%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP119^1 : TPTP v9.3.1. Released v7.5.0.
% 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 : n009.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 08:06:50 AM UTC 2026
% Result : ContradictoryAxioms 77.43s 35.37s
% Output : Refutation 77.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 91 ( 13 ~; 4 |; 0 &; 72 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_list_list_a_type,type,
list_list_list_a: $tType ).
thf(list_list_a_type,type,
list_list_a: $tType ).
thf(list_a_type,type,
list_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(a2_decl,type,
a2: a ).
thf(b_decl,type,
b: a ).
thf(c_decl,type,
c: a ).
thf(inf_decl,type,
inf: a > a > a ).
thf(less_decl,type,
less: a > a > $o ).
thf(sup_decl,type,
sup: a > a > a ).
thf(357,axiom,
( a2
= ( sup @ b @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(1826,plain,
( a2
= ( sup @ b @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1827,plain,
( ( sup @ b @ c )
= a2 ),
inference(lifteq,[status(thm)],[1826]) ).
thf(356,axiom,
( ( inf @ c @ ( sup @ b @ c ) )
= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(1824,plain,
( ( inf @ c @ ( sup @ b @ c ) )
= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(1825,plain,
( ( inf @ c @ ( sup @ b @ c ) )
= b ),
inference(lifteq,[status(thm)],[1824]) ).
thf(1900,plain,
( ( inf @ c @ a2 )
= b ),
inference(rewrite,[status(thm)],[1825,1827]) ).
thf(359,axiom,
( ( inf @ c @ ( sup @ b @ c ) )
= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(1829,plain,
( ( inf @ c @ ( sup @ b @ c ) )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(1830,plain,
( ( inf @ c @ ( sup @ b @ c ) )
= c ),
inference(lifteq,[status(thm)],[1829]) ).
thf(1906,plain,
( ( inf @ c @ a2 )
= c ),
inference(rewrite,[status(thm)],[1830,1827]) ).
thf(1907,plain,
c = b,
inference(rewrite,[status(thm)],[1900,1906]) ).
thf(1914,plain,
( ( sup @ b @ b )
= a2 ),
inference(rewrite,[status(thm)],[1827,1907]) ).
thf(54,axiom,
! [A: a] :
( ( sup @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_local_Osup_Oidem) ).
thf(521,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(522,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(cnf,[status(esa)],[521]) ).
thf(523,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(lifteq,[status(thm)],[522]) ).
thf(2847,plain,
b = a2,
inference(rewrite,[status(thm)],[1914,523]) ).
thf(358,axiom,
less @ b @ ( sup @ b @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(1828,plain,
less @ b @ ( sup @ b @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(1873,plain,
less @ b @ a2,
inference(rewrite,[status(thm)],[1828,1827]) ).
thf(4,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_local_Odual__order_Ostrict__implies__not__eq) ).
thf(363,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(364,plain,
! [B: a,A: a] :
( ~ ( less @ A @ B )
| ( B != A ) ),
inference(cnf,[status(esa)],[363]) ).
thf(365,plain,
! [B: a,A: a] :
( ( B != A )
| ~ ( less @ A @ B ) ),
inference(lifteq,[status(thm)],[364]) ).
thf(366,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(simp,[status(thm)],[365]) ).
thf(1874,plain,
! [A: a] :
( ~ $true
| ( ( less @ b @ a2 )
!= ( less @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1873,366]) ).
thf(1875,plain,
! [A: a] :
( ( less @ b @ a2 )
!= ( less @ A @ A ) ),
inference(simp,[status(thm)],[1874]) ).
thf(1888,plain,
! [A: a] :
( ( b != A )
| ( a2 != A ) ),
inference(simp,[status(thm)],[1875]) ).
thf(1889,plain,
b != a2,
inference(simp,[status(thm)],[1888]) ).
thf(2857,plain,
$false,
inference(simplifyReflect,[status(thm)],[2847,1889]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP119^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % 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
% 0.08/0.20 % Computer : n009.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 19:56:30 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 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
% 0.93/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.56/1.21 % [INFO] Parsing done (437ms).
% 2.56/1.23 % [INFO] Running in sequential loop mode.
% 3.61/1.55 % [INFO] eprover registered as external prover.
% 3.61/1.55 % [INFO] Scanning for conjecture ...
% 3.92/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 357 axioms. Running axiom selection ...
% 3.92/1.68 % [INFO] Axiom selection finished. Selected 357 axioms (removed 0 axioms).
% 5.44/2.06 % [INFO] Problem is higher-order (TPTP THF).
% 5.44/2.11 % [INFO] Type checking passed.
% 5.44/2.12 % [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 ...
% 77.43/35.36 % [INFO] Killing All external provers ...
% 77.43/35.36 % Time passed: 35016ms (effective reasoning time: 34127ms)
% 77.43/35.37 % Axioms used in derivation (6): conj_3, fact_51_local_Osup_Oidem, conj_2, fact_1_local_Odual__order_Ostrict__implies__not__eq, conj_1, conj_4
% 77.43/35.37 % No. of inferences in proof: 31
% 77.43/35.37 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 35016 ms resp. 34127 ms w/o parsing
% 77.43/35.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.43/35.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------