TSTP Solution File: ANA015-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ANA015-2 : 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 : n031.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 17:13:18 EDT 2023
% Result : Unsatisfiable 1.63s 1.72s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : ANA015-2 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 19:07:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 1.63/1.71 %-------------------------------------------
% 1.63/1.71 % File :CSE---1.6
% 1.63/1.71 % Problem :theBenchmark
% 1.63/1.71 % Transform :cnf
% 1.63/1.71 % Format :tptp:raw
% 1.63/1.71 % Command :java -jar mcs_scs.jar %d %s
% 1.63/1.71
% 1.63/1.71 % Result :Theorem 1.060000s
% 1.63/1.71 % Output :CNFRefutation 1.060000s
% 1.63/1.71 %-------------------------------------------
% 1.63/1.71 %------------------------------------------------------------------------------
% 1.63/1.71 % File : ANA015-2 : TPTP v8.1.2. Released v3.2.0.
% 1.63/1.71 % Domain : Analysis
% 1.63/1.71 % Problem : Problem about Big-O notation
% 1.63/1.71 % Version : [Pau06] axioms : Reduced > Especial.
% 1.63/1.71 % English :
% 1.63/1.71
% 1.63/1.71 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 1.63/1.71 % Source : [Pau06]
% 1.63/1.71 % Names :
% 1.63/1.71
% 1.63/1.71 % Status : Unsatisfiable
% 1.63/1.71 % Rating : 0.08 v8.1.0, 0.00 v7.5.0, 0.10 v7.4.0, 0.22 v7.3.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.14 v6.3.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.07 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.17 v3.3.0, 0.29 v3.2.0
% 1.63/1.71 % Syntax : Number of clauses : 12 ( 3 unt; 0 nHn; 8 RR)
% 1.63/1.71 % Number of literals : 23 ( 2 equ; 12 neg)
% 1.63/1.71 % Maximal clause size : 4 ( 1 avg)
% 1.63/1.71 % Maximal term depth : 5 ( 1 avg)
% 1.63/1.71 % Number of predicates : 8 ( 7 usr; 0 prp; 1-3 aty)
% 1.63/1.71 % Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% 1.63/1.71 % Number of variables : 20 ( 1 sgn)
% 1.63/1.71 % SPC : CNF_UNS_RFO_SEQ_HRN
% 1.63/1.71
% 1.63/1.71 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 1.63/1.71 % of which only a small selection are required for the refutation.
% 1.63/1.71 % The mission is to find those few axioms, after which a refutation
% 1.63/1.71 % can be quite easily found. This version has only the necessary
% 1.63/1.71 % axioms.
% 1.63/1.71 %------------------------------------------------------------------------------
% 1.63/1.71 cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
% 1.63/1.71 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
% 1.63/1.71 | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ).
% 1.63/1.71
% 1.63/1.71 cnf(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
% 1.63/1.71 ( ~ class_OrderedGroup_Osemigroup__mult(T_a)
% 1.63/1.71 | c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ).
% 1.63/1.72
% 1.63/1.72 cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
% 1.63/1.72 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 1.63/1.72 | 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) ) ).
% 1.63/1.72
% 1.63/1.72 cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
% 1.63/1.72 ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
% 1.63/1.72 | ~ c_lessequals(V_a,V_b,T_a)
% 1.63/1.72 | ~ c_lessequals(c_0,V_c,T_a)
% 1.63/1.72 | c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) ).
% 1.63/1.72
% 1.63/1.72 cnf(cls_conjecture_1,negated_conjecture,
% 1.63/1.72 c_lessequals(c_HOL_Oabs(v_g(V_U),t_a),c_times(v_d,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a) ).
% 1.63/1.72
% 1.63/1.72 cnf(cls_conjecture_2,negated_conjecture,
% 1.63/1.72 ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(V_U)),t_a),t_a),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a) ).
% 1.63/1.72
% 1.63/1.72 cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
% 1.63/1.72 ( ~ class_Ring__and__Field_Ofield(T)
% 1.63/1.72 | class_OrderedGroup_Osemigroup__mult(T) ) ).
% 1.63/1.72
% 1.63/1.72 cnf(clsrel_Ring__and__Field_Oordered__field_0,axiom,
% 1.63/1.72 ( ~ class_Ring__and__Field_Oordered__field(T)
% 1.63/1.72 | class_Ring__and__Field_Ofield(T) ) ).
% 1.63/1.72
% 1.63/1.72 cnf(clsrel_Ring__and__Field_Oordered__field_34,axiom,
% 1.63/1.72 ( ~ class_Ring__and__Field_Oordered__field(T)
% 1.63/1.72 | class_Ring__and__Field_Oordered__idom(T) ) ).
% 1.63/1.72
% 1.63/1.72 cnf(clsrel_Ring__and__Field_Oordered__field_46,axiom,
% 1.63/1.72 ( ~ class_Ring__and__Field_Oordered__field(T)
% 1.63/1.72 | class_Ring__and__Field_Opordered__semiring(T) ) ).
% 1.63/1.72
% 1.63/1.72 cnf(clsrel_Ring__and__Field_Oordered__field_47,axiom,
% 1.63/1.72 ( ~ class_Ring__and__Field_Oordered__field(T)
% 1.63/1.72 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ).
% 1.63/1.72
% 1.63/1.72 cnf(tfree_tcs,negated_conjecture,
% 1.63/1.72 class_Ring__and__Field_Oordered__field(t_a) ).
% 1.63/1.72
% 1.63/1.72 %------------------------------------------------------------------------------
% 1.63/1.72 %-------------------------------------------
% 1.63/1.72 % Proof found
% 1.63/1.72 % SZS status Theorem for theBenchmark
% 1.63/1.72 % SZS output start Proof
% 1.63/1.72 %ClaNum:34(EqnAxiom:22)
% 1.63/1.72 %VarNum:53(SingletonVarNum:20)
% 1.63/1.72 %MaxLitNum:4
% 1.63/1.72 %MaxfuncDepth:4
% 1.63/1.72 %SharedTerms:6
% 1.63/1.72 %goalClause: 23 24 25
% 1.63/1.72 %singleGoalClaCount:3
% 1.63/1.72 [23]P1(a1)
% 1.63/1.72 [24]P2(f2(f6(x241),a1),f4(a7,f2(f9(x241),a1),a1),a1)
% 1.63/1.72 [25]~P2(f2(f4(f5(a8,a1),f6(f10(x251)),a1),a1),f4(x251,f2(f9(f10(x251)),a1),a1),a1)
% 1.63/1.72 [26]~P1(x261)+P3(x261)
% 1.63/1.72 [27]~P5(x271)+P4(x271)
% 1.63/1.72 [28]~P1(x281)+P6(x281)
% 1.63/1.72 [29]~P1(x291)+P7(x291)
% 1.63/1.72 [30]~P1(x301)+P5(x301)
% 1.63/1.72 [31]~P3(x312)+P2(a3,f2(x311,x312),x312)
% 1.63/1.72 [32]~P6(x322)+E(f4(f2(x321,x322),f2(x323,x322),x322),f2(f4(x321,x323,x322),x322))
% 1.63/1.72 [33]~P4(x333)+E(f4(f4(x331,x332,x333),x334,x333),f4(x331,f4(x332,x334,x333),x333))
% 1.63/1.72 [34]~P7(x343)+~P2(x342,x344,x343)+~P2(a3,x341,x343)+P2(f4(x341,x342,x343),f4(x341,x344,x343),x343)
% 1.63/1.72 %EqnAxiom
% 1.63/1.72 [1]E(x11,x11)
% 1.63/1.72 [2]E(x22,x21)+~E(x21,x22)
% 1.63/1.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.63/1.72 [4]~E(x41,x42)+E(f6(x41),f6(x42))
% 1.63/1.72 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53))
% 1.63/1.72 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62))
% 1.63/1.72 [7]~E(x71,x72)+E(f9(x71),f9(x72))
% 1.63/1.72 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84))
% 1.63/1.72 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94))
% 1.63/1.72 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102))
% 1.63/1.72 [11]~E(x111,x112)+E(f10(x111),f10(x112))
% 1.63/1.72 [12]~E(x121,x122)+E(f5(x121,x123),f5(x122,x123))
% 1.63/1.72 [13]~E(x131,x132)+E(f5(x133,x131),f5(x133,x132))
% 1.63/1.72 [14]~P1(x141)+P1(x142)+~E(x141,x142)
% 1.63/1.72 [15]P2(x152,x153,x154)+~E(x151,x152)+~P2(x151,x153,x154)
% 1.63/1.72 [16]P2(x163,x162,x164)+~E(x161,x162)+~P2(x163,x161,x164)
% 1.63/1.72 [17]P2(x173,x174,x172)+~E(x171,x172)+~P2(x173,x174,x171)
% 1.63/1.72 [18]~P4(x181)+P4(x182)+~E(x181,x182)
% 1.63/1.72 [19]~P3(x191)+P3(x192)+~E(x191,x192)
% 1.63/1.72 [20]~P6(x201)+P6(x202)+~E(x201,x202)
% 1.63/1.72 [21]~P5(x211)+P5(x212)+~E(x211,x212)
% 1.63/1.72 [22]~P7(x221)+P7(x222)+~E(x221,x222)
% 1.63/1.72
% 1.63/1.72 %-------------------------------------------
% 1.63/1.72 cnf(41,plain,
% 1.63/1.72 (P7(a1)),
% 1.63/1.72 inference(scs_inference,[],[23,24,25,15,2,30,29])).
% 1.63/1.72 cnf(49,plain,
% 1.63/1.72 (P2(a3,f2(x491,a1),a1)),
% 1.63/1.72 inference(scs_inference,[],[23,24,25,15,2,30,29,28,27,26,31])).
% 1.63/1.72 cnf(51,plain,
% 1.63/1.72 (E(f4(f4(x511,x512,a1),x513,a1),f4(x511,f4(x512,x513,a1),a1))),
% 1.63/1.72 inference(scs_inference,[],[23,24,25,15,2,30,29,28,27,26,31,33])).
% 1.63/1.72 cnf(53,plain,
% 1.63/1.72 (E(f4(f2(x531,a1),f2(x532,a1),a1),f2(f4(x531,x532,a1),a1))),
% 1.63/1.72 inference(scs_inference,[],[23,24,25,15,2,30,29,28,27,26,31,33,32])).
% 1.63/1.72 cnf(72,plain,
% 1.63/1.72 (P2(f4(f2(x721,a1),f2(f6(x722),a1),a1),f4(f2(x721,a1),f4(a7,f2(f9(x722),a1),a1),a1),a1)),
% 1.63/1.72 inference(scs_inference,[],[24,51,49,41,13,12,11,10,9,8,7,6,4,34])).
% 1.63/1.72 cnf(74,plain,
% 1.63/1.72 (E(f4(x741,f4(x742,x743,a1),a1),f4(f4(x741,x742,a1),x743,a1))),
% 1.63/1.72 inference(scs_inference,[],[24,51,49,41,13,12,11,10,9,8,7,6,4,34,2])).
% 1.63/1.72 cnf(76,plain,
% 1.63/1.72 (~P2(f4(f2(f5(a8,a1),a1),f2(f6(f10(x761)),a1),a1),f4(x761,f2(f9(f10(x761)),a1),a1),a1)),
% 1.63/1.72 inference(scs_inference,[],[24,25,51,53,49,41,13,12,11,10,9,8,7,6,4,34,2,5,15])).
% 1.63/1.72 cnf(539,plain,
% 1.63/1.72 ($false),
% 1.63/1.72 inference(scs_inference,[],[72,76,74,16]),
% 1.63/1.72 ['proof']).
% 1.63/1.72 % SZS output end Proof
% 1.63/1.72 % Total time :1.060000s
%------------------------------------------------------------------------------