TSTP Solution File: ANA009-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA009-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 10:08:45 EDT 2023
% Result : Unsatisfiable 2.57s 1.61s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 26 ( 7 unt; 11 typ; 0 def)
% Number of atoms : 25 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 100 ( 12 ~; 10 |; 0 &; 78 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_lb_type,type,
v_lb: $i > $i ).
thf(v_f_type,type,
v_f: $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(c_0_type,type,
c_0: $i ).
thf(c_plus_type,type,
c_plus: $i > $i > $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_uminus_type,type,
c_uminus: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(3,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(10,plain,
class_Ring__and__Field_Oordered__idom @ t_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_plus @ B @ ( c_uminus @ B @ A ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_plus @ B @ ( c_uminus @ B @ A ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,negated_conjecture,
~ ( c_lessequals @ c_0 @ ( c_plus @ ( v_f @ v_x ) @ ( c_uminus @ ( v_lb @ v_x ) @ t_b ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
~ ( c_lessequals @ c_0 @ ( c_plus @ ( v_f @ v_x ) @ ( c_uminus @ ( v_lb @ v_x ) @ t_b ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
thf(17,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_plus @ B @ D @ A ) @ ( c_plus @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
thf(12,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_plus @ B @ D @ A ) @ ( c_plus @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
! [A: $i] : ( c_lessequals @ ( v_lb @ A ) @ ( v_f @ A ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(8,plain,
! [A: $i] : ( c_lessequals @ ( v_lb @ A ) @ ( v_f @ A ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(19,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[10,14,9,17,12,8,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA009-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 17:49:51 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.94/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.01 % [INFO] Parsing done (123ms).
% 1.23/1.02 % [INFO] Running in sequential loop mode.
% 1.57/1.21 % [INFO] eprover registered as external prover.
% 1.57/1.22 % [INFO] cvc4 registered as external prover.
% 1.57/1.22 % [INFO] Scanning for conjecture ...
% 1.85/1.27 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.85/1.29 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.85/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.85/1.30 % [INFO] Type checking passed.
% 1.85/1.30 % [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 ...
% 2.57/1.61 % External prover 'e' found a proof!
% 2.57/1.61 % [INFO] Killing All external provers ...
% 2.57/1.61 % Time passed: 1097ms (effective reasoning time: 584ms)
% 2.57/1.61 % 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)>
% 2.57/1.61 % Axioms used in derivation (4): cls_OrderedGroup_Oright__minus_0, clsrel_Ring__and__Field_Oordered__idom_37, cls_OrderedGroup_Oadd__le__cancel__right_1, clsrel_Ring__and__Field_Oordered__idom_4
% 2.57/1.61 % No. of inferences in proof: 15
% 2.57/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1097 ms resp. 584 ms w/o parsing
% 2.57/1.63 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.57/1.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------