TSTP Solution File: ANA034-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ANA034-2 : 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 : n001.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 17:13:24 EDT 2023
% Result : Unsatisfiable 0.24s 0.76s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : ANA034-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.16 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.17/0.37 % Computer : n001.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Fri Aug 25 19:05:59 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.24/0.63 start to proof:theBenchmark
% 0.24/0.75 %-------------------------------------------
% 0.24/0.75 % File :CSE---1.6
% 0.24/0.75 % Problem :theBenchmark
% 0.24/0.75 % Transform :cnf
% 0.24/0.75 % Format :tptp:raw
% 0.24/0.75 % Command :java -jar mcs_scs.jar %d %s
% 0.24/0.75
% 0.24/0.75 % Result :Theorem 0.080000s
% 0.24/0.75 % Output :CNFRefutation 0.080000s
% 0.24/0.75 %-------------------------------------------
% 0.24/0.75 %------------------------------------------------------------------------------
% 0.24/0.75 % File : ANA034-2 : TPTP v8.1.2. Released v3.2.0.
% 0.24/0.75 % Domain : Analysis
% 0.24/0.75 % Problem : Problem about Big-O notation
% 0.24/0.75 % Version : [Pau06] axioms : Reduced > Especial.
% 0.24/0.75 % English :
% 0.24/0.75
% 0.24/0.75 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.24/0.75 % Source : [Pau06]
% 0.24/0.75 % Names :
% 0.24/0.75
% 0.24/0.75 % Status : Unsatisfiable
% 0.24/0.76 % Rating : 0.00 v7.3.0, 0.11 v7.2.0, 0.00 v6.0.0, 0.33 v5.5.0, 0.38 v5.4.0, 0.33 v5.3.0, 0.42 v5.2.0, 0.25 v5.1.0, 0.14 v4.1.0, 0.11 v4.0.1, 0.17 v4.0.0, 0.33 v3.5.0, 0.17 v3.3.0, 0.29 v3.2.0
% 0.24/0.76 % Syntax : Number of clauses : 15 ( 6 unt; 0 nHn; 13 RR)
% 0.24/0.76 % Number of literals : 31 ( 2 equ; 17 neg)
% 0.24/0.76 % Maximal clause size : 6 ( 2 avg)
% 0.24/0.76 % Maximal term depth : 5 ( 2 avg)
% 0.24/0.76 % Number of predicates : 8 ( 7 usr; 0 prp; 1-3 aty)
% 0.24/0.76 % Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% 0.24/0.76 % Number of variables : 20 ( 1 sgn)
% 0.24/0.76 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.24/0.76
% 0.24/0.76 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.24/0.76 % of which only a small selection are required for the refutation.
% 0.24/0.76 % The mission is to find those few axioms, after which a refutation
% 0.24/0.76 % can be quite easily found. This version has only the necessary
% 0.24/0.76 % axioms.
% 0.24/0.76 %------------------------------------------------------------------------------
% 0.24/0.76 cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
% 0.24/0.76 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.24/0.76 | 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) ) ).
% 0.24/0.76
% 0.24/0.76 cnf(cls_Ring__and__Field_Omult__mono_0,axiom,
% 0.24/0.76 ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
% 0.24/0.76 | ~ c_lessequals(V_c,V_d,T_a)
% 0.24/0.76 | ~ c_lessequals(V_a,V_b,T_a)
% 0.24/0.76 | ~ c_lessequals(c_0,V_c,T_a)
% 0.24/0.76 | ~ c_lessequals(c_0,V_b,T_a)
% 0.24/0.76 | c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a) ) ).
% 0.24/0.76
% 0.24/0.76 cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
% 0.24/0.76 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
% 0.24/0.76 | ~ c_lessequals(c_0,V_b,T_a)
% 0.24/0.76 | ~ c_lessequals(c_0,V_a,T_a)
% 0.24/0.76 | c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) ).
% 0.24/0.76
% 0.24/0.76 cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
% 0.24/0.76 ( ~ class_Orderings_Oorder(T_a)
% 0.24/0.76 | ~ c_less(V_x,V_y,T_a)
% 0.24/0.76 | c_lessequals(V_x,V_y,T_a) ) ).
% 0.24/0.76
% 0.24/0.76 cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
% 0.24/0.76 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
% 0.24/0.76 | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ).
% 0.24/0.76
% 0.24/0.76 cnf(cls_conjecture_0,negated_conjecture,
% 0.24/0.76 c_less(c_0,v_c,t_b) ).
% 0.24/0.76
% 0.24/0.76 cnf(cls_conjecture_2,negated_conjecture,
% 0.24/0.76 c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ).
% 0.24/0.76
% 0.24/0.76 cnf(cls_conjecture_3,negated_conjecture,
% 0.24/0.76 c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ).
% 0.24/0.76
% 0.24/0.76 cnf(cls_conjecture_4,negated_conjecture,
% 0.24/0.76 c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ).
% 0.24/0.76
% 0.24/0.76 cnf(cls_conjecture_5,negated_conjecture,
% 0.24/0.76 ~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) ).
% 0.24/0.76
% 0.24/0.76 cnf(tfree_tcs,negated_conjecture,
% 0.24/0.76 class_Ring__and__Field_Oordered__idom(t_b) ).
% 0.24/0.76
% 0.24/0.76 cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
% 0.24/0.76 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
% 0.24/0.76 | class_Orderings_Oorder(T) ) ).
% 0.24/0.76
% 0.24/0.76 cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
% 0.24/0.76 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.24/0.76 | class_Ring__and__Field_Opordered__cancel__semiring(T) ) ).
% 0.24/0.76
% 0.24/0.76 cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
% 0.24/0.76 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.24/0.76 | class_Ring__and__Field_Opordered__semiring(T) ) ).
% 0.24/0.76
% 0.24/0.76 cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
% 0.24/0.76 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.24/0.76 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ).
% 0.24/0.76
% 0.24/0.76 %------------------------------------------------------------------------------
% 0.24/0.76 %-------------------------------------------
% 0.24/0.76 % Proof found
% 0.24/0.76 % SZS status Theorem for theBenchmark
% 0.24/0.76 % SZS output start Proof
% 0.24/0.76 %ClaNum:38(EqnAxiom:23)
% 0.24/0.76 %VarNum:56(SingletonVarNum:20)
% 0.24/0.76 %MaxLitNum:6
% 0.24/0.76 %MaxfuncDepth:4
% 0.24/0.76 %SharedTerms:28
% 0.24/0.76 %goalClause: 24 25 26 27 28 29
% 0.24/0.76 %singleGoalClaCount:6
% 0.24/0.76 [24]P1(a1)
% 0.24/0.76 [25]P2(a2,a5,a1)
% 0.24/0.76 [26]P3(f3(f6(a8),a1),f4(a5,f3(f9(a8),a1),a1),a1)
% 0.24/0.76 [27]P3(f3(f7(a8),a1),f4(a10,f3(f11(a8),a1),a1),a1)
% 0.24/0.76 [28]E(f4(f4(a5,f3(f9(a8),a1),a1),f4(a10,f3(f11(a8),a1),a1),a1),f4(f4(a5,a10,a1),f3(f4(f9(a8),f11(a8),a1),a1),a1))
% 0.24/0.76 [29]~P3(f3(f4(f6(a8),f7(a8),a1),a1),f4(f4(a5,a10,a1),f3(f4(f9(a8),f11(a8),a1),a1),a1),a1)
% 0.24/0.76 [30]~P1(x301)+P6(x301)
% 0.24/0.76 [31]~P1(x311)+P7(x311)
% 0.24/0.76 [32]~P5(x321)+P4(x321)
% 0.24/0.76 [33]~P1(x331)+P5(x331)
% 0.24/0.76 [34]~P5(x342)+P3(a2,f3(x341,x342),x342)
% 0.24/0.76 [36]~P1(x362)+E(f4(f3(x361,x362),f3(x363,x362),x362),f3(f4(x361,x363,x362),x362))
% 0.24/0.76 [35]~P4(x353)+~P2(x351,x352,x353)+P3(x351,x352,x353)
% 0.24/0.76 [37]~P7(x373)+~P3(a2,x371,x373)+~P3(a2,x372,x373)+P3(a2,f4(x371,x372,x373),x373)
% 0.24/0.76 [38]~P6(x383)+~P3(x381,x384,x383)+~P3(x382,x385,x383)+~P3(a2,x384,x383)+~P3(a2,x382,x383)+P3(f4(x381,x382,x383),f4(x384,x385,x383),x383)
% 0.24/0.76 %EqnAxiom
% 0.24/0.76 [1]E(x11,x11)
% 0.24/0.76 [2]E(x22,x21)+~E(x21,x22)
% 0.24/0.76 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.24/0.76 [4]~E(x41,x42)+E(f6(x41),f6(x42))
% 0.24/0.76 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 0.24/0.76 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 0.24/0.76 [7]~E(x71,x72)+E(f9(x71),f9(x72))
% 0.24/0.76 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84))
% 0.24/0.76 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94))
% 0.24/0.76 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102))
% 0.24/0.76 [11]~E(x111,x112)+E(f7(x111),f7(x112))
% 0.24/0.76 [12]~E(x121,x122)+E(f11(x121),f11(x122))
% 0.24/0.76 [13]~P1(x131)+P1(x132)+~E(x131,x132)
% 0.24/0.76 [14]P2(x142,x143,x144)+~E(x141,x142)+~P2(x141,x143,x144)
% 0.24/0.76 [15]P2(x153,x152,x154)+~E(x151,x152)+~P2(x153,x151,x154)
% 0.24/0.76 [16]P2(x163,x164,x162)+~E(x161,x162)+~P2(x163,x164,x161)
% 0.24/0.76 [17]P3(x172,x173,x174)+~E(x171,x172)+~P3(x171,x173,x174)
% 0.24/0.76 [18]P3(x183,x182,x184)+~E(x181,x182)+~P3(x183,x181,x184)
% 0.24/0.76 [19]P3(x193,x194,x192)+~E(x191,x192)+~P3(x193,x194,x191)
% 0.24/0.76 [20]~P7(x201)+P7(x202)+~E(x201,x202)
% 0.24/0.76 [21]~P6(x211)+P6(x212)+~E(x211,x212)
% 0.24/0.76 [22]~P5(x221)+P5(x222)+~E(x221,x222)
% 0.24/0.76 [23]~P4(x231)+P4(x232)+~E(x231,x232)
% 0.24/0.76
% 0.24/0.76 %-------------------------------------------
% 0.24/0.76 cnf(40,plain,
% 0.24/0.76 (P5(a1)),
% 0.24/0.76 inference(scs_inference,[],[24,28,2,33])).
% 0.24/0.76 cnf(42,plain,
% 0.24/0.76 (P4(a1)),
% 0.24/0.76 inference(scs_inference,[],[24,28,2,33,32])).
% 0.24/0.76 cnf(44,plain,
% 0.24/0.76 (P7(a1)),
% 0.24/0.76 inference(scs_inference,[],[24,28,2,33,32,31])).
% 0.24/0.76 cnf(46,plain,
% 0.24/0.76 (P6(a1)),
% 0.24/0.76 inference(scs_inference,[],[24,28,2,33,32,31,30])).
% 0.24/0.76 cnf(48,plain,
% 0.24/0.76 (P3(a2,f3(x481,a1),a1)),
% 0.24/0.76 inference(scs_inference,[],[24,28,2,33,32,31,30,34])).
% 0.24/0.76 cnf(50,plain,
% 0.24/0.76 (E(f4(f3(x501,a1),f3(x502,a1),a1),f3(f4(x501,x502,a1),a1))),
% 0.24/0.76 inference(scs_inference,[],[24,28,2,33,32,31,30,34,36])).
% 0.24/0.76 cnf(54,plain,
% 0.24/0.76 (~P3(f4(f3(f6(a8),a1),f3(f7(a8),a1),a1),f4(f4(a5,a10,a1),f3(f4(f9(a8),f11(a8),a1),a1),a1),a1)),
% 0.24/0.76 inference(scs_inference,[],[24,29,28,2,33,32,31,30,34,36,23,18,17])).
% 0.24/0.76 cnf(55,plain,
% 0.24/0.76 (P3(a2,a5,a1)),
% 0.24/0.76 inference(scs_inference,[],[24,25,29,28,2,33,32,31,30,34,36,23,18,17,35])).
% 0.24/0.76 cnf(57,plain,
% 0.24/0.76 (P3(a2,f4(f3(x571,a1),f3(x571,a1),a1),a1)),
% 0.24/0.76 inference(scs_inference,[],[24,25,29,28,2,33,32,31,30,34,36,23,18,17,35,37])).
% 0.24/0.76 cnf(71,plain,
% 0.24/0.76 (E(f4(f4(f3(x711,a1),f3(x712,a1),a1),x713,x714),f4(f3(f4(x711,x712,a1),a1),x713,x714))),
% 0.24/0.76 inference(scs_inference,[],[50,12,11,10,9,8])).
% 0.24/0.76 cnf(81,plain,
% 0.24/0.76 (~P2(f3(f4(f6(a8),f7(a8),a1),a1),f4(f4(a5,a10,a1),f3(f4(f9(a8),f11(a8),a1),a1),a1),a1)),
% 0.24/0.76 inference(scs_inference,[],[29,50,57,40,42,44,12,11,10,9,8,7,6,5,4,37,18,3,22,35])).
% 0.24/0.76 cnf(86,plain,
% 0.24/0.76 (P3(f4(a2,f3(f6(a8),a1),a1),f4(f4(f3(x861,a1),f3(x861,a1),a1),f4(a5,f3(f9(a8),a1),a1),a1),a1)),
% 0.24/0.76 inference(scs_inference,[],[26,25,29,28,50,57,48,40,42,44,46,12,11,10,9,8,7,6,5,4,37,18,3,22,35,14,16,15,38])).
% 0.24/0.76 cnf(105,plain,
% 0.24/0.76 (~P2(f4(f3(f6(a8),a1),f3(f7(a8),a1),a1),f4(f4(a5,a10,a1),f3(f4(f9(a8),f11(a8),a1),a1),a1),a1)),
% 0.24/0.76 inference(scs_inference,[],[27,28,71,55,81,86,48,44,46,50,37,38,15,18,21,14])).
% 0.24/0.76 cnf(118,plain,
% 0.24/0.76 (~P3(a2,f4(a5,f3(f9(a8),a1),a1),a1)),
% 0.24/0.76 inference(scs_inference,[],[26,27,28,105,54,48,44,46,18,15,20,38])).
% 0.24/0.76 cnf(192,plain,
% 0.24/0.76 ($false),
% 0.24/0.76 inference(scs_inference,[],[118,55,48,44,37]),
% 0.24/0.76 ['proof']).
% 0.24/0.76 % SZS output end Proof
% 0.24/0.76 % Total time :0.080000s
%------------------------------------------------------------------------------