TSTP Solution File: HEN004-6 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : HEN004-6 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 : Tue May 7 07:45:36 EDT 2024
% Result : Unsatisfiable 2.66s 1.70s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 26 ( 15 unt; 5 typ; 0 def)
% Number of atoms : 29 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 10 ~; 8 |; 0 &; 76 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 30 ( 0 ^ 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(divide_type,type,
divide: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(zero_type,type,
zero: $i ).
thf(less_equal_type,type,
less_equal: $i > $i > $o ).
thf(identity_type,type,
identity: $i ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( ( divide @ A @ B )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( ( divide @ A @ B )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,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(21,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)],[5]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( less_equal @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( less_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( divide @ a @ zero )
!= a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_zero_is_x) ).
thf(11,plain,
( ( divide @ a @ zero )
!= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( less_equal @ ( divide @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(20,plain,
! [B: $i,A: $i] : ( less_equal @ ( divide @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i] :
( ( divide @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(29,plain,
! [A: $i] :
( ( divide @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i] : ( less_equal @ zero @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(22,plain,
! [A: $i] : ( less_equal @ zero @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i] :
( ( divide @ A @ identity )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_id_is_zero) ).
thf(27,plain,
! [A: $i] :
( ( divide @ A @ identity )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
! [A: $i] : ( less_equal @ A @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(26,plain,
! [A: $i] : ( less_equal @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,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)],[7]) ).
thf(31,plain,
$false,
inference(e,[status(thm)],[14,21,17,11,20,29,22,27,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : HEN004-6 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 6 11:27:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (105ms).
% 1.26/0.96 % [INFO] Running in sequential loop mode.
% 1.53/1.15 % [INFO] eprover registered as external prover.
% 1.68/1.16 % [INFO] cvc4 registered as external prover.
% 1.68/1.16 % [INFO] Scanning for conjecture ...
% 1.78/1.20 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.78/1.22 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.78/1.23 % [INFO] Problem is propositional (TPTP CNF).
% 1.89/1.23 % [INFO] Type checking passed.
% 1.89/1.24 % [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 ...
% 2.66/1.70 % External prover 'e' found a proof!
% 2.66/1.70 % [INFO] Killing All external provers ...
% 2.66/1.70 % Time passed: 1176ms (effective reasoning time: 730ms)
% 2.66/1.70 % 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)>
% 2.66/1.70 % Axioms used in derivation (9): identity_is_largest, zero_divide_anything_is_zero, everything_divide_id_is_zero, quotient_less_equal2, less_equal_and_equal, zero_is_smallest, quotient_less_equal1, quotient_smaller_than_numerator, quotient_property
% 2.66/1.70 % No. of inferences in proof: 21
% 2.66/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1176 ms resp. 730 ms w/o parsing
% 2.66/1.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.66/1.75 % [INFO] Killing All external provers ...
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