TSTP Solution File: ANA029-2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA029-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 10:08:54 EDT 2023
% Result : Unsatisfiable 2.72s 1.58s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 30
% Syntax : Number of formulae : 45 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 67 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 274 ( 40 ~; 38 |; 0 &; 196 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_type,type,
c_0: $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(v_k_type,type,
v_k: $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(c_Orderings_Omax_type,type,
c_Orderings_Omax: $i > $i > $i > $i ).
thf(c_HOL_Oabs_type,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_g_type,type,
v_g: $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_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,negated_conjecture,
~ ( c_lessequals @ ( c_Orderings_Omax @ ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ c_0 @ t_b ) @ ( c_HOL_Oabs @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(16,plain,
~ ( c_lessequals @ ( c_Orderings_Omax @ ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ c_0 @ t_b ) @ ( c_HOL_Oabs @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
~ ( c_lessequals @ c_0 @ ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(15,plain,
~ ( c_lessequals @ c_0 @ ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,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(38,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)],[13]) ).
thf(3,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(17,plain,
class_Ring__and__Field_Oordered__idom @ t_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
thf(32,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)],[10]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
thf(34,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,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(40,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)],[14]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_less @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_less @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Orderings_Olinorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
thf(36,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Orderings_Olinorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
thf(30,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)],[9]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[24,20,22,16,15,28,38,17,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA029-2 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n002.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 18:09:20 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.97 % [INFO] Parsing done (126ms).
% 1.26/0.98 % [INFO] Running in sequential loop mode.
% 1.63/1.18 % [INFO] eprover registered as external prover.
% 1.63/1.18 % [INFO] cvc4 registered as external prover.
% 1.73/1.18 % [INFO] Scanning for conjecture ...
% 1.85/1.24 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.90/1.26 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.90/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.90/1.27 % [INFO] Type checking passed.
% 1.90/1.28 % [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 ...
% 2.72/1.58 % External prover 'e' found a proof!
% 2.72/1.58 % [INFO] Killing All external provers ...
% 2.72/1.58 % Time passed: 1054ms (effective reasoning time: 596ms)
% 2.72/1.58 % 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)>
% 2.72/1.58 % Axioms used in derivation (11): cls_OrderedGroup_Odiff__le__0__iff__le_0, cls_OrderedGroup_Oabs__ge__zero_0, cls_OrderedGroup_Odiff__le__0__iff__le_1, clsrel_OrderedGroup_Opordered__ab__group__add_10, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_Orderings_Oorder__less__imp__le_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_Orderings_Olinorder__not__le_0, cls_Orderings_Oorder__class_Oorder__trans_0, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_Ring__and__Field_Oordered__idom_33
% 2.72/1.58 % No. of inferences in proof: 29
% 2.72/1.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1054 ms resp. 596 ms w/o parsing
% 2.72/1.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.72/1.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------