%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM926_1 : TPTP v9.3.1. Released v5.3.0.
% 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 : n002.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 08:10:26 AM UTC 2026
% Result : Theorem 217.94s 59.73s
% Output : Refutation 217.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 26 unt; 0 typ; 4 def)
% Number of atoms : 94 ( 54 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 573 ( 29 ~; 22 |; 9 &; 504 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 38 !; 16 ?; 58 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_one_int_decl,type,
one_one_int: int ).
thf(plus_plus_int_decl,type,
plus_plus_int: int > int > int ).
thf(times_times_int_decl,type,
times_times_int: int > int > int ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_int_decl,type,
number_number_of_int: int > int ).
thf(number_number_of_nat_decl,type,
number_number_of_nat: int > nat ).
thf(ord_less_int_decl,type,
ord_less_int: int > int > $o ).
thf(ord_less_eq_int_decl,type,
ord_less_eq_int: int > int > $o ).
thf(power_power_int_decl,type,
power_power_int: int > nat > int ).
thf(m_decl,type,
m: int ).
thf(t_decl,type,
t: int ).
thf(sk1_decl,type,
sk1: int ).
thf(sk2_decl,type,
sk2: int ).
thf(sk5_decl,type,
sk5: int ).
thf(sk6_decl,type,
sk6: int ).
thf(sk1_def,definition,
( sk1
= ( @+[A: int] :
? [B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( sk1 @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: int] :
? [B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( sk5 @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ) ) ).
thf(95,axiom,
t @ ( one_one_int @ ord_less_eq_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(481,plain,
t @ ( one_one_int @ ord_less_eq_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(6,axiom,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
<=> ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_zless__le) ).
thf(137,plain,
! [A: int,B: int] :
( ( ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) )
=> ( B @ ( A @ ord_less_int ) ) )
& ( ( B @ ( A @ ord_less_int ) )
=> ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(138,plain,
( ! [A: int,B: int] :
( ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) )
=> ( B @ ( A @ ord_less_int ) ) )
& ! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
=> ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) ) ) ),
inference(miniscope,[status(thm)],[137]) ).
thf(139,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( D @ ( C @ ord_less_int ) )
| ( C = D )
| ~ ( D @ ( C @ ord_less_eq_int ) ) )
& ( ( A != B )
| ~ ( B @ ( A @ ord_less_int ) ) )
& ( ( B @ ( A @ ord_less_eq_int ) )
| ~ ( B @ ( A @ ord_less_int ) ) ) ),
inference(cnf,[status(esa)],[138]) ).
thf(142,plain,
! [B: int,A: int] :
( ( B @ ( A @ ord_less_int ) )
| ( A = B )
| ~ ( B @ ( A @ ord_less_eq_int ) ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(145,plain,
! [B: int,A: int] :
( ( B @ ( A @ ord_less_int ) )
| ~ ( B @ ( A @ ord_less_eq_int ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(146,plain,
! [B: int,A: int] :
( ( B @ ( A @ ord_less_int ) )
| ~ ( B @ ( A @ ord_less_eq_int ) )
| ( A = B ) ),
inference(simp,[status(thm)],[145]) ).
thf(777,plain,
! [B: int,A: int] :
( ( ( t @ ( one_one_int @ ord_less_eq_int ) )
!= ( B @ ( A @ ord_less_eq_int ) ) )
| ( B @ ( A @ ord_less_int ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[481,146]) ).
thf(778,plain,
! [B: int,A: int] :
( ( ( t @ ( one_one_int @ ord_less_eq_int ) )
!= ( B @ ( A @ ord_less_eq_int ) ) )
| ( B @ ( A @ ord_less_int ) )
| ( A = B ) ),
inference(simp,[status(thm)],[777]) ).
thf(779,plain,
( ( t @ ( one_one_int @ ord_less_int ) )
| ( t = one_one_int ) ),
inference(pattern_uni,[status(thm)],[778:[bind(A,$thf( one_one_int )),bind(B,$thf( t ))]]) ).
thf(40,axiom,
( ( t = one_one_int )
=> ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(249,plain,
( ( t = one_one_int )
=> ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(250,plain,
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( sk2 @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( sk1 @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) )
| ( t != one_one_int ) ),
inference(cnf,[status(esa)],[249]) ).
thf(251,plain,
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( sk2 @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( sk1 @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) )
| ( t != one_one_int ) ),
inference(lifteq,[status(thm)],[250]) ).
thf(29,axiom,
! [A: int] :
( ( A @ ( A @ times_times_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(212,plain,
! [A: int] :
( ( A @ ( A @ times_times_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(213,plain,
! [A: int] :
( ( A @ ( A @ times_times_int ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) ) ),
inference(cnf,[status(esa)],[212]) ).
thf(214,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= ( A @ ( A @ times_times_int ) ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(43,axiom,
! [A: int] :
( ( A @ number_number_of_int )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_number__of__is__id) ).
thf(267,plain,
! [A: int] :
( ( A @ number_number_of_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(268,plain,
! [A: int] :
( ( A @ number_number_of_int )
= A ),
inference(cnf,[status(esa)],[267]) ).
thf(269,plain,
! [A: int] :
( ( A @ number_number_of_int )
= A ),
inference(lifteq,[status(thm)],[268]) ).
thf(21792,plain,
( ( ( sk2 @ ( sk2 @ times_times_int ) @ ( sk1 @ ( sk1 @ times_times_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ times_times_int ) @ plus_plus_int ) ) )
| ( t != one_one_int ) ),
inference(rewrite,[status(thm)],[251,214,269]) ).
thf(1,conjecture,
? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(126,plain,
~ ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(127,plain,
! [B: int,A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
!= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(cnf,[status(esa)],[126]) ).
thf(128,plain,
! [B: int,A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
!= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(lifteq,[status(thm)],[127]) ).
thf(682,plain,
! [B: int,A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
!= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ times_times_int ) @ plus_plus_int ) ) ),
inference(rewrite,[status(thm)],[128,269]) ).
thf(146367,plain,
! [B: int,A: int] :
( ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) )
!= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ times_times_int ) @ plus_plus_int ) ) ),
inference(rewrite,[status(thm)],[682,214]) ).
thf(146368,plain,
t != one_one_int,
inference(simplifyReflect,[status(thm)],[21792,146367]) ).
thf(146862,plain,
t @ ( one_one_int @ ord_less_int ),
inference(simplifyReflect,[status(thm)],[779,146368]) ).
thf(46,axiom,
( ( t @ ( one_one_int @ ord_less_int ) )
=> ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(275,plain,
( ( t @ ( one_one_int @ ord_less_int ) )
=> ? [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(276,plain,
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( sk6 @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( sk5 @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) )
| ~ ( t @ ( one_one_int @ ord_less_int ) ) ),
inference(cnf,[status(esa)],[275]) ).
thf(277,plain,
( ~ ( t @ ( one_one_int @ ord_less_int ) )
| ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( sk6 @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( sk5 @ power_power_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ) ),
inference(lifteq,[status(thm)],[276]) ).
thf(26754,plain,
( ~ ( t @ ( one_one_int @ ord_less_int ) )
| ( ( sk6 @ ( sk6 @ times_times_int ) @ ( sk5 @ ( sk5 @ times_times_int ) @ plus_plus_int ) )
= ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ times_times_int ) @ plus_plus_int ) ) ) ),
inference(rewrite,[status(thm)],[277,214,269]) ).
thf(146369,plain,
~ ( t @ ( one_one_int @ ord_less_int ) ),
inference(simplifyReflect,[status(thm)],[26754,146367]) ).
thf(147219,plain,
$false,
inference(rewrite,[status(thm)],[146862,146369]) ).
thf(147220,plain,
$false,
inference(simp,[status(thm)],[147219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM926_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % 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
% 0.11/0.52 % Computer : n002.cluster.edu
% 0.11/0.52 % Model : x86_64 x86_64
% 0.11/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.52 % Memory : 8046.5625MB
% 0.11/0.52 % OS : Linux 6.8.0-71-generic
% 0.11/0.52 % CPULimit : 300
% 0.11/0.52 % WCLimit : 300
% 0.11/0.52 % DateTime : Sat Sep 26 04:22:22 UTC 2026
% 0.11/0.52 % CPUTime :
% 0.11/0.53 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
% 0.64/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.88/0.99 % [INFO] Parsing done (157ms).
% 0.88/1.00 % [INFO] Running in sequential loop mode.
% 1.91/1.20 % [INFO] eprover registered as external prover.
% 1.91/1.21 % [INFO] Scanning for conjecture ...
% 1.91/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 123 axioms. Running axiom selection ...
% 2.21/1.35 % [INFO] Axiom selection finished. Selected 123 axioms (removed 0 axioms).
% 2.56/1.45 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.56/1.46 % [INFO] Type checking passed.
% 2.56/1.47 % [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 ...
% 217.94/59.72 % [INFO] Killing All external provers ...
% 217.94/59.73 % Time passed: 59096ms (effective reasoning time: 58718ms)
% 217.94/59.73 % 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)>
% 217.94/59.73 % Axioms used in derivation (6): fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06, fact_0_tpos, fact_28_zless__le, fact_111_number__of__is__id, fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06, fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J
% 217.94/59.73 % No. of inferences in proof: 42
% 217.94/59.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 59096 ms resp. 58718 ms w/o parsing
% 217.94/59.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 217.94/59.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------