%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV289^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 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 : n017.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 08:37:07 AM UTC 2026
% Result : Theorem 6.72s 2.99s
% Output : Refutation 7.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 19 ( 7 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 63 ( 9 ~; 0 |; 11 &; 34 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 29 ( 13 ^; 9 !; 7 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(cNAT_decl,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(cSUCC_decl,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(cZERO_decl,type,
cZERO: ( $i > $o ) > $o ).
thf(cNAT_def,definition,
( cNAT
= ( ^ [A: ( $i > $o ) > $o] :
! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B @ cZERO )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B @ ( cSUCC @ C ) ) ) )
=> ( B @ A ) ) ) ) ).
thf(cSUCC_def,definition,
( cSUCC
= ( ^ [A: ( $i > $o ) > $o,B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ) ).
thf(cZERO_def,definition,
( cZERO
= ( ^ [A: $i > $o] :
~ ? [B: $i] : ( A @ B ) ) ) ).
thf(1,conjecture,
! [A: ( $i > $o ) > $o] :
( ( cNAT @ A )
=> ( cNAT @ ( cSUCC @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTTTP6101) ).
thf(2,negated_conjecture,
~ ! [A: ( $i > $o ) > $o] :
( ( cNAT @ A )
=> ( cNAT @ ( cSUCC @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( $i > $o ) > $o] :
( ! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B
@ ^ [C: $i > $o] :
~ ? [D: $i] : ( C @ D ) )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) ) ) )
=> ( B @ A ) )
=> ! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B
@ ^ [C: $i > $o] :
~ ? [D: $i] : ( C @ D ) )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) ) ) )
=> ( B
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( A
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV289^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.11 % 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
% 0.28/0.30 % Computer : n017.cluster.edu
% 0.28/0.30 % Model : x86_64 x86_64
% 0.28/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.28/0.30 % Memory : 8046.5625MB
% 0.28/0.30 % OS : Linux 6.8.0-71-generic
% 0.28/0.31 % CPULimit : 300
% 0.28/0.31 % WCLimit : 300
% 0.28/0.31 % DateTime : Tue Sep 29 15:26:52 UTC 2026
% 0.28/0.31 % CPUTime :
% 0.28/0.31 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
% 1.16/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/0.96 % [INFO] Parsing done (157ms).
% 1.41/0.97 % [INFO] Running in sequential loop mode.
% 2.36/1.43 % [INFO] eprover registered as external prover.
% 2.36/1.44 % [INFO] Scanning for conjecture ...
% 2.53/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.74/1.64 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.74/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.74/1.65 % [INFO] Type checking passed.
% 2.74/1.65 % [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 ...
% 6.72/2.98 % External prover 'e' found a proof!
% 6.72/2.98 % [INFO] Killing All external provers ...
% 6.72/2.98 % Time passed: 2526ms (effective reasoning time: 2009ms)
% 6.72/2.98 % 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)>
% 6.72/2.98 % Axioms used in derivation (0):
% 6.72/2.99 % No. of inferences in proof: 4
% 6.72/2.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2526 ms resp. 2009 ms w/o parsing
% 7.35/3.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.35/3.05 % [INFO] Killing All external provers ...
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