TSTP Solution File: HEN009-5 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : HEN009-5 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 2.68s 1.58s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 23 ( 11 unt; 4 typ; 0 def)
% Number of atoms : 31 ( 30 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 134 ( 14 ~; 12 |; 0 &; 108 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(divide_type,type,
divide: $i > $i > $i ).
thf(identity_type,type,
identity: $i ).
thf(a_type,type,
a: $i ).
thf(zero_type,type,
zero: $i ).
thf(1,negated_conjecture,
( ( divide @ identity @ a )
!= ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(10,plain,
( ( divide @ identity @ a )
!= ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( ( divide @ B @ C )
!= zero )
| ( ( divide @ A @ C )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_divide_to_zero) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( ( divide @ B @ C )
!= zero )
| ( ( divide @ A @ C )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( divide @ ( divide @ A @ B ) @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( divide @ ( divide @ A @ B ) @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i] :
( ( divide @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(17,plain,
! [A: $i] :
( ( divide @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( divide @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) @ ( divide @ ( divide @ A @ C ) @ B ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) @ ( divide @ ( divide @ A @ C ) @ B ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i] :
( ( divide @ A @ identity )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).
thf(22,plain,
! [A: $i] :
( ( divide @ A @ identity )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( divide @ ( divide @ A @ B ) @ C )
!= zero )
| ( ( divide @ ( divide @ A @ C ) @ B )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( ( divide @ ( divide @ A @ B ) @ C )
!= zero )
| ( ( divide @ ( divide @ A @ C ) @ B )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( ( divide @ ( divide @ C @ B ) @ ( divide @ C @ A ) )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide2) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( ( divide @ ( divide @ C @ B ) @ ( divide @ C @ A ) )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( ( divide @ B @ A )
!= zero )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divide_and_equal) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( ( divide @ B @ A )
!= zero )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[10,24,13,17,15,22,27,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN009-5 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n014.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 15:11:43 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.87/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.95 % [INFO] Parsing done (113ms).
% 1.20/0.96 % [INFO] Running in sequential loop mode.
% 1.55/1.15 % [INFO] eprover registered as external prover.
% 1.55/1.15 % [INFO] cvc4 registered as external prover.
% 1.55/1.16 % [INFO] Scanning for conjecture ...
% 1.80/1.21 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.80/1.22 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.91/1.24 % [INFO] Problem is propositional (TPTP CNF).
% 1.91/1.24 % [INFO] Type checking passed.
% 1.91/1.24 % [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 ...
% 2.68/1.57 % External prover 'e' found a proof!
% 2.68/1.57 % [INFO] Killing All external provers ...
% 2.68/1.57 % Time passed: 1054ms (effective reasoning time: 611ms)
% 2.68/1.57 % 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)>
% 2.68/1.58 % Axioms used in derivation (8): identity_is_largest, property_of_divide2, property_of_divide1, transitivity_of_divide_to_zero, divide_and_equal, zero_is_smallest, quotient_smaller_than_numerator, quotient_property
% 2.68/1.58 % No. of inferences in proof: 19
% 2.68/1.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1054 ms resp. 611 ms w/o parsing
% 3.02/1.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.02/1.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------