%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP166^1 : 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 : n013.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 08:07:01 AM UTC 2026
% Result : Theorem 36.23s 12.85s
% Output : Refutation 36.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 290 ( 32 ~; 20 |; 9 &; 229 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 28 ( 27 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-6 aty)
% Number of variables : 18 ( 0 ^; 12 !; 6 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1333062727ar_int_type,type,
set_Pr1333062727ar_int: $tType ).
thf(produc1346207591ar_int_type,type,
produc1346207591ar_int: $tType ).
thf(set_li1762364675ar_int_type,type,
set_li1762364675ar_int: $tType ).
thf(set_Pr446800905yperep_type,type,
set_Pr446800905yperep: $tType ).
thf(list_P1741976099ar_int_type,type,
list_P1741976099ar_int: $tType ).
thf(set_Pr1148378109ar_int_type,type,
set_Pr1148378109ar_int: $tType ).
thf(set_Pr1560408065st_nat_type,type,
set_Pr1560408065st_nat: $tType ).
thf(produc490010537yperep_type,type,
produc490010537yperep: $tType ).
thf(produc1260470173ar_int_type,type,
produc1260470173ar_int: $tType ).
thf(produc1699244961st_nat_type,type,
produc1699244961st_nat: $tType ).
thf(set_Pr1097818217yperep_type,type,
set_Pr1097818217yperep: $tType ).
thf(set_Pr1986765409at_nat_type,type,
set_Pr1986765409at_nat: $tType ).
thf(produc1788831497yperep_type,type,
produc1788831497yperep: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(set_list_typerep_type,type,
set_list_typerep: $tType ).
thf(list_typerep_type,type,
list_typerep: $tType ).
thf(set_typerep_type,type,
set_typerep: $tType ).
thf(list_char_type,type,
list_char: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(typerep_type,type,
typerep: $tType ).
thf(literal_type,type,
literal: $tType ).
thf(bexp_type,type,
bexp: $tType ).
thf(aexp_type,type,
aexp: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(com_type,type,
com: $tType ).
thf(bval_decl,type,
bval: bexp > ( list_char > int ) > $o ).
thf(big_big_step_decl,type,
big_big_step: produc1260470173ar_int > ( list_char > int ) > $o ).
thf(suc_decl,type,
suc: nat > nat ).
thf(produc1193801173ar_int_decl,type,
produc1193801173ar_int: com > ( list_char > int ) > produc1260470173ar_int ).
thf(relati23543761ar_int_decl,type,
relati23543761ar_int: ( ( list_char > int ) > ( list_char > int ) > $o ) > bexp > com > nat > ( list_char > int ) > ( list_char > int ) > $o ).
thf(p_decl,type,
p: ( list_char > int ) > ( list_char > int ) > $o ).
thf(b_decl,type,
b: bexp ).
thf(c_decl,type,
c: com ).
thf(c2_decl,type,
c2: com ).
thf(ka_decl,type,
ka: nat ).
thf(s_a_decl,type,
s_a: list_char > int ).
thf(sa_decl,type,
sa: list_char > int ).
thf(t_a_decl,type,
t_a: list_char > int ).
thf(ta_decl,type,
ta: list_char > int ).
thf(95,axiom,
relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ s_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Suc_Oprems_I7_J) ).
thf(551,plain,
relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ s_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(181,axiom,
big_big_step @ ( produc1193801173ar_int @ c2 @ s_a ) @ t_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Suc_Oprems_I4_J) ).
thf(839,plain,
big_big_step @ ( produc1193801173ar_int @ c2 @ s_a ) @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(134,axiom,
big_big_step @ ( produc1193801173ar_int @ c @ sa ) @ ta,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Suc_Oprems_I3_J) ).
thf(669,plain,
big_big_step @ ( produc1193801173ar_int @ c @ sa ) @ ta,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1,conjecture,
? [A: list_char > int,B: list_char > int] :
( ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ A @ B )
& ( bval @ b @ A )
& ( big_big_step @ ( produc1193801173ar_int @ c @ A ) @ ta )
& ( big_big_step @ ( produc1193801173ar_int @ c2 @ B ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: list_char > int,B: list_char > int] :
( ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ A @ B )
& ( bval @ b @ A )
& ( big_big_step @ ( produc1193801173ar_int @ c @ A ) @ ta )
& ( big_big_step @ ( produc1193801173ar_int @ c2 @ B ) @ t_a ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(188,plain,
~ ? [A: list_char > int,B: list_char > int] :
( ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ A @ B )
& ( bval @ b @ A )
& ( big_big_step @ ( produc1193801173ar_int @ c @ A ) @ ta )
& ( big_big_step @ ( produc1193801173ar_int @ c2 @ B ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(189,plain,
! [B: list_char > int,A: list_char > int] :
( ~ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ A @ B )
| ~ ( bval @ b @ A )
| ~ ( big_big_step @ ( produc1193801173ar_int @ c @ A ) @ ta )
| ~ ( big_big_step @ ( produc1193801173ar_int @ c2 @ B ) @ t_a ) ),
inference(cnf,[status(esa)],[188]) ).
thf(878,plain,
! [B: list_char > int,A: list_char > int] :
( ~ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ A @ B )
| ~ ( bval @ b @ A )
| ~ $true
| ~ ( big_big_step @ ( produc1193801173ar_int @ c2 @ B ) @ t_a )
| ( ( big_big_step @ ( produc1193801173ar_int @ c @ sa ) @ ta )
!= ( big_big_step @ ( produc1193801173ar_int @ c @ A ) @ ta ) ) ),
inference(paramod_ordered,[status(thm)],[669,189]) ).
thf(879,plain,
! [B: list_char > int,A: list_char > int] :
( ~ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ A @ B )
| ~ ( bval @ b @ A )
| ~ ( big_big_step @ ( produc1193801173ar_int @ c2 @ B ) @ t_a )
| ( ( big_big_step @ ( produc1193801173ar_int @ c @ sa ) @ ta )
!= ( big_big_step @ ( produc1193801173ar_int @ c @ A ) @ ta ) ) ),
inference(simp,[status(thm)],[878]) ).
thf(880,plain,
! [A: list_char > int] :
( ~ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ A )
| ~ ( bval @ b @ sa )
| ~ ( big_big_step @ ( produc1193801173ar_int @ c2 @ A ) @ t_a ) ),
inference(pattern_uni,[status(thm)],[879:[bind(A,$thf( sa )),bind(B,$thf( B ))]]) ).
thf(884,plain,
! [A: list_char > int] :
( ~ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ A )
| ~ ( bval @ b @ sa )
| ~ ( big_big_step @ ( produc1193801173ar_int @ c2 @ A ) @ t_a ) ),
inference(simp,[status(thm)],[880]) ).
thf(144,axiom,
bval @ b @ sa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Suc_Oprems_I6_J) ).
thf(699,plain,
bval @ b @ sa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(891,plain,
! [A: list_char > int] :
( ~ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ A )
| ~ $true
| ~ ( big_big_step @ ( produc1193801173ar_int @ c2 @ A ) @ t_a ) ),
inference(rewrite,[status(thm)],[884,699]) ).
thf(892,plain,
! [A: list_char > int] :
( ~ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ A )
| ~ ( big_big_step @ ( produc1193801173ar_int @ c2 @ A ) @ t_a ) ),
inference(simp,[status(thm)],[891]) ).
thf(895,plain,
! [A: list_char > int] :
( ~ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ A )
| ~ $true
| ( ( big_big_step @ ( produc1193801173ar_int @ c2 @ s_a ) @ t_a )
!= ( big_big_step @ ( produc1193801173ar_int @ c2 @ A ) @ t_a ) ) ),
inference(paramod_ordered,[status(thm)],[839,892]) ).
thf(896,plain,
! [A: list_char > int] :
( ~ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ A )
| ( ( big_big_step @ ( produc1193801173ar_int @ c2 @ s_a ) @ t_a )
!= ( big_big_step @ ( produc1193801173ar_int @ c2 @ A ) @ t_a ) ) ),
inference(simp,[status(thm)],[895]) ).
thf(897,plain,
~ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ s_a ),
inference(pattern_uni,[status(thm)],[896:[bind(A,$thf( s_a ))]]) ).
thf(972,plain,
$false,
inference(rewrite,[status(thm)],[551,897]) ).
thf(973,plain,
$false,
inference(simp,[status(thm)],[972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP166^1 : 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
% 0.11/0.22 % Computer : n013.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 20:04:06 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.03/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.35/1.22 % [INFO] Parsing done (413ms).
% 2.35/1.24 % [INFO] Running in sequential loop mode.
% 3.19/1.62 % [INFO] eprover registered as external prover.
% 3.19/1.63 % [INFO] Scanning for conjecture ...
% 3.39/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 221 axioms. Running axiom selection ...
% 3.80/1.94 % [INFO] Axiom selection finished. Selected 185 axioms (removed 36 axioms).
% 4.69/2.20 % [INFO] Problem is higher-order (TPTP THF).
% 4.69/2.23 % [INFO] Type checking passed.
% 4.69/2.23 % [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 ...
% 36.23/12.84 % [INFO] Killing All external provers ...
% 36.23/12.85 % Time passed: 12483ms (effective reasoning time: 11600ms)
% 36.23/12.85 % 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)>
% 36.23/12.85 % Axioms used in derivation (4): fact_4_Suc_Oprems_I7_J, fact_3_Suc_Oprems_I4_J, fact_2_Suc_Oprems_I3_J, fact_0_Suc_Oprems_I6_J
% 36.23/12.85 % No. of inferences in proof: 23
% 36.23/12.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12483 ms resp. 11600 ms w/o parsing
% 36.23/12.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 36.23/12.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------