%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM295+1 : TPTP v9.3.1. Released v3.1.0.
% 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 : n026.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 08:08:31 AM UTC 2026
% Result : Theorem 5.89s 7.56s
% Output : Refutation 6.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 46 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 146 ( 12 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 504 ( 8 ~; 3 |; 60 &; 396 @)
% ( 3 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 144 ( 0 ^; 138 !; 6 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_decl,type,
less: $i > $i > $o ).
thf(rdn_translate_decl,type,
rdn_translate: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(rdn_pos_decl,type,
rdn_pos: $i > $i ).
thf(rdnn_decl,type,
rdnn: $i > $i ).
thf(rdn_add_with_carry_decl,type,
rdn_add_with_carry: $i > $i > $i > $i > $o ).
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(rdn_positive_less_decl,type,
rdn_positive_less: $i > $i > $o ).
thf(n1_decl,type,
n1: $i ).
thf(rdn_neg_decl,type,
rdn_neg: $i > $i ).
thf(nn1_decl,type,
nn1: $i ).
thf(difference_decl,type,
difference: $i > $i > $i > $o ).
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less_or_equal ) )
<=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ less ) ) )
=> ( B @ ( A @ less_or_equal ) ) )
& ( ( B @ ( A @ less_or_equal ) )
=> ( ( A = B )
| ( B @ ( A @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,conjecture,
? [A: $i,B: $i] : ( B @ ( A @ less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',something_less_something) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] : ( B @ ( A @ less ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(24,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
n1 @ rdnn @ rdn_neg @ ( nn1 @ rdn_translate ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn1) ).
thf(53,plain,
n1 @ rdnn @ rdn_neg @ ( nn1 @ rdn_translate ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ sum ) ) )
<=> ( C @ ( B @ ( A @ difference ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus_entry_point) ).
thf(54,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ difference ) ) )
=> ( A @ ( C @ ( B @ sum ) ) ) )
& ( ( A @ ( C @ ( B @ sum ) ) )
=> ( C @ ( B @ ( A @ difference ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
n1 @ rdnn @ rdn_pos @ ( n1 @ rdn_translate ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn1) ).
thf(39,plain,
n1 @ rdnn @ rdn_pos @ ( n1 @ rdn_translate ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ less ) )
& ( B @ ( n1 @ ( A @ sum ) ) ) )
=> ( A @ ( C @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_successor) ).
thf(80,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ less ) )
& ( B @ ( n1 @ ( A @ sum ) ) ) )
=> ( A @ ( C @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ rdn_positive_less ) )
& ( D @ rdn_neg @ ( B @ rdn_translate ) )
& ( C @ rdn_neg @ ( A @ rdn_translate ) ) )
=> ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_entry_point_neg_neg) ).
thf(82,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ rdn_positive_less ) )
& ( D @ rdn_neg @ ( B @ rdn_translate ) )
& ( C @ rdn_neg @ ( A @ rdn_translate ) ) )
=> ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( B @ sum ) ) )
& ( E @ rdn_pos @ ( B @ rdn_translate ) )
& ( D @ rdn_neg @ ( A @ rdn_translate ) ) )
=> ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_neg_pos) ).
thf(47,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( B @ sum ) ) )
& ( E @ rdn_pos @ ( B @ rdn_translate ) )
& ( D @ rdn_neg @ ( A @ rdn_translate ) ) )
=> ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( A @ sum ) ) )
& ( D @ ( B @ ( A @ sum ) ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_RHS) ).
thf(60,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( A @ sum ) ) )
& ( D @ ( B @ ( A @ sum ) ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ rdn_positive_less ) )
& ( D @ rdn_pos @ ( B @ rdn_translate ) )
& ( C @ rdn_pos @ ( A @ rdn_translate ) ) )
=> ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_entry_point_pos_pos) ).
thf(85,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ rdn_positive_less ) )
& ( D @ rdn_pos @ ( B @ rdn_translate ) )
& ( C @ rdn_pos @ ( A @ rdn_translate ) ) )
=> ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
<=> ( ( B != A )
& ~ ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_property) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ~ ( A @ ( B @ less ) ) )
=> ( B @ ( A @ less ) ) )
& ( ( B @ ( A @ less ) )
=> ( ( B != A )
& ~ ( A @ ( B @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ rdn_neg @ ( C @ rdn_translate ) )
& ( F @ ( E @ ( D @ ( n0 @ rdnn @ rdn_add_with_carry ) ) ) )
& ( E @ rdn_neg @ ( B @ rdn_translate ) )
& ( D @ rdn_neg @ ( A @ rdn_translate ) ) )
=> ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_neg_neg) ).
thf(33,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ rdn_neg @ ( C @ rdn_translate ) )
& ( F @ ( E @ ( D @ ( n0 @ rdnn @ rdn_add_with_carry ) ) ) )
& ( E @ rdn_neg @ ( B @ rdn_translate ) )
& ( D @ rdn_neg @ ( A @ rdn_translate ) ) )
=> ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
n1 @ rdnn @ ( n0 @ rdnn @ rdn_positive_less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less01) ).
thf(32,plain,
n1 @ rdnn @ ( n0 @ rdnn @ rdn_positive_less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ rdn_neg @ ( B @ rdn_translate ) )
& ( C @ rdn_pos @ ( A @ rdn_translate ) ) )
=> ( n0 @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_posx_negx) ).
thf(64,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ rdn_neg @ ( B @ rdn_translate ) )
& ( C @ rdn_pos @ ( A @ rdn_translate ) ) )
=> ( n0 @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ rdn_pos @ ( C @ rdn_translate ) )
& ( D @ ( F @ ( E @ ( n0 @ rdnn @ rdn_add_with_carry ) ) ) )
& ( D @ ( E @ rdn_positive_less ) )
& ( E @ rdn_neg @ ( B @ rdn_translate ) )
& ( D @ rdn_pos @ ( A @ rdn_translate ) ) )
=> ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_neg_2) ).
thf(44,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ rdn_pos @ ( C @ rdn_translate ) )
& ( D @ ( F @ ( E @ ( n0 @ rdnn @ rdn_add_with_carry ) ) ) )
& ( D @ ( E @ rdn_positive_less ) )
& ( E @ rdn_neg @ ( B @ rdn_translate ) )
& ( D @ rdn_pos @ ( A @ rdn_translate ) ) )
=> ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ rdn_pos @ ( C @ rdn_translate ) )
& ( F @ ( E @ ( D @ ( n0 @ rdnn @ rdn_add_with_carry ) ) ) )
& ( E @ rdn_pos @ ( B @ rdn_translate ) )
& ( D @ rdn_pos @ ( A @ rdn_translate ) ) )
=> ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_pos) ).
thf(27,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ rdn_pos @ ( C @ rdn_translate ) )
& ( F @ ( E @ ( D @ ( n0 @ rdnn @ rdn_add_with_carry ) ) ) )
& ( E @ rdn_pos @ ( B @ rdn_translate ) )
& ( D @ rdn_pos @ ( A @ rdn_translate ) ) )
=> ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ rdn_neg @ ( C @ rdn_translate ) )
& ( E @ ( F @ ( D @ ( n0 @ rdnn @ rdn_add_with_carry ) ) ) )
& ( E @ ( D @ rdn_positive_less ) )
& ( E @ rdn_neg @ ( B @ rdn_translate ) )
& ( D @ rdn_pos @ ( A @ rdn_translate ) ) )
=> ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_neg_1) ).
thf(50,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ rdn_neg @ ( C @ rdn_translate ) )
& ( E @ ( F @ ( D @ ( n0 @ rdnn @ rdn_add_with_carry ) ) ) )
& ( E @ ( D @ rdn_positive_less ) )
& ( E @ rdn_neg @ ( B @ rdn_translate ) )
& ( D @ rdn_pos @ ( A @ rdn_translate ) ) )
=> ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ rdn_pos @ ( B @ rdn_translate ) )
& ( C @ rdn_neg @ ( A @ rdn_translate ) ) )
=> ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_entry_point_neg_pos) ).
thf(67,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ rdn_pos @ ( B @ rdn_translate ) )
& ( C @ rdn_neg @ ( A @ rdn_translate ) ) )
=> ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( B @ sum ) ) )
& ( D @ ( C @ ( A @ sum ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_LHS) ).
thf(40,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( B @ sum ) ) )
& ( D @ ( C @ ( A @ sum ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
n0 @ rdnn @ rdn_pos @ ( n0 @ rdn_translate ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn0) ).
thf(26,plain,
n0 @ rdnn @ rdn_pos @ ( n0 @ rdn_translate ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ sum ) ) )
& ( C @ ( B @ ( A @ sum ) ) ) )
=> ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_sum) ).
thf(36,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ sum ) ) )
& ( C @ ( B @ ( A @ sum ) ) ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ rdnn @ ( B @ rdnn @ rdn_positive_less ) )
& ( B @ rdnn @ ( A @ rdnn @ rdn_positive_less ) ) )
=> ( C @ rdnn @ ( A @ rdnn @ rdn_positive_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less_transitivity) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ rdnn @ ( B @ rdnn @ rdn_positive_less ) )
& ( B @ rdnn @ ( A @ rdnn @ rdn_positive_less ) ) )
=> ( C @ rdnn @ ( A @ rdnn @ rdn_positive_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(99,plain,
$false,
inference(e,[status(thm)],[88,24,53,54,39,80,82,47,60,85,70,33,32,64,44,27,50,67,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM295+1 : TPTP v9.3.1. Released v3.1.0.
% 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
% 0.14/5.41 % Computer : n026.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Sat Sep 26 02:27:30 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 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
% 0.18/5.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/6.29 % [INFO] Parsing done (299ms).
% 1.78/6.31 % [INFO] Running in sequential loop mode.
% 2.64/6.69 % [INFO] eprover registered as external prover.
% 2.64/6.69 % [INFO] Scanning for conjecture ...
% 3.15/6.86 % [INFO] Found a conjecture (or negated_conjecture) and 401 axioms. Running axiom selection ...
% 3.48/7.00 % [INFO] Axiom selection finished. Selected 21 axioms (removed 380 axioms).
% 4.03/7.06 % [INFO] Problem is first-order (TPTP FOF).
% 4.03/7.06 % [INFO] Type checking passed.
% 4.03/7.07 % [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 ...
% 5.89/7.55 % External prover 'e' found a proof!
% 5.89/7.55 % [INFO] Killing All external provers ...
% 5.89/7.56 % Time passed: 2004ms (effective reasoning time: 1243ms)
% 5.89/7.56 % 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)>
% 5.89/7.56 % Axioms used in derivation (21): rdn1, unique_sum, sum_entry_point_pos_neg_1, unique_RHS, sum_entry_point_neg_neg, rdn_positive_less01, less_entry_point_neg_pos, sum_entry_point_pos_pos, rdnn1, less_entry_point_neg_neg, rdn_positive_less_transitivity, less_entry_point_pos_pos, rdn0, less_successor, less_or_equal, less_property, unique_LHS, sum_entry_point_neg_pos, sum_entry_point_posx_negx, sum_entry_point_pos_neg_2, minus_entry_point
% 5.89/7.56 % No. of inferences in proof: 46
% 5.89/7.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2004 ms resp. 1243 ms w/o parsing
% 6.36/7.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.36/7.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------