%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV486+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n014.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 08:59:35 AM UTC 2026
% Result : Theorem 4.58s 2.64s
% Output : Refutation 4.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 13
% Syntax : Number of formulae : 28 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 25 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 269 ( 6 ~; 5 |; 32 &; 198 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 59 ( 0 ^; 56 !; 3 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(int_leq_decl,type,
int_leq: $i > $i > $o ).
thf(int_one_decl,type,
int_one: $i ).
thf(int_less_decl,type,
int_less: $i > $i > $o ).
thf(n_decl,type,
n: $i ).
thf(a_decl,type,
a: $i > $i > $i ).
thf(real_zero_decl,type,
real_zero: $i ).
thf(int_zero_decl,type,
int_zero: $i ).
thf(plus_decl,type,
plus: $i > $i > $i ).
thf(real_one_decl,type,
real_one: $i ).
thf(qr_decl,type,
qr: $i > $i > $i ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_total) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_commutative) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
<=> ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_inverse) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) )
=> ( B @ ( A @ int_less ) ) )
& ( ( B @ ( A @ int_less ) )
=> ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ! [C: $i] :
( ( ( B
= ( C @ ( A @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( D @ plus ) @ ( D @ a ) )
= real_zero ) ) )
& ! [C: $i] :
( ( ( A
= ( C @ ( B @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( B @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( D @ ( C @ ( D @ plus ) @ a ) )
= ( D @ ( C @ ( D @ plus ) @ qr ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qih) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ! [C: $i] :
( ( ( B
= ( C @ ( A @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( D @ plus ) @ ( D @ a ) )
= real_zero ) ) )
& ! [C: $i] :
( ( ( A
= ( C @ ( B @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( B @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( D @ ( C @ ( D @ plus ) @ a ) )
= ( D @ ( C @ ( D @ plus ) @ qr ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
int_one @ ( int_zero @ int_less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_zero_one) ).
thf(40,plain,
int_one @ ( int_zero @ int_less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
<=> ( A @ ( int_one @ int_leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_successor_of_zero) ).
thf(58,plain,
! [A: $i] :
( ( ( A @ ( int_one @ int_leq ) )
=> ( A @ ( int_zero @ int_less ) ) )
& ( ( A @ ( int_zero @ int_less ) )
=> ( A @ ( int_one @ int_leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).
thf(64,plain,
real_zero != real_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ int_less ) )
& ( B @ ( A @ int_less ) ) )
=> ( C @ ( A @ int_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_transitive) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ int_less ) )
& ( B @ ( A @ int_less ) ) )
=> ( C @ ( A @ int_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_irreflexive) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_leq ) )
<=> ( ( A = B )
| ( B @ ( A @ int_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ int_less ) ) )
=> ( B @ ( A @ int_leq ) ) )
& ( ( B @ ( A @ int_leq ) )
=> ( ( A = B )
| ( B @ ( A @ int_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
thf(44,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ int_leq ) )
& ( B @ ( A @ int_less ) ) )
=> ( D @ ( B @ plus ) @ ( C @ ( A @ plus ) @ int_leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_order1) ).
thf(47,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ int_leq ) )
& ( B @ ( A @ int_less ) ) )
=> ( D @ ( B @ plus ) @ ( C @ ( A @ plus ) @ int_leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lt) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(181,plain,
$false,
inference(e,[status(thm)],[38,41,49,67,40,58,64,32,34,22,44,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV486+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.13/0.40 % Computer : n014.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 13:57:46 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.18 % [INFO] Parsing done (199ms).
% 1.28/1.19 % [INFO] Running in sequential loop mode.
% 2.14/1.60 % [INFO] eprover registered as external prover.
% 2.14/1.61 % [INFO] Scanning for conjecture ...
% 2.31/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.31/1.75 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.31/1.78 % [INFO] Problem is first-order (TPTP FOF).
% 2.31/1.79 % [INFO] Type checking passed.
% 2.31/1.79 % [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 ...
% 4.58/2.63 % External prover 'e' found a proof!
% 4.58/2.63 % [INFO] Killing All external provers ...
% 4.58/2.63 % Time passed: 2091ms (effective reasoning time: 1431ms)
% 4.58/2.63 % 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)>
% 4.58/2.63 % Axioms used in derivation (12): plus_and_order1, int_less_total, qih, int_leq, int_less_transitive, int_zero_one, plus_and_inverse, int_less_irreflexive, plus_commutative, real_constants, plus_zero, one_successor_of_zero
% 4.58/2.63 % No. of inferences in proof: 28
% 4.58/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2091 ms resp. 1431 ms w/o parsing
% 4.58/2.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.58/2.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------