%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV678+1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n015.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 : Sun Sep 27 08:48:20 AM UTC 2026
% Result : Theorem 26.83s 8.15s
% Output : Refutation 26.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 61 ( 3 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 130 ( 16 ~; 15 |; 5 &; 77 @)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 11 !; 0 ?; 12 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cCoq_2eInit_2eDatatypes_2enat___24t_decl,type,
cCoq_2eInit_2eDatatypes_2enat___24t: $i > $o ).
thf(cUseAuto_2eP___24a1_decl,type,
cUseAuto_2eP___24a1: $i > $o ).
thf(p_decl,type,
p: $i > $o ).
thf(cUseAuto_2emyFact_decl,type,
cUseAuto_2emyFact: $i ).
thf(cCoq_2eInit_2eDatatypes_2eO_decl,type,
cCoq_2eInit_2eDatatypes_2eO: $i ).
thf(cCoq_2eInit_2eDatatypes_2eS___24a1_decl,type,
cCoq_2eInit_2eDatatypes_2eS___24a1: $i > $i ).
thf(cCoq_2eInit_2ePeano_2ele___24a2_decl,type,
cCoq_2eInit_2ePeano_2ele___24a2: $i > $i > $o ).
thf(sk110_decl,type,
sk110: $i ).
thf(sk110_def,definition,
( sk110
= ( @+[A: $i] :
~ ( ( A @ cCoq_2eInit_2eDatatypes_2enat___24t )
=> ( ( cCoq_2eInit_2eDatatypes_2eO @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ ( A @ cCoq_2eInit_2ePeano_2ele___24a2 ) )
=> ( A @ cUseAuto_2eP___24a1 ) ) ) ) ) ).
thf(212,axiom,
( ( cUseAuto_2emyFact @ p )
<=> ! [A: $i] :
( ( A @ cCoq_2eInit_2eDatatypes_2enat___24t )
=> ( ( cCoq_2eInit_2eDatatypes_2eO @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ ( A @ cCoq_2eInit_2ePeano_2ele___24a2 ) )
=> ( A @ cUseAuto_2eP___24a1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_UseAuto.myFact') ).
thf(1313,plain,
( ( ! [A: $i] :
( ( A @ cCoq_2eInit_2eDatatypes_2enat___24t )
=> ( ( cCoq_2eInit_2eDatatypes_2eO @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ ( A @ cCoq_2eInit_2ePeano_2ele___24a2 ) )
=> ( A @ cUseAuto_2eP___24a1 ) ) )
=> ( cUseAuto_2emyFact @ p ) )
& ( ( cUseAuto_2emyFact @ p )
=> ! [A: $i] :
( ( A @ cCoq_2eInit_2eDatatypes_2enat___24t )
=> ( ( cCoq_2eInit_2eDatatypes_2eO @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ ( A @ cCoq_2eInit_2ePeano_2ele___24a2 ) )
=> ( A @ cUseAuto_2eP___24a1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1314,plain,
! [A: $i] :
( ( ( cUseAuto_2emyFact @ p )
| ~ ( sk110 @ cUseAuto_2eP___24a1 ) )
& ( ( cUseAuto_2emyFact @ p )
| ( cCoq_2eInit_2eDatatypes_2eO @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ ( sk110 @ cCoq_2eInit_2ePeano_2ele___24a2 ) ) )
& ( ( cUseAuto_2emyFact @ p )
| ( sk110 @ cCoq_2eInit_2eDatatypes_2enat___24t ) )
& ( ( A @ cUseAuto_2eP___24a1 )
| ~ ( cCoq_2eInit_2eDatatypes_2eO @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ cCoq_2eInit_2eDatatypes_2eS___24a1 @ ( A @ cCoq_2eInit_2ePeano_2ele___24a2 ) )
| ~ ( A @ cCoq_2eInit_2eDatatypes_2enat___24t )
| ~ ( cUseAuto_2emyFact @ p ) ) ),
inference(cnf,[status(esa)],[1313]) ).
thf(1318,plain,
( ( cUseAuto_2emyFact @ p )
| ~ ( sk110 @ cUseAuto_2eP___24a1 ) ),
inference(cnfConj,[status(thm)],[1314]) ).
thf(1,conjecture,
( ! [A: $i] :
( ( A @ cCoq_2eInit_2eDatatypes_2enat___24t )
=> ( A @ cUseAuto_2eP___24a1 ) )
=> ( cUseAuto_2emyFact @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( A @ cCoq_2eInit_2eDatatypes_2enat___24t )
=> ( A @ cUseAuto_2eP___24a1 ) )
=> ( cUseAuto_2emyFact @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(294,plain,
~ ( ! [A: $i] :
( ( A @ cCoq_2eInit_2eDatatypes_2enat___24t )
=> ( A @ cUseAuto_2eP___24a1 ) )
=> ( cUseAuto_2emyFact @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(295,plain,
! [A: $i] :
( ~ ( cUseAuto_2emyFact @ p )
& ( ( A @ cUseAuto_2eP___24a1 )
| ~ ( A @ cCoq_2eInit_2eDatatypes_2enat___24t ) ) ),
inference(cnf,[status(esa)],[294]) ).
thf(297,plain,
~ ( cUseAuto_2emyFact @ p ),
inference(cnfConj,[status(thm)],[295]) ).
thf(1316,plain,
( ( cUseAuto_2emyFact @ p )
| ( sk110 @ cCoq_2eInit_2eDatatypes_2enat___24t ) ),
inference(cnfConj,[status(thm)],[1314]) ).
thf(1861,plain,
( $false
| ( sk110 @ cCoq_2eInit_2eDatatypes_2enat___24t ) ),
inference(rewrite,[status(thm)],[1316,297]) ).
thf(1862,plain,
sk110 @ cCoq_2eInit_2eDatatypes_2enat___24t,
inference(simp,[status(thm)],[1861]) ).
thf(296,plain,
! [A: $i] :
( ( A @ cUseAuto_2eP___24a1 )
| ~ ( A @ cCoq_2eInit_2eDatatypes_2enat___24t ) ),
inference(cnfConj,[status(thm)],[295]) ).
thf(1881,plain,
! [A: $i] :
( ( ( sk110 @ cCoq_2eInit_2eDatatypes_2enat___24t )
!= ( A @ cCoq_2eInit_2eDatatypes_2enat___24t ) )
| ( A @ cUseAuto_2eP___24a1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1862,296]) ).
thf(1882,plain,
! [A: $i] :
( ( ( sk110 @ cCoq_2eInit_2eDatatypes_2enat___24t )
!= ( A @ cCoq_2eInit_2eDatatypes_2enat___24t ) )
| ( A @ cUseAuto_2eP___24a1 ) ),
inference(simp,[status(thm)],[1881]) ).
thf(1883,plain,
sk110 @ cUseAuto_2eP___24a1,
inference(pattern_uni,[status(thm)],[1882:[bind(A,$thf( sk110 ))]]) ).
thf(2180,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[1318,297,1883]) ).
thf(2181,plain,
$false,
inference(simp,[status(thm)],[2180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV678+1 : TPTP v9.3.1. Released v9.3.0.
% 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
% 0.12/0.59 % Computer : n015.cluster.edu
% 0.12/0.59 % Model : x86_64 x86_64
% 0.12/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.59 % Memory : 8046.5625MB
% 0.12/0.59 % OS : Linux 6.8.0-71-generic
% 0.12/0.59 % CPULimit : 300
% 0.12/0.59 % WCLimit : 300
% 0.12/0.59 % DateTime : Sat Sep 26 11:40:46 UTC 2026
% 0.12/0.60 % CPUTime :
% 0.12/0.60 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
% 0.89/1.17 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.66/2.09 % [INFO] Parsing done (914ms).
% 3.66/2.11 % [INFO] Running in sequential loop mode.
% 4.69/2.48 % [INFO] eprover registered as external prover.
% 4.69/2.49 % [INFO] Scanning for conjecture ...
% 6.06/2.82 % [INFO] Found a conjecture (or negated_conjecture) and 2924 axioms. Running axiom selection ...
% 7.52/3.18 % [INFO] Axiom selection finished. Selected 291 axioms (removed 2633 axioms).
% 8.30/3.43 % [INFO] Problem is first-order (TPTP FOF).
% 8.30/3.46 % [INFO] Type checking passed.
% 8.30/3.46 % [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 ...
% 26.83/8.14 % [INFO] Killing All external provers ...
% 26.83/8.15 % Time passed: 7401ms (effective reasoning time: 6028ms)
% 26.83/8.15 % 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)>
% 26.83/8.15 % Axioms used in derivation (1): $_def_UseAuto.myFact
% 26.83/8.15 % No. of inferences in proof: 18
% 26.83/8.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7401 ms resp. 6028 ms w/o parsing
% 26.83/8.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.83/8.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------