A )
& ! [A: n,B: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) )
& ! [A: n] :
( ( c_star @ A @ c0 )
= c0 )
& ! [A: n,B: n] :
( ( c_star @ A @ ( cS @ B ) )
= ( c_plus @ ( c_star @ A @ B ) @ A ) ) )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM830^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.07 % 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
% 0.10/0.21 % Computer : n010.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:04:03 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (196ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 2.03/1.41 % [INFO] eprover registered as external prover.
% 2.03/1.42 % [INFO] Scanning for conjecture ...
% 2.22/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.57 % [INFO] Type checking passed.
% 2.22/1.57 % [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 ...
% 3.24/2.12 % External prover 'e' found a proof!
% 3.24/2.12 % [INFO] Killing All external provers ...
% 3.24/2.12 % Time passed: 1764ms (effective reasoning time: 1109ms)
% 3.24/2.12 % 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)>
% 3.24/2.12 % Axioms used in derivation (0):
% 3.24/2.12 % No. of inferences in proof: 4
% 3.24/2.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1764 ms resp. 1109 ms w/o parsing
% 3.50/2.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.50/2.16 % [INFO] Killing All external provers ...
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