TSTP Solution File: HEN009-4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : HEN009-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 : Fri May 19 11:16:54 EDT 2023
% Result : Unsatisfiable 2.94s 1.67s
% Output : Refutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 38 ( 19 unt; 5 typ; 0 def)
% Number of atoms : 51 ( 16 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 194 ( 20 ~; 18 |; 0 &; 156 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(divide_type,type,
divide: $i > $i > $i ).
thf(identity_type,type,
identity: $i ).
thf(a_type,type,
a: $i ).
thf(less_equal_type,type,
less_equal: $i > $i > $o ).
thf(zero_type,type,
zero: $i ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( ( divide @ A @ B )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( ( divide @ A @ B )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2,axiom,
! [A: $i] : ( less_equal @ zero @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(20,plain,
! [A: $i] : ( less_equal @ zero @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i] : ( less_equal @ A @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(39,plain,
! [A: $i] : ( less_equal @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
( ( divide @ a @ zero )
= a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_zero_is_x) ).
thf(31,plain,
( ( divide @ a @ zero )
= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i] :
( ( divide @ A @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
thf(36,plain,
! [A: $i] :
( ( divide @ A @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( less_equal @ ( divide @ A @ C ) @ ( divide @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide3) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( less_equal @ ( divide @ A @ C ) @ ( divide @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,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(21,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)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] : ( less_equal @ ( divide @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(33,plain,
! [B: $i,A: $i] : ( less_equal @ ( divide @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( less_equal @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( less_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] : ( less_equal @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) @ ( divide @ ( divide @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] : ( less_equal @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) @ ( divide @ ( divide @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( less_equal @ ( divide @ C @ B ) @ ( divide @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide2) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( less_equal @ ( divide @ C @ B ) @ ( divide @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i] :
( ( divide @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(45,plain,
! [A: $i] :
( ( divide @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,negated_conjecture,
( ( divide @ identity @ a )
!= ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(17,plain,
( ( divide @ identity @ a )
!= ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [A: $i] :
( ( divide @ A @ identity )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_id_is_zero) ).
thf(40,plain,
! [A: $i] :
( ( divide @ A @ identity )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_equal @ ( divide @ A @ B ) @ C )
| ( less_equal @ ( divide @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_equal @ ( divide @ A @ B ) @ C )
| ( less_equal @ ( divide @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,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(23,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(84,plain,
$false,
inference(e,[status(thm)],[42,20,39,31,36,47,21,33,28,38,34,45,17,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN009-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 14:42:46 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.82/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.96 % [INFO] Parsing done (109ms).
% 1.24/0.96 % [INFO] Running in sequential loop mode.
% 1.51/1.15 % [INFO] eprover registered as external prover.
% 1.51/1.15 % [INFO] cvc4 registered as external prover.
% 1.51/1.15 % [INFO] Scanning for conjecture ...
% 1.82/1.20 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 1.91/1.23 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 1.91/1.24 % [INFO] Problem is propositional (TPTP CNF).
% 1.91/1.25 % [INFO] Type checking passed.
% 1.91/1.25 % [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 ...
% 2.94/1.67 % External prover 'e' found a proof!
% 2.94/1.67 % [INFO] Killing All external provers ...
% 2.94/1.67 % Time passed: 1146ms (effective reasoning time: 705ms)
% 2.94/1.67 % 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)>
% 2.94/1.67 % Axioms used in derivation (15): identity_is_largest, x_divide_x_is_zero, property_of_divide3, property_of_divide2, zero_divide_anything_is_zero, property_of_divide1, everything_divide_id_is_zero, quotient_less_equal2, less_equal_and_equal, zero_is_smallest, x_divide_zero_is_x, quotient_less_equal1, transitivity_of_less_equal, quotient_smaller_than_numerator, quotient_property
% 2.94/1.67 % No. of inferences in proof: 33
% 2.94/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1146 ms resp. 705 ms w/o parsing
% 2.94/1.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.94/1.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------