TSTP Solution File: ANA010-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ANA010-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n006.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 : Wed Aug 30 17:13:16 EDT 2023
% Result : Unsatisfiable 1.53s 1.63s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA010-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 18:13:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 1.53/1.62 %-------------------------------------------
% 1.53/1.62 % File :CSE---1.6
% 1.53/1.62 % Problem :theBenchmark
% 1.53/1.62 % Transform :cnf
% 1.53/1.62 % Format :tptp:raw
% 1.53/1.62 % Command :java -jar mcs_scs.jar %d %s
% 1.53/1.62
% 1.53/1.62 % Result :Theorem 0.990000s
% 1.53/1.62 % Output :CNFRefutation 0.990000s
% 1.53/1.62 %-------------------------------------------
% 1.53/1.63 %------------------------------------------------------------------------------
% 1.53/1.63 % File : ANA010-2 : TPTP v8.1.2. Released v3.2.0.
% 1.53/1.63 % Domain : Analysis
% 1.53/1.63 % Problem : Problem about Big-O notation
% 1.53/1.63 % Version : [Pau06] axioms : Reduced > Especial.
% 1.53/1.63 % English :
% 1.53/1.63
% 1.53/1.63 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 1.53/1.63 % Source : [Pau06]
% 1.53/1.63 % Names :
% 1.53/1.63
% 1.53/1.63 % Status : Unsatisfiable
% 1.53/1.63 % Rating : 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v5.0.0, 0.14 v4.1.0, 0.11 v4.0.1, 0.17 v3.3.0, 0.29 v3.2.0
% 1.53/1.63 % Syntax : Number of clauses : 9 ( 4 unt; 0 nHn; 6 RR)
% 1.53/1.63 % Number of literals : 17 ( 2 equ; 9 neg)
% 1.53/1.63 % Maximal clause size : 4 ( 1 avg)
% 1.53/1.63 % Maximal term depth : 5 ( 1 avg)
% 1.53/1.63 % Number of predicates : 5 ( 4 usr; 0 prp; 1-3 aty)
% 1.53/1.63 % Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% 1.53/1.63 % Number of variables : 14 ( 1 sgn)
% 1.53/1.63 % SPC : CNF_UNS_RFO_SEQ_HRN
% 1.53/1.63
% 1.53/1.63 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 1.53/1.63 % of which only a small selection are required for the refutation.
% 1.53/1.63 % The mission is to find those few axioms, after which a refutation
% 1.53/1.63 % can be quite easily found. This version has only the necessary
% 1.53/1.63 % axioms.
% 1.53/1.63 %------------------------------------------------------------------------------
% 1.53/1.63 cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
% 1.53/1.63 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
% 1.53/1.63 | ~ c_lessequals(c_0,V_y,T_a)
% 1.53/1.63 | c_HOL_Oabs(V_y,T_a) = V_y ) ).
% 1.53/1.63
% 1.53/1.63 cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
% 1.53/1.63 ( ~ class_Orderings_Oorder(T_a)
% 1.53/1.63 | ~ c_lessequals(V_y,V_z,T_a)
% 1.53/1.63 | ~ c_lessequals(V_x,V_y,T_a)
% 1.53/1.63 | c_lessequals(V_x,V_z,T_a) ) ).
% 1.53/1.63
% 1.53/1.63 cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
% 1.53/1.63 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 1.53/1.63 | c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ).
% 1.53/1.63
% 1.53/1.63 cnf(cls_conjecture_0,negated_conjecture,
% 1.53/1.63 c_lessequals(c_0,v_f(V_U),t_b) ).
% 1.53/1.63
% 1.53/1.63 cnf(cls_conjecture_1,negated_conjecture,
% 1.53/1.63 c_lessequals(v_f(V_U),c_times(v_c,v_g(V_U),t_b),t_b) ).
% 1.53/1.63
% 1.53/1.63 cnf(cls_conjecture_2,negated_conjecture,
% 1.53/1.63 ~ c_lessequals(v_f(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b) ).
% 1.53/1.63
% 1.53/1.63 cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
% 1.53/1.63 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
% 1.53/1.63 | class_Orderings_Oorder(T) ) ).
% 1.53/1.63
% 1.53/1.63 cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
% 1.53/1.63 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 1.53/1.63 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ).
% 1.53/1.63
% 1.53/1.63 cnf(tfree_tcs,negated_conjecture,
% 1.53/1.63 class_Ring__and__Field_Oordered__idom(t_b) ).
% 1.53/1.63
% 1.53/1.63 %------------------------------------------------------------------------------
% 1.53/1.63 %-------------------------------------------
% 1.53/1.63 % Proof found
% 1.53/1.63 % SZS status Theorem for theBenchmark
% 1.53/1.63 % SZS output start Proof
% 1.53/1.63 %ClaNum:26(EqnAxiom:17)
% 1.53/1.63 %VarNum:36(SingletonVarNum:14)
% 1.53/1.63 %MaxLitNum:4
% 1.53/1.63 %MaxfuncDepth:4
% 1.53/1.63 %SharedTerms:4
% 1.53/1.63 %goalClause: 18 19 20 21
% 1.53/1.63 %singleGoalClaCount:4
% 1.53/1.63 [18]P1(a1)
% 1.53/1.63 [19]P2(a2,f5(x191),a1)
% 1.53/1.63 [20]P2(f5(x201),f3(a6,f7(x201),a1),a1)
% 1.53/1.63 [21]~P2(f5(f8(x211)),f3(x211,f4(f7(f8(x211)),a1),a1),a1)
% 1.53/1.63 [22]~P1(x221)+P3(x221)
% 1.53/1.63 [23]~P3(x231)+P4(x231)
% 1.53/1.63 [25]~P1(x252)+E(f3(f4(x251,x252),f4(x253,x252),x252),f4(f3(x251,x253,x252),x252))
% 1.53/1.63 [24]~P3(x242)+~P2(a2,x241,x242)+E(f4(x241,x242),x241)
% 1.53/1.63 [26]~P4(x263)+~P2(x264,x262,x263)+P2(x261,x262,x263)+~P2(x261,x264,x263)
% 1.53/1.63 %EqnAxiom
% 1.53/1.63 [1]E(x11,x11)
% 1.53/1.63 [2]E(x22,x21)+~E(x21,x22)
% 1.53/1.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.53/1.63 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 1.53/1.63 [5]~E(x51,x52)+E(f4(x51,x53),f4(x52,x53))
% 1.53/1.63 [6]~E(x61,x62)+E(f4(x63,x61),f4(x63,x62))
% 1.53/1.63 [7]~E(x71,x72)+E(f7(x71),f7(x72))
% 1.53/1.63 [8]~E(x81,x82)+E(f3(x81,x83,x84),f3(x82,x83,x84))
% 1.53/1.63 [9]~E(x91,x92)+E(f3(x93,x91,x94),f3(x93,x92,x94))
% 1.53/1.63 [10]~E(x101,x102)+E(f3(x103,x104,x101),f3(x103,x104,x102))
% 1.53/1.63 [11]~E(x111,x112)+E(f8(x111),f8(x112))
% 1.53/1.63 [12]~P1(x121)+P1(x122)+~E(x121,x122)
% 1.53/1.63 [13]P2(x132,x133,x134)+~E(x131,x132)+~P2(x131,x133,x134)
% 1.53/1.63 [14]P2(x143,x142,x144)+~E(x141,x142)+~P2(x143,x141,x144)
% 1.53/1.63 [15]P2(x153,x154,x152)+~E(x151,x152)+~P2(x153,x154,x151)
% 1.53/1.63 [16]~P4(x161)+P4(x162)+~E(x161,x162)
% 1.53/1.63 [17]~P3(x171)+P3(x172)+~E(x171,x172)
% 1.53/1.63
% 1.53/1.63 %-------------------------------------------
% 1.53/1.63 cnf(27,plain,
% 1.53/1.63 (P3(a1)),
% 1.53/1.63 inference(scs_inference,[],[18,22])).
% 1.53/1.63 cnf(28,plain,
% 1.53/1.63 (E(f3(f4(x281,a1),f4(x282,a1),a1),f4(f3(x281,x282,a1),a1))),
% 1.53/1.63 inference(scs_inference,[],[18,22,25])).
% 1.53/1.63 cnf(30,plain,
% 1.53/1.63 (E(f4(f5(x301),a1),f5(x301))),
% 1.53/1.63 inference(scs_inference,[],[18,19,22,25,17,24])).
% 1.53/1.63 cnf(32,plain,
% 1.53/1.63 (E(f4(f3(x321,x322,a1),a1),f3(f4(x321,a1),f4(x322,a1),a1))),
% 1.53/1.63 inference(scs_inference,[],[18,19,22,25,17,24,2])).
% 1.53/1.63 cnf(42,plain,
% 1.53/1.63 (P4(a1)),
% 1.53/1.63 inference(scs_inference,[],[27,23])).
% 1.53/1.63 cnf(47,plain,
% 1.53/1.63 (E(f3(f4(f5(x471),a1),x472,x473),f3(f5(x471),x472,x473))),
% 1.53/1.63 inference(scs_inference,[],[30,27,23,11,10,9,8])).
% 1.53/1.63 cnf(49,plain,
% 1.53/1.63 (E(f4(x491,f4(f5(x492),a1)),f4(x491,f5(x492)))),
% 1.53/1.63 inference(scs_inference,[],[30,27,23,11,10,9,8,7,6])).
% 1.53/1.63 cnf(53,plain,
% 1.53/1.63 (P2(f5(x531),f3(a6,f7(x531),a1),a1)),
% 1.53/1.63 inference(rename_variables,[],[20])).
% 1.53/1.63 cnf(54,plain,
% 1.53/1.63 (E(f4(f4(f5(x541),a1),a1),f5(x541))),
% 1.53/1.63 inference(scs_inference,[],[20,30,27,23,11,10,9,8,7,6,5,4,13,3])).
% 1.53/1.64 cnf(56,plain,
% 1.53/1.64 (P2(a2,f3(a6,f7(x561),a1),a1)),
% 1.53/1.64 inference(scs_inference,[],[20,53,19,30,27,23,11,10,9,8,7,6,5,4,13,3,16,26])).
% 1.53/1.64 cnf(75,plain,
% 1.53/1.64 (E(f3(f5(x751),x752,x753),f3(f4(f5(x751),a1),x752,x753))),
% 1.53/1.64 inference(scs_inference,[],[47,2])).
% 1.53/1.64 cnf(76,plain,
% 1.53/1.64 (E(f4(f3(a6,f7(x761),a1),a1),f3(a6,f7(x761),a1))),
% 1.53/1.64 inference(scs_inference,[],[27,47,56,2,24])).
% 1.53/1.64 cnf(84,plain,
% 1.53/1.64 (E(f3(x841,f3(f4(x842,a1),f4(x843,a1),a1),x844),f3(x841,f4(f3(x842,x843,a1),a1),x844))),
% 1.53/1.64 inference(scs_inference,[],[28,11,10,8,7,6,9])).
% 1.53/1.64 cnf(108,plain,
% 1.53/1.64 (E(f5(x1081),f4(f5(x1081),a1))),
% 1.53/1.64 inference(scs_inference,[],[32,30,17,2])).
% 1.53/1.64 cnf(115,plain,
% 1.53/1.64 (E(f3(x1151,x1152,f4(f3(x1153,x1154,a1),a1)),f3(x1151,x1152,f3(f4(x1153,a1),f4(x1154,a1),a1)))),
% 1.53/1.64 inference(scs_inference,[],[32,10])).
% 1.53/1.64 cnf(122,plain,
% 1.53/1.64 (E(f4(f4(f3(x1221,x1222,a1),a1),x1223),f4(f3(f4(x1221,a1),f4(x1222,a1),a1),x1223))),
% 1.53/1.64 inference(scs_inference,[],[32,10,8,6,16,11,9,7,5])).
% 1.53/1.64 cnf(130,plain,
% 1.53/1.64 (P2(a2,f4(f5(x1301),a1),a1)),
% 1.53/1.64 inference(scs_inference,[],[49,108,19,2,14])).
% 1.53/1.64 cnf(131,plain,
% 1.53/1.64 (E(f5(x1311),f4(f5(x1311),a1))),
% 1.53/1.64 inference(rename_variables,[],[108])).
% 1.53/1.64 cnf(132,plain,
% 1.53/1.64 (P2(f4(f5(x1321),a1),f3(a6,f7(x1321),a1),a1)),
% 1.53/1.64 inference(scs_inference,[],[49,108,131,20,19,2,14,13])).
% 1.53/1.64 cnf(156,plain,
% 1.53/1.64 (E(f3(x1561,x1562,f4(f4(f5(x1563),a1),a1)),f3(x1561,x1562,f5(x1563)))),
% 1.53/1.64 inference(scs_inference,[],[42,32,122,54,130,3,8,6,26,11,10])).
% 1.53/1.64 cnf(178,plain,
% 1.53/1.64 (E(f4(f5(x1781),x1782),f4(f4(f5(x1781),a1),x1782))),
% 1.53/1.64 inference(scs_inference,[],[108,10,9,7,5])).
% 1.53/1.64 cnf(194,plain,
% 1.53/1.64 (P2(f4(f4(f5(x1941),a1),a1),f3(a6,f7(x1941),a1),a1)),
% 1.53/1.64 inference(scs_inference,[],[178,132,13])).
% 1.53/1.64 cnf(200,plain,
% 1.53/1.64 (P2(f4(f4(f5(x2001),a1),a1),x2002,a1)+~E(f3(a6,f7(x2001),a1),x2002)),
% 1.53/1.64 inference(scs_inference,[],[156,194,2,14])).
% 1.53/1.64 cnf(277,plain,
% 1.53/1.64 (E(f5(x2771),f4(f4(f5(x2771),a1),a1))),
% 1.53/1.64 inference(scs_inference,[],[54,84,115,3,2])).
% 1.53/1.64 cnf(279,plain,
% 1.53/1.64 (E(f3(x2791,f5(x2792),x2793),f3(x2791,f4(f4(f5(x2792),a1),a1),x2793))),
% 1.53/1.64 inference(scs_inference,[],[277,11,9])).
% 1.53/1.64 cnf(302,plain,
% 1.53/1.64 (P2(f4(f4(f5(x3021),a1),a1),f4(f3(a6,f7(x3021),a1),a1),a1)),
% 1.53/1.64 inference(scs_inference,[],[76,75,279,2,3,200])).
% 1.53/1.64 cnf(326,plain,
% 1.53/1.64 (P2(f5(x3261),f4(f3(a6,f7(x3261),a1),a1),a1)),
% 1.53/1.64 inference(scs_inference,[],[302,54,13])).
% 1.53/1.64 cnf(331,plain,
% 1.53/1.64 ($false),
% 1.53/1.64 inference(scs_inference,[],[326,21,32,14]),
% 1.53/1.64 ['proof']).
% 1.53/1.64 % SZS output end Proof
% 1.53/1.64 % Total time :0.990000s
%------------------------------------------------------------------------------