%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP105^1 : TPTP v9.3.1. Released v7.5.0.
% 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 : n004.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 08:06:47 AM UTC 2026
% Result : Theorem 128.45s 56.05s
% Output : Refutation 128.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 56 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 232 ( 53 ~; 29 |; 0 &; 144 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 0 ^; 43 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_l2071841302list_a_type,type,
list_l2071841302list_a: $tType ).
thf(option_list_list_a_type,type,
option_list_list_a: $tType ).
thf(list_list_list_a_type,type,
list_list_list_a: $tType ).
thf(option_list_a_type,type,
option_list_a: $tType ).
thf(list_list_a_type,type,
list_list_a: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(option_a_type,type,
option_a: $tType ).
thf(list_a_type,type,
list_a: $tType ).
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(a_type,type,
a: $tType ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(listSl97544552lice_a_decl,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(nil_list_a_decl,type,
nil_list_a: list_list_a ).
thf(nil_a_decl,type,
nil_a: list_a ).
thf(size_size_list_a_decl,type,
size_size_list_a: list_a > nat ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(k_decl,type,
k: nat ).
thf(65,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_zero__less__iff__neq__zero) ).
thf(358,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(359,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(cnf,[status(esa)],[358]) ).
thf(360,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(lifteq,[status(thm)],[359]) ).
thf(159,axiom,
! [A: list_a,B: nat] :
( ( ord_less_nat @ ( size_size_list_a @ A ) @ B )
=> ( ( listSl97544552lice_a @ A @ B )
= nil_list_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_list__slice__less) ).
thf(673,plain,
! [A: list_a,B: nat] :
( ( ord_less_nat @ ( size_size_list_a @ A ) @ B )
=> ( ( listSl97544552lice_a @ A @ B )
= nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(674,plain,
! [B: nat,A: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ A ) @ B )
| ( ( listSl97544552lice_a @ A @ B )
= nil_list_a ) ),
inference(cnf,[status(esa)],[673]) ).
thf(675,plain,
! [B: nat,A: list_a] :
( ( ( listSl97544552lice_a @ A @ B )
= nil_list_a )
| ~ ( ord_less_nat @ ( size_size_list_a @ A ) @ B ) ),
inference(lifteq,[status(thm)],[674]) ).
thf(1,conjecture,
( ( listSl97544552lice_a @ nil_a @ k )
= nil_list_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(172,plain,
( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(173,plain,
( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a ),
inference(lifteq,[status(thm)],[172]) ).
thf(81830,plain,
! [B: nat,A: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ A ) @ B )
| ( nil_list_a != nil_list_a )
| ( ( listSl97544552lice_a @ A @ B )
!= ( listSl97544552lice_a @ nil_a @ k ) ) ),
inference(paramod_ordered,[status(thm)],[675,173]) ).
thf(81831,plain,
! [B: nat,A: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ A ) @ B )
| ( ( listSl97544552lice_a @ A @ B )
!= ( listSl97544552lice_a @ nil_a @ k ) ) ),
inference(simp,[status(thm)],[81830]) ).
thf(81832,plain,
~ ( ord_less_nat @ ( size_size_list_a @ nil_a ) @ k ),
inference(pattern_uni,[status(thm)],[81831:[bind(A,$thf( nil_a )),bind(B,$thf( k ))]]) ).
thf(147,axiom,
( ( size_size_list_a @ nil_a )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_list_Osize_I3_J) ).
thf(639,plain,
( ( size_size_list_a @ nil_a )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(640,plain,
( ( size_size_list_a @ nil_a )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[639]) ).
thf(81994,plain,
~ ( ord_less_nat @ zero_zero_nat @ k ),
inference(rewrite,[status(thm)],[81832,640]) ).
thf(82073,plain,
! [A: nat] :
( ~ ( ( A != zero_zero_nat ) )
| ( ( ord_less_nat @ zero_zero_nat @ A )
!= ( ord_less_nat @ zero_zero_nat @ k ) ) ),
inference(paramod_ordered,[status(thm)],[360,81994]) ).
thf(82074,plain,
! [A: nat] :
( ( A = zero_zero_nat )
| ( ( ord_less_nat @ zero_zero_nat @ A )
!= ( ord_less_nat @ zero_zero_nat @ k ) ) ),
inference(simp,[status(thm)],[82073]) ).
thf(82075,plain,
k = zero_zero_nat,
inference(pattern_uni,[status(thm)],[82074:[bind(A,$thf( k ))]]) ).
thf(82135,plain,
k = zero_zero_nat,
inference(lifteq,[status(thm)],[82075]) ).
thf(15,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_le0) ).
thf(202,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(203,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(cnf,[status(esa)],[202]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_le__antisym) ).
thf(177,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(178,plain,
! [B: nat,A: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[177]) ).
thf(179,plain,
! [B: nat,A: nat] :
( ( A = B )
| ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A ) ),
inference(lifteq,[status(thm)],[178]) ).
thf(731,plain,
! [B: nat,A: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A )
| ( ( listSl97544552lice_a @ nil_a @ A )
!= nil_list_a )
| ( B != k ) ),
inference(paramod_ordered,[status(thm)],[179,173]) ).
thf(732,plain,
! [A: nat] :
( ~ ( ord_less_eq_nat @ A @ k )
| ~ ( ord_less_eq_nat @ k @ A )
| ( ( listSl97544552lice_a @ nil_a @ A )
!= nil_list_a ) ),
inference(pattern_uni,[status(thm)],[731:[bind(A,$thf( A )),bind(B,$thf( k ))]]) ).
thf(832,plain,
! [B: nat,A: nat] :
( ~ $true
| ~ ( ord_less_eq_nat @ k @ B )
| ( ( listSl97544552lice_a @ nil_a @ B )
!= nil_list_a )
| ( ( ord_less_eq_nat @ zero_zero_nat @ A )
!= ( ord_less_eq_nat @ B @ k ) ) ),
inference(paramod_ordered,[status(thm)],[203,732]) ).
thf(833,plain,
! [B: nat,A: nat] :
( ~ ( ord_less_eq_nat @ k @ B )
| ( ( listSl97544552lice_a @ nil_a @ B )
!= nil_list_a )
| ( ( ord_less_eq_nat @ zero_zero_nat @ A )
!= ( ord_less_eq_nat @ B @ k ) ) ),
inference(simp,[status(thm)],[832]) ).
thf(834,plain,
( ~ ( ord_less_eq_nat @ k @ zero_zero_nat )
| ( ( listSl97544552lice_a @ nil_a @ zero_zero_nat )
!= nil_list_a ) ),
inference(pattern_uni,[status(thm)],[833:[bind(A,$thf( k )),bind(B,$thf( zero_zero_nat ))]]) ).
thf(853,plain,
! [A: nat] :
( ~ $true
| ( ( listSl97544552lice_a @ nil_a @ zero_zero_nat )
!= nil_list_a )
| ( ( ord_less_eq_nat @ zero_zero_nat @ A )
!= ( ord_less_eq_nat @ k @ zero_zero_nat ) ) ),
inference(paramod_ordered,[status(thm)],[203,834]) ).
thf(854,plain,
! [A: nat] :
( ( ( listSl97544552lice_a @ nil_a @ zero_zero_nat )
!= nil_list_a )
| ( ( ord_less_eq_nat @ zero_zero_nat @ A )
!= ( ord_less_eq_nat @ k @ zero_zero_nat ) ) ),
inference(simp,[status(thm)],[853]) ).
thf(867,plain,
! [A: nat] :
( ( ( listSl97544552lice_a @ nil_a @ zero_zero_nat )
!= nil_list_a )
| ( k != zero_zero_nat )
| ( A != zero_zero_nat ) ),
inference(simp,[status(thm)],[854]) ).
thf(868,plain,
( ( ( listSl97544552lice_a @ nil_a @ zero_zero_nat )
!= nil_list_a )
| ( k != zero_zero_nat ) ),
inference(simp,[status(thm)],[867]) ).
thf(154,axiom,
! [A: list_a] :
( ( listSl97544552lice_a @ A @ zero_zero_nat )
= nil_list_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_list__slice__0) ).
thf(658,plain,
! [A: list_a] :
( ( listSl97544552lice_a @ A @ zero_zero_nat )
= nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(659,plain,
! [A: list_a] :
( ( listSl97544552lice_a @ A @ zero_zero_nat )
= nil_list_a ),
inference(cnf,[status(esa)],[658]) ).
thf(660,plain,
! [A: list_a] :
( ( listSl97544552lice_a @ A @ zero_zero_nat )
= nil_list_a ),
inference(lifteq,[status(thm)],[659]) ).
thf(1319,plain,
( ( nil_list_a != nil_list_a )
| ( k != zero_zero_nat ) ),
inference(rewrite,[status(thm)],[868,660]) ).
thf(1320,plain,
k != zero_zero_nat,
inference(simp,[status(thm)],[1319]) ).
thf(82227,plain,
$false,
inference(simplifyReflect,[status(thm)],[82135,1320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP105^1 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.09/0.22 % Computer : n004.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 19:54:07 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.23 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
% 1.03/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.29/1.24 % [INFO] Parsing done (417ms).
% 2.29/1.26 % [INFO] Running in sequential loop mode.
% 3.62/1.64 % [INFO] eprover registered as external prover.
% 3.62/1.65 % [INFO] Scanning for conjecture ...
% 4.06/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 349 axioms. Running axiom selection ...
% 4.29/1.94 % [INFO] Axiom selection finished. Selected 169 axioms (removed 180 axioms).
% 4.77/2.10 % [INFO] Problem is higher-order (TPTP THF).
% 4.77/2.12 % [INFO] Type checking passed.
% 5.03/2.13 % [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 ...
% 128.45/56.04 % [INFO] Killing All external provers ...
% 128.45/56.04 % Time passed: 55676ms (effective reasoning time: 54776ms)
% 128.45/56.04 % 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)>
% 128.45/56.05 % Axioms used in derivation (6): fact_1_list__slice__0, fact_57_list_Osize_I3_J, fact_282_le__antisym, fact_9_list__slice__less, fact_150_le0, fact_87_zero__less__iff__neq__zero
% 128.45/56.05 % No. of inferences in proof: 46
% 128.45/56.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 55676 ms resp. 54776 ms w/o parsing
% 128.45/56.08 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 128.45/56.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------