TSTP Solution File: HEN010-3 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : HEN010-3 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 21:34:13 EDT 2024
% Result : Unsatisfiable 2.73s 1.65s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 22 ( 11 unt; 5 typ; 0 def)
% Number of atoms : 25 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 102 ( 10 ~; 8 |; 0 &; 84 @)
% ( 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 : 26 ( 0 ^ 26 !; 0 ?; 26 :)
% 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(8,axiom,
! [A: $i] : ( less_equal @ A @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(24,plain,
! [A: $i] : ( less_equal @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,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)],[6]) ).
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(21,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(1,negated_conjecture,
( ( divide @ identity @ a )
!= ( divide @ ( divide @ identity @ a ) @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_inversion) ).
thf(9,plain,
( ( divide @ identity @ a )
!= ( divide @ ( divide @ identity @ a ) @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
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(12,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( ( divide @ A @ B )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(18,plain,
! [B: $i,A: $i] : ( less_equal @ ( divide @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(19,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(15,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( less_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,plain,
$false,
inference(e,[status(thm)],[24,20,21,9,12,18,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : HEN010-3 : TPTP v8.2.0. Released v1.0.0.
% 0.10/0.12 % Command : run_Leo-III %s %d
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun May 19 22:49:08 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.79/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/0.90 % [INFO] Parsing done (106ms).
% 1.21/0.91 % [INFO] Running in sequential loop mode.
% 1.50/1.13 % [INFO] eprover registered as external prover.
% 1.50/1.13 % [INFO] cvc4 registered as external prover.
% 1.50/1.13 % [INFO] Scanning for conjecture ...
% 1.72/1.19 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 1.73/1.21 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.73/1.22 % [INFO] Problem is propositional (TPTP CNF).
% 1.73/1.22 % [INFO] Type checking passed.
% 1.80/1.22 % [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 ...
% 2.73/1.64 % External prover 'e' found a proof!
% 2.73/1.64 % [INFO] Killing All external provers ...
% 2.73/1.64 % Time passed: 1176ms (effective reasoning time: 733ms)
% 2.73/1.64 % Axioms used in derivation (7): identity_is_largest, quotient_less_equal2, less_equal_and_equal, zero_is_smallest, quotient_less_equal1, quotient_smaller_than_numerator, quotient_property
% 2.73/1.64 % No. of inferences in proof: 17
% 2.73/1.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1176 ms resp. 733 ms w/o parsing
% 2.73/1.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.73/1.68 % [INFO] Killing All external provers ...
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