%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM179^1 : 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 : n016.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 07:46:19 AM UTC 2026
% Result : Theorem 269.34s 221.27s
% Output : Refutation 269.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 7 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 306 ( 17 ~; 8 |; 6 &; 275 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 15 ( 0 ^; 9 !; 6 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(node_type,type,
node: $tType ).
thf(finite_finite2_decl,type,
finite_finite2:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(koenig317145564le_via_decl,type,
koenig317145564le_via:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > TA > ( set @ TA ) ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(f_decl,type,
f: ( product_prod @ node @ ( set @ node ) ) > ( coinductive_llist @ node ) ).
thf(graph_decl,type,
graph: node > node > $o ).
thf(n_decl,type,
n: node ).
thf(219,axiom,
~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062infinite_A_Ireachable__via_Agraph_A_I_N_A_123n_125_J_An_J_092_060close_062) ).
thf(1003,plain,
~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1004,plain,
~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ) ),
inference(polarity_switch,[status(thm)],[1003]) ).
thf(93,axiom,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_finite_OemptyI) ).
thf(586,plain,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(587,plain,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[586]) ).
thf(1,conjecture,
? [A: node,B: set @ node] :
( ( ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ( bot_bot @ ( set @ node ) ) ) )
= ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) )
& ( finite_finite2 @ node @ B )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: node,B: set @ node] :
( ( ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ( bot_bot @ ( set @ node ) ) ) )
= ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) )
& ( finite_finite2 @ node @ B )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ B ) ) @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(293,plain,
~ ? [A: node,B: set @ node] :
( ( ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ( bot_bot @ ( set @ node ) ) ) )
= ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) )
& ( finite_finite2 @ node @ B )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(294,plain,
! [B: set @ node,A: node] :
( ( ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ( bot_bot @ ( set @ node ) ) ) )
!= ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) )
| ~ ( finite_finite2 @ node @ B )
| ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ B ) ) @ A ) ) ),
inference(cnf,[status(esa)],[293]) ).
thf(295,plain,
! [B: set @ node,A: node] :
( ( ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ( bot_bot @ ( set @ node ) ) ) )
!= ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) )
| ~ ( finite_finite2 @ node @ B )
| ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ B ) ) @ A ) ) ),
inference(lifteq,[status(thm)],[294]) ).
thf(1255,plain,
( ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ) )
| ~ ( finite_finite2 @ node @ ( bot_bot @ ( set @ node ) ) ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( n )),bind(B,$thf( bot_bot @ ( set @ node ) ))]]) ).
thf(1383,plain,
! [TA: $tType] :
( ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ) )
| ~ $true
| ( ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) )
!= ( finite_finite2 @ node @ ( bot_bot @ ( set @ node ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[587,1255]) ).
thf(1384,plain,
! [TA: $tType] :
( ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ) )
| ( ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) )
!= ( finite_finite2 @ node @ ( bot_bot @ ( set @ node ) ) ) ) ),
inference(simp,[status(thm)],[1383]) ).
thf(1385,plain,
finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ),
inference(pattern_uni,[status(thm)],[1384:[bind_type(TA,$thf( node ))]]) ).
thf(1496,plain,
~ $true,
inference(rewrite,[status(thm)],[1004,1385]) ).
thf(1497,plain,
$false,
inference(simp,[status(thm)],[1496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM179^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n016.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 17:54:19 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.13/1.19 % [INFO] Parsing done (398ms).
% 2.46/1.20 % [INFO] Running in sequential loop mode.
% 3.34/1.41 % [INFO] eprover registered as external prover.
% 3.34/1.41 % [INFO] Scanning for conjecture ...
% 3.76/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 291 axioms. Running axiom selection ...
% 4.16/1.60 % [INFO] Axiom selection finished. Selected 290 axioms (removed 1 axioms).
% 5.03/1.80 % [INFO] Problem is higher-order (TPTP THF).
% 5.03/1.82 % [INFO] Type checking passed.
% 5.03/1.83 % [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 ...
% 269.34/221.27 % [INFO] Killing All external provers ...
% 269.34/221.27 % Time passed: 220906ms (effective reasoning time: 220057ms)
% 269.34/221.27 % 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)>
% 269.34/221.27 % Axioms used in derivation (2): fact_2__092_060open_062infinite_A_Ireachable__via_Agraph_A_I_N_A_123n_125_J_An_J_092_060close_062, fact_103_finite_OemptyI
% 269.34/221.27 % No. of inferences in proof: 17
% 269.34/221.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 220906 ms resp. 220057 ms w/o parsing
% 269.50/221.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 269.50/221.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------