%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO113^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:45:15 AM UTC 2026
% Result : Theorem 2.93s 1.32s
% Output : Refutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 3 equ; 0 cnn)
% Maximal formula atoms : 16 ( 14 avg)
% Number of connectives : 137 ( 2 ~; 3 |; 30 &; 87 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(cNUMBER_decl,type,
cNUMBER: $i > $o ).
thf(cODD_decl,type,
cODD: $i > $o ).
thf(cEVEN_decl,type,
cEVEN: $i > $o ).
thf(cS_decl,type,
cS: $i > $i ).
thf(c0_decl,type,
c0: $i ).
thf(1,conjecture,
( ( ( cEVEN @ c0 )
& ! [A: $i] :
( ( cEVEN @ A )
=> ( cEVEN @ ( cS @ ( cS @ A ) ) ) )
& ( cODD @ ( cS @ c0 ) )
& ! [A: $i] :
( ( cODD @ A )
=> ( cODD @ ( cS @ ( cS @ A ) ) ) )
& ( ( ( cNUMBER @ c0 )
& ( cNUMBER @ ( cS @ c0 ) )
& ! [A: $i] :
( ( ( cNUMBER @ A )
& ( cNUMBER @ ( cS @ A ) ) )
=> ( ( cNUMBER @ ( cS @ A ) )
& ( cNUMBER @ ( cS @ ( cS @ A ) ) ) ) ) )
=> ! [A: $i] :
( ( cNUMBER @ A )
& ( cNUMBER @ ( cS @ A ) ) ) )
& ! [A: $i] :
( ( cNUMBER @ A )
= ( ( cEVEN @ A )
| ( cODD @ A ) ) ) )
=> ! [A: $i] : ( cNUMBER @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM350) ).
thf(2,negated_conjecture,
~ ( ( ( cEVEN @ c0 )
& ! [A: $i] :
( ( cEVEN @ A )
=> ( cEVEN @ ( cS @ ( cS @ A ) ) ) )
& ( cODD @ ( cS @ c0 ) )
& ! [A: $i] :
( ( cODD @ A )
=> ( cODD @ ( cS @ ( cS @ A ) ) ) )
& ( ( ( cNUMBER @ c0 )
& ( cNUMBER @ ( cS @ c0 ) )
& ! [A: $i] :
( ( ( cNUMBER @ A )
& ( cNUMBER @ ( cS @ A ) ) )
=> ( ( cNUMBER @ ( cS @ A ) )
& ( cNUMBER @ ( cS @ ( cS @ A ) ) ) ) ) )
=> ! [A: $i] :
( ( cNUMBER @ A )
& ( cNUMBER @ ( cS @ A ) ) ) )
& ! [A: $i] :
( ( cNUMBER @ A )
= ( ( cEVEN @ A )
| ( cODD @ A ) ) ) )
=> ! [A: $i] : ( cNUMBER @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( cEVEN @ c0 )
& ! [A: $i] :
( ( cEVEN @ A )
=> ( cEVEN @ ( cS @ ( cS @ A ) ) ) )
& ( cODD @ ( cS @ c0 ) )
& ! [A: $i] :
( ( cODD @ A )
=> ( cODD @ ( cS @ ( cS @ A ) ) ) )
& ( ( ( cNUMBER @ c0 )
& ( cNUMBER @ ( cS @ c0 ) )
& ! [A: $i] :
( ( ( cNUMBER @ A )
& ( cNUMBER @ ( cS @ A ) ) )
=> ( ( cNUMBER @ ( cS @ A ) )
& ( cNUMBER @ ( cS @ ( cS @ A ) ) ) ) ) )
=> ! [A: $i] :
( ( cNUMBER @ A )
& ( cNUMBER @ ( cS @ A ) ) ) )
& ! [A: $i] :
( ( cNUMBER @ A )
= ( ( cEVEN @ A )
| ( cODD @ A ) ) ) )
=> ! [A: $i] : ( cNUMBER @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO113^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.12/0.20 % Computer : n007.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.21 % CPULimit : 300
% 0.12/0.21 % WCLimit : 300
% 0.12/0.21 % DateTime : Tue Sep 29 16:32:11 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 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
% 0.66/0.52 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.87/0.62 % [INFO] Parsing done (100ms).
% 1.04/0.63 % [INFO] Running in sequential loop mode.
% 1.33/0.83 % [INFO] eprover registered as external prover.
% 1.33/0.83 % [INFO] Scanning for conjecture ...
% 1.33/0.89 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.60/0.91 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.60/0.91 % [INFO] Problem is higher-order (TPTP THF).
% 1.60/0.91 % [INFO] Type checking passed.
% 1.60/0.91 % [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 ...
% 2.93/1.32 % External prover 'e' found a proof!
% 2.93/1.32 % [INFO] Killing All external provers ...
% 2.93/1.32 % Time passed: 1026ms (effective reasoning time: 687ms)
% 2.93/1.32 % 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)>
% 2.93/1.32 % Axioms used in derivation (0):
% 2.93/1.32 % No. of inferences in proof: 4
% 2.93/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1026 ms resp. 687 ms w/o parsing
% 2.93/1.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.93/1.36 % [INFO] Killing All external provers ...
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