TSTP Solution File: ANA028-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA028-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 10:08:53 EDT 2023
% Result : Unsatisfiable 3.15s 1.74s
% Output : Refutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 40 ( 7 unt; 13 typ; 0 def)
% Number of atoms : 51 ( 10 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 246 ( 26 ~; 24 |; 0 &; 196 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_g_type,type,
v_g: $i > $i ).
thf(v_k_type,type,
v_k: $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(v_f_type,type,
v_f: $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_plus_type,type,
c_plus: $i > $i > $i > $i ).
thf(c_0_type,type,
c_0: $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(1,negated_conjecture,
! [A: $i] : ( c_lessequals @ ( v_g @ A ) @ ( v_k @ A ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(14,plain,
! [A: $i] : ( c_lessequals @ ( v_g @ A ) @ ( v_k @ A ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_plus @ B @ ( c_minus @ C @ D @ A ) @ A )
= ( c_minus @ ( c_plus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_plus @ B @ ( c_minus @ C @ D @ A ) @ A )
= ( c_minus @ ( c_plus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
thf(41,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ B @ ( c_minus @ C @ D @ A ) @ A )
= ( c_minus @ ( c_plus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__5_0) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ B @ ( c_minus @ C @ D @ A ) @ A )
= ( c_minus @ ( c_plus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(39,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_plus @ c_0 @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_plus @ c_0 @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(16,plain,
class_Ring__and__Field_Oordered__idom @ t_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ ( c_plus @ C @ D @ A ) @ A )
| ( c_lessequals @ ( c_minus @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ ( c_plus @ C @ D @ A ) @ A )
| ( c_lessequals @ ( c_minus @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,negated_conjecture,
~ ( c_lessequals @ ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(15,plain,
~ ( c_lessequals @ ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_plus @ ( c_minus @ B @ C @ A ) @ D @ A )
= ( c_minus @ ( c_plus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_0) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_plus @ ( c_minus @ B @ C @ A ) @ D @ A )
= ( c_minus @ ( c_plus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
thf(37,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_plus @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ ( c_minus @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_plus @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ ( c_minus @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ B @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ B @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,plain,
$false,
inference(e,[status(thm)],[14,21,41,27,39,18,16,30,15,24,37,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA028-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n004.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 17:48:55 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.96 % [INFO] Parsing done (112ms).
% 1.17/0.97 % [INFO] Running in sequential loop mode.
% 1.64/1.18 % [INFO] eprover registered as external prover.
% 1.64/1.18 % [INFO] cvc4 registered as external prover.
% 1.64/1.18 % [INFO] Scanning for conjecture ...
% 1.81/1.24 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.81/1.26 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.93/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.93/1.28 % [INFO] Type checking passed.
% 1.93/1.28 % [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 ...
% 3.15/1.74 % External prover 'e' found a proof!
% 3.15/1.74 % [INFO] Killing All external provers ...
% 3.15/1.74 % Time passed: 1213ms (effective reasoning time: 767ms)
% 3.15/1.74 % 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)>
% 3.15/1.74 % Axioms used in derivation (10): cls_OrderedGroup_Odiff__self_0, clsrel_Ring__and__Field_Oordered__idom_23, cls_OrderedGroup_Ocompare__rls__9_1, cls_OrderedGroup_Ocompare__rls__2_0, cls_OrderedGroup_Ocompare__rls__3_0, cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, cls_OrderedGroup_Ocompare__rls__8_1, clsrel_Ring__and__Field_Oordered__idom_54, cls_OrderedGroup_Ocompare__rls__5_0, clsrel_Ring__and__Field_Oordered__idom_4
% 3.15/1.74 % No. of inferences in proof: 27
% 3.15/1.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1213 ms resp. 767 ms w/o parsing
% 3.30/1.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.30/1.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------