TSTP Solution File: HEN006-2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : HEN006-2 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 21:34:07 EDT 2024
% Result : Unsatisfiable 4.05s 2.28s
% Output : Refutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 28
% Syntax : Number of formulae : 47 ( 23 unt; 10 typ; 0 def)
% Number of atoms : 65 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 216 ( 30 ~; 28 |; 0 &; 158 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 8 con; 0-3 aty)
% Number of variables : 64 ( 0 ^ 64 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_equal_type,type,
less_equal: $i > $i > $o ).
thf(xQz_type,type,
xQz: $i ).
thf(y_type,type,
y: $i ).
thf(quotient_type,type,
quotient: $i > $i > $i > $o ).
thf(zero_type,type,
zero: $i ).
thf(divide_type,type,
divide: $i > $i > $i ).
thf(identity_type,type,
identity: $i ).
thf(x_type,type,
x: $i ).
thf(z_type,type,
z: $i ).
thf(xQy_type,type,
xQy: $i ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( quotient @ A @ B @ zero )
| ( less_equal @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
thf(29,plain,
! [B: $i,A: $i] :
( ~ ( quotient @ A @ B @ zero )
| ( less_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
quotient @ x @ y @ xQy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQy) ).
thf(41,plain,
quotient @ x @ y @ xQy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ( less_equal @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ( less_equal @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i] : ( less_equal @ zero @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(31,plain,
! [A: $i] : ( less_equal @ zero @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
less_equal @ xQy @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz) ).
thf(43,plain,
less_equal @ xQy @ z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i] : ( quotient @ A @ identity @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_identity_is_zero) ).
thf(23,plain,
! [A: $i] : ( quotient @ A @ identity @ zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i] : ( less_equal @ A @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(42,plain,
! [A: $i] : ( less_equal @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ~ ( quotient @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ~ ( quotient @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ~ ( quotient @ B @ D @ E )
| ~ ( quotient @ A @ D @ F )
| ~ ( quotient @ F @ E @ G )
| ~ ( quotient @ C @ D @ H )
| ( less_equal @ G @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
thf(37,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ~ ( quotient @ B @ D @ E )
| ~ ( quotient @ A @ D @ F )
| ~ ( quotient @ F @ E @ G )
| ~ ( quotient @ C @ D @ H )
| ( less_equal @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i] : ( quotient @ A @ A @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
thf(28,plain,
! [A: $i] : ( quotient @ A @ A @ zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [A: $i] : ( quotient @ A @ zero @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
thf(21,plain,
! [A: $i] : ( quotient @ A @ zero @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ C )
| ( less_equal @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ C )
| ( less_equal @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( quotient @ A @ B @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( quotient @ A @ B @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( quotient @ A @ B @ ( divide @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
thf(22,plain,
! [B: $i,A: $i] : ( quotient @ A @ B @ ( divide @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: $i] : ( quotient @ zero @ A @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(27,plain,
! [A: $i] : ( quotient @ zero @ A @ zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
quotient @ x @ z @ xQz,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQz) ).
thf(36,plain,
quotient @ x @ z @ xQz,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
~ ( less_equal @ xQz @ y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_xQzLEy) ).
thf(19,plain,
~ ( less_equal @ xQz @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(49,plain,
$false,
inference(e,[status(thm)],[29,41,39,31,43,23,42,24,37,28,21,32,34,22,44,27,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : HEN006-2 : TPTP v8.2.0. Released v1.0.0.
% 0.18/0.19 % Command : run_Leo-III %s %d
% 0.19/0.42 % Computer : n020.cluster.edu
% 0.19/0.42 % Model : x86_64 x86_64
% 0.19/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.42 % Memory : 8042.1875MB
% 0.19/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.42 % CPULimit : 300
% 0.19/0.42 % WCLimit : 300
% 0.19/0.42 % DateTime : Sun May 19 22:48:39 EDT 2024
% 0.19/0.42 % CPUTime :
% 1.14/1.06 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/1.20 % [INFO] Parsing done (135ms).
% 1.54/1.21 % [INFO] Running in sequential loop mode.
% 2.06/1.50 % [INFO] eprover registered as external prover.
% 2.06/1.51 % [INFO] cvc4 registered as external prover.
% 2.06/1.51 % [INFO] Scanning for conjecture ...
% 2.18/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ...
% 2.39/1.63 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.39/1.65 % [INFO] Problem is propositional (TPTP CNF).
% 2.39/1.66 % [INFO] Type checking passed.
% 2.39/1.66 % [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 ...
% 3.73/2.20 % External prover 'e' found a proof!
% 4.05/2.27 % [INFO] Killing All external provers ...
% 4.05/2.27 % Time passed: 1642ms (effective reasoning time: 1055ms)
% 4.05/2.28 % Axioms used in derivation (17): quotient_property, xQz, closure, everything_divide_identity_is_zero, zero_divide_anything_is_zero, zero_is_smallest, xQyLEz, xQy, transitivity_of_less_equal, less_equal_quotient, identity_is_largest, x_divide_x_is_zero, quotient_less_equal, divisor_existence, well_defined, x_divde_zero_is_x, less_equal_and_equal
% 4.05/2.28 % No. of inferences in proof: 37
% 4.05/2.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1642 ms resp. 1055 ms w/o parsing
% 4.16/2.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.16/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------