TSTP Solution File: ANA014-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA014-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 10:08:46 EDT 2023
% Result : Unsatisfiable 2.61s 1.56s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 43 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 49 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 186 ( 24 ~; 22 |; 0 &; 140 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_c_type,type,
v_c: $i ).
thf(c_0_type,type,
c_0: $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oabs_type,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_f_type,type,
v_f: $i > $i ).
thf(v_x_type,type,
v_x: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_times_type,type,
c_times: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__field_type,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(c_1_type,type,
c_1: $i ).
thf(class_OrderedGroup_Osemigroup__mult_type,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(c_HOL_Oinverse_type,type,
c_HOL_Oinverse: $i > $i > $i ).
thf(13,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
thf(42,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(14,plain,
v_c != c_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ c_1 @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ c_1 @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
thf(34,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
thf(36,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,negated_conjecture,
! [A: $i] :
~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_a ) @ ( c_times @ A @ ( c_times @ ( c_HOL_Oabs @ v_c @ t_a ) @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_a ) @ t_a ) @ t_a ) @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(15,plain,
! [A: $i] :
~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_a ) @ ( c_times @ A @ ( c_times @ ( c_HOL_Oabs @ v_c @ t_a ) @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_a ) @ t_a ) @ t_a ) @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs @ ( c_times @ B @ C @ A ) @ A )
= ( c_times @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs @ ( c_times @ B @ C @ A ) @ A )
= ( c_times @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( class_Ring__and__Field_Ofield @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
thf(38,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( class_Ring__and__Field_Ofield @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,negated_conjecture,
class_Ring__and__Field_Oordered__field @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(16,plain,
class_Ring__and__Field_Oordered__field @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ B @ A ) @ B @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ B @ A ) @ B @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
thf(40,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__mult @ A )
| ( ( c_times @ ( c_times @ B @ C @ A ) @ D @ A )
= ( c_times @ B @ ( c_times @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__mult @ A )
| ( ( c_times @ ( c_times @ B @ C @ A ) @ D @ A )
= ( c_times @ B @ ( c_times @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(44,plain,
$false,
inference(e,[status(thm)],[42,14,20,34,36,15,28,38,16,31,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA014-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n009.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 17:52:34 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.93/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.96 % [INFO] Parsing done (103ms).
% 1.18/0.97 % [INFO] Running in sequential loop mode.
% 1.56/1.15 % [INFO] eprover registered as external prover.
% 1.56/1.15 % [INFO] cvc4 registered as external prover.
% 1.66/1.16 % [INFO] Scanning for conjecture ...
% 1.66/1.21 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.66/1.23 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.87/1.24 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.24 % [INFO] Type checking passed.
% 1.87/1.25 % [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 ...
% 2.61/1.56 % External prover 'e' found a proof!
% 2.61/1.56 % [INFO] Killing All external provers ...
% 2.61/1.56 % Time passed: 1026ms (effective reasoning time: 589ms)
% 2.61/1.56 % 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)>
% 2.61/1.56 % Axioms used in derivation (10): cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0, clsrel_Ring__and__Field_Oordered__field_58, clsrel_Ring__and__Field_Oordered__field_34, cls_Ring__and__Field_Ofield__class_Oaxioms__1_0, cls_Orderings_Oorder__class_Oaxioms__1_0, cls_Ring__and__Field_Oabs__mult_0, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0, clsrel_Ring__and__Field_Ofield_12, clsrel_Ring__and__Field_Ofield_21, clsrel_Ring__and__Field_Oordered__field_0
% 2.61/1.56 % No. of inferences in proof: 27
% 2.61/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1026 ms resp. 589 ms w/o parsing
% 2.80/1.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.80/1.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------