TSTP Solution File: ANA018-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA018-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 10:08:47 EDT 2023
% Result : Unsatisfiable 2.24s 1.45s
% Output : Refutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 30
% Syntax : Number of formulae : 44 ( 11 unt; 17 typ; 0 def)
% Number of atoms : 53 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 248 ( 28 ~; 26 |; 0 &; 194 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
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(t_b_type,type,
t_b: $i ).
thf(c_times_type,type,
c_times: $i > $i > $i > $i ).
thf(v_c_type,type,
v_c: $i ).
thf(v_g_type,type,
v_g: $i > $i ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(c_0_type,type,
c_0: $i ).
thf(v_ca_type,type,
v_ca: $i ).
thf(v_x_type,type,
v_x: $i > $i ).
thf(v_xa_type,type,
v_xa: $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
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_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_LOrder_Ojoin__semilorder_type,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(14,plain,
class_Ring__and__Field_Oordered__idom @ t_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(33,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,negated_conjecture,
! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_x @ A ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_f @ A ) @ t_b ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(17,plain,
! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_x @ A ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_f @ A ) @ t_b ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ c_0 @ D @ A )
| ( c_lessequals @ ( c_times @ D @ B @ A ) @ ( c_times @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ c_0 @ D @ A )
| ( c_lessequals @ ( c_times @ D @ B @ A ) @ ( c_times @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(35,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,negated_conjecture,
~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_x @ v_xa ) @ t_b ) @ ( c_times @ ( c_times @ v_ca @ v_c @ t_b ) @ ( c_HOL_Oabs @ ( v_g @ v_xa ) @ t_b ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(18,plain,
~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_x @ v_xa ) @ t_b ) @ ( c_times @ ( c_times @ v_ca @ v_c @ t_b ) @ ( c_HOL_Oabs @ ( v_g @ v_xa ) @ t_b ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ A ) @ t_b ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_g @ A ) @ t_b ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(15,plain,
! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ A ) @ t_b ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_g @ A ) @ t_b ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,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_Omult__ac__1_0) ).
thf(20,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)],[6]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(29,plain,
! [A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,negated_conjecture,
c_less @ c_0 @ v_ca @ t_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(16,plain,
c_less @ c_0 @ v_ca @ t_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
thf(31,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[25,14,33,17,27,35,18,23,15,20,29,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : ANA018-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.09 % Command : run_Leo-III %s %d
% 0.07/0.28 % Computer : n032.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Thu May 18 17:54:50 EDT 2023
% 0.07/0.28 % CPUTime :
% 0.62/0.68 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.91/0.81 % [INFO] Parsing done (126ms).
% 0.91/0.81 % [INFO] Running in sequential loop mode.
% 1.33/1.02 % [INFO] eprover registered as external prover.
% 1.33/1.03 % [INFO] cvc4 registered as external prover.
% 1.33/1.03 % [INFO] Scanning for conjecture ...
% 1.50/1.09 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.50/1.12 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.50/1.13 % [INFO] Problem is propositional (TPTP CNF).
% 1.50/1.13 % [INFO] Type checking passed.
% 1.50/1.14 % [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 ...
% 2.24/1.44 % External prover 'e' found a proof!
% 2.24/1.44 % [INFO] Killing All external provers ...
% 2.24/1.45 % Time passed: 1060ms (effective reasoning time: 629ms)
% 2.24/1.45 % 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)>
% 2.24/1.45 % Axioms used in derivation (8): cls_Orderings_Oorder__class_Oorder__trans_0, clsrel_Ring__and__Field_Oordered__idom_21, clsrel_Ring__and__Field_Oordered__idom_42, cls_Orderings_Oorder__less__imp__le_0, cls_OrderedGroup_Omult__ac__1_0, cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0, clsrel_LOrder_Ojoin__semilorder_1, clsrel_Ring__and__Field_Oordered__idom_35
% 2.24/1.45 % No. of inferences in proof: 27
% 2.24/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1060 ms resp. 629 ms w/o parsing
% 2.49/1.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.49/1.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------