TSTP Solution File: ANA044-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA044-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 10:09:00 EDT 2023
% Result : Unsatisfiable 2.46s 1.52s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 30 ( 9 unt; 13 typ; 0 def)
% Number of atoms : 31 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 132 ( 16 ~; 14 |; 0 &; 102 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_type,type,
c_0: $i ).
thf(v_l_type,type,
v_l: $i > $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(v_h_type,type,
v_h: $i > $i ).
thf(c_times_type,type,
c_times: $i > $i > $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(v_xa_type,type,
v_xa: $i ).
thf(v_k_type,type,
v_k: $i > $i > $i ).
thf(c_HOL_Oabs_type,type,
c_HOL_Oabs: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(2,negated_conjecture,
! [A: $i] : ( c_lessequals @ c_0 @ ( v_h @ A ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(10,plain,
! [A: $i] : ( c_lessequals @ c_0 @ ( v_h @ A ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(20,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( v_l @ A @ B ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(9,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( v_l @ A @ B ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(22,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(12,plain,
class_Ring__and__Field_Oordered__idom @ t_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ~ ( c_lessequals @ c_0 @ C @ A )
| ( c_lessequals @ c_0 @ ( c_times @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ~ ( c_lessequals @ c_0 @ C @ A )
| ( c_lessequals @ c_0 @ ( c_times @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,negated_conjecture,
( ( c_times @ ( v_l @ v_x @ v_xa ) @ ( v_h @ ( v_k @ v_x @ v_xa ) ) @ t_b )
!= ( c_HOL_Oabs @ ( c_times @ ( v_l @ v_x @ v_xa ) @ ( v_h @ ( v_k @ v_x @ v_xa ) ) @ t_b ) @ t_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(11,plain,
( ( c_times @ ( v_l @ v_x @ v_xa ) @ ( v_h @ ( v_k @ v_x @ v_xa ) ) @ t_b )
!= ( c_HOL_Oabs @ ( c_times @ ( v_l @ v_x @ v_xa ) @ ( v_h @ ( v_k @ v_x @ v_xa ) ) @ t_b ) @ t_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_HOL_Oabs @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_HOL_Oabs @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[10,20,9,22,12,18,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA044-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 17:56:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (108ms).
% 1.19/0.97 % [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.
% 1.56/1.16 % [INFO] Scanning for conjecture ...
% 1.67/1.21 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.67/1.23 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.88/1.24 % [INFO] Problem is propositional (TPTP CNF).
% 1.88/1.24 % [INFO] Type checking passed.
% 1.88/1.24 % [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 ...
% 2.46/1.52 % External prover 'e' found a proof!
% 2.46/1.52 % [INFO] Killing All external provers ...
% 2.46/1.52 % Time passed: 990ms (effective reasoning time: 550ms)
% 2.46/1.52 % 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)>
% 2.46/1.52 % Axioms used in derivation (4): clsrel_Ring__and__Field_Oordered__idom_40, clsrel_Ring__and__Field_Oordered__idom_50, cls_Ring__and__Field_Omult__nonneg__nonneg_0, cls_OrderedGroup_Oabs__of__nonneg_0
% 2.46/1.52 % No. of inferences in proof: 17
% 2.46/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 990 ms resp. 550 ms w/o parsing
% 2.76/1.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.76/1.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------