TSTP Solution File: HEN011-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : HEN011-1 : TPTP v8.1.2. Released v1.0.0.
% 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 11:16:56 EDT 2023
% Result : Unsatisfiable 6.39s 2.35s
% Output : Refutation 6.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 46 ( 21 unt; 13 typ; 0 def)
% Number of atoms : 57 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 188 ( 26 ~; 24 |; 0 &; 138 @)
% ( 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 : 15 ( 13 usr; 11 con; 0-3 aty)
% Number of variables : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(idQa_Q__idQ_idQb_type,type,
idQa_Q__idQ_idQb: $i ).
thf(idQb_Q__idQ_idQa_type,type,
idQb_Q__idQ_idQa: $i ).
thf(less_equal_type,type,
less_equal: $i > $i > $o ).
thf(zero_type,type,
zero: $i ).
thf(identity_type,type,
identity: $i ).
thf(quotient_type,type,
quotient: $i > $i > $i > $o ).
thf(b_type,type,
b: $i ).
thf(idQb_type,type,
idQb: $i ).
thf(divide_type,type,
divide: $i > $i > $i ).
thf(idQ_idQb_type,type,
idQ_idQb: $i ).
thf(a_type,type,
a: $i ).
thf(idQa_type,type,
idQa: $i ).
thf(idQ_idQa_type,type,
idQ_idQa: $i ).
thf(15,axiom,
quotient @ idQb @ idQ_idQa @ idQb_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idQb_divide_idQ_idQa) ).
thf(41,plain,
quotient @ idQb @ idQ_idQa @ idQb_Q__idQ_idQa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,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(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ( less_equal @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( quotient @ A @ B @ zero )
| ( less_equal @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( quotient @ A @ B @ zero )
| ( less_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
quotient @ idQa @ idQ_idQb @ idQa_Q__idQ_idQb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idQa_divide_idQ_idQb) ).
thf(42,plain,
quotient @ idQa @ idQ_idQb @ idQa_Q__idQ_idQb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
quotient @ identity @ idQa @ idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
thf(37,plain,
quotient @ identity @ idQa @ idQ_idQa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( quotient @ A @ B @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( quotient @ A @ B @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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(8,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(29,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)],[8]) ).
thf(3,axiom,
! [A: $i] : ( less_equal @ A @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(21,plain,
! [A: $i] : ( less_equal @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
quotient @ identity @ idQb @ idQ_idQb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQb) ).
thf(33,plain,
quotient @ identity @ idQb @ idQ_idQb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [B: $i,A: $i] : ( quotient @ A @ B @ ( divide @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
thf(28,plain,
! [B: $i,A: $i] : ( quotient @ A @ B @ ( divide @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,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(38,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)],[14]) ).
thf(11,axiom,
quotient @ identity @ a @ idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
thf(34,plain,
quotient @ identity @ a @ idQa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,negated_conjecture,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa) ).
thf(17,plain,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
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(22,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(6,axiom,
quotient @ identity @ b @ idQb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_b) ).
thf(27,plain,
quotient @ identity @ b @ idQb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(621,plain,
$false,
inference(e,[status(thm)],[41,35,31,42,37,25,20,29,21,33,28,38,34,17,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN011-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n014.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 15:12:58 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.87/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.96 % [INFO] Parsing done (120ms).
% 1.22/0.97 % [INFO] Running in sequential loop mode.
% 1.52/1.17 % [INFO] eprover registered as external prover.
% 1.52/1.18 % [INFO] cvc4 registered as external prover.
% 1.70/1.18 % [INFO] Scanning for conjecture ...
% 1.74/1.23 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 1.84/1.26 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 1.84/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/1.29 % [INFO] Type checking passed.
% 1.84/1.29 % [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 ...
% 6.39/2.34 % External prover 'e' found a proof!
% 6.39/2.34 % [INFO] Killing All external provers ...
% 6.39/2.35 % Time passed: 1818ms (effective reasoning time: 1376ms)
% 6.39/2.35 % 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)>
% 6.39/2.35 % Axioms used in derivation (15): quotient_property, idQa_divide_idQ_idQb, quotient_less_equal, identity_divide_a, identity_divide_b, identity_divide_idQb, closure, idQb_divide_idQ_idQa, less_equal_and_equal, less_equal_quotient, identity_is_largest, divisor_existence, well_defined, identity_divide_idQa, zero_is_smallest
% 6.39/2.35 % No. of inferences in proof: 33
% 6.39/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1818 ms resp. 1376 ms w/o parsing
% 6.39/2.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.39/2.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------