%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP227^2 : TPTP v9.3.1. Bugfixed v9.2.1.
% 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 : n012.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 08:07:17 AM UTC 2026
% Result : Theorem 7.11s 2.31s
% Output : Refutation 7.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 173 ( 14 ~; 4 |; 7 &; 116 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 0 ^; 52 !; 4 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(char_type,type,
char: $tType ).
thf(real_type,type,
real: $tType ).
thf(rat_type,type,
rat: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ma_decl,type,
ma: nat ).
thf(mi_decl,type,
mi: nat ).
thf(xa_decl,type,
xa: nat ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_nat__le__linear) ).
thf(46,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
ord_less_eq @ nat @ mi @ ma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C5_Ohyps_C_I7_J) ).
thf(74,plain,
ord_less_eq @ nat @ mi @ ma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
( ( xa != mi )
& ( xa != ma ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( xa != mi )
& ( xa != ma ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ( ( xa != mi )
& ( xa != ma ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_le__antisym) ).
thf(64,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)],[10]) ).
thf(9,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Nat_Oex__has__greatest__nat) ).
thf(48,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_eq__imp__le) ).
thf(23,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_bounded__Max__nat) ).
thf(30,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_le__refl) ).
thf(44,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_le__trans) ).
thf(27,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
~ ( ( xa = mi )
| ( xa = ma ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_False) ).
thf(67,plain,
~ ( ( xa = mi )
| ( xa = ma ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat] :
( ( A @ B )
=> ? [D: TA] :
( ( A @ D )
& ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ nat @ ( C @ D ) @ ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_890_ex__has__least__nat) ).
thf(16,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat] :
( ( A @ B )
=> ? [D: TA] :
( ( A @ D )
& ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ nat @ ( C @ D ) @ ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(75,plain,
$false,
inference(e,[status(thm)],[46,74,13,64,48,23,30,44,27,67,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP227^2 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.04 % 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
% 0.07/0.13 % Computer : n012.cluster.edu
% 0.07/0.13 % Model : x86_64 x86_64
% 0.07/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.13 % Memory : 8046.5625MB
% 0.07/0.13 % OS : Linux 6.8.0-71-generic
% 0.07/0.13 % CPULimit : 300
% 0.07/0.13 % WCLimit : 300
% 0.07/0.13 % DateTime : Tue Sep 29 20:21:03 UTC 2026
% 0.07/0.13 % CPUTime :
% 0.07/0.13 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
% 0.39/0.42 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.45/1.20 % [INFO] Parsing done (778ms).
% 3.45/1.21 % [INFO] Running in sequential loop mode.
% 3.71/1.39 % [INFO] eprover registered as external prover.
% 3.71/1.40 % [INFO] Scanning for conjecture ...
% 4.98/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 8952 axioms. Running axiom selection ...
% 5.78/1.90 % [INFO] Axiom selection finished. Selected 10 axioms (removed 8942 axioms).
% 5.78/1.92 % [INFO] Problem is higher-order (TPTP THF).
% 5.78/1.92 % [INFO] Type checking passed.
% 5.78/1.92 % [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 ...
% 7.11/2.31 % External prover 'e' found a proof!
% 7.11/2.31 % [INFO] Killing All external provers ...
% 7.11/2.31 % Time passed: 2103ms (effective reasoning time: 1097ms)
% 7.11/2.31 % 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)>
% 7.11/2.31 % Axioms used in derivation (10): fact_1__C5_Ohyps_C_I7_J, fact_218_le__refl, fact_220_eq__imp__le, fact_890_ex__has__least__nat, fact_223_Nat_Oex__has__greatest__nat, fact_421_bounded__Max__nat, fact_219_le__trans, fact_222_nat__le__linear, fact_0_False, fact_221_le__antisym
% 7.11/2.31 % No. of inferences in proof: 24
% 7.11/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2103 ms resp. 1097 ms w/o parsing
% 7.11/2.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.11/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------