TSTP Solution File: ANA043-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ANA043-2 : 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 : n003.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 17:13:27 EDT 2023
% Result : Unsatisfiable 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA043-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 18:55:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % File :CSE---1.6
% 0.19/0.63 % Problem :theBenchmark
% 0.19/0.63 % Transform :cnf
% 0.19/0.63 % Format :tptp:raw
% 0.19/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.63
% 0.19/0.63 % Result :Theorem 0.010000s
% 0.19/0.63 % Output :CNFRefutation 0.010000s
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 % File : ANA043-2 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.63 % Domain : Analysis
% 0.19/0.63 % Problem : Problem about Big-O notation
% 0.19/0.63 % Version : [Pau06] axioms : Reduced > Especial.
% 0.19/0.63 % English :
% 0.19/0.63
% 0.19/0.63 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.19/0.63 % Source : [Pau06]
% 0.19/0.63 % Names :
% 0.19/0.63
% 0.19/0.63 % Status : Unsatisfiable
% 0.19/0.63 % Rating : 0.00 v5.5.0, 0.06 v5.4.0, 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v5.0.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.17 v3.3.0, 0.29 v3.2.0
% 0.19/0.63 % Syntax : Number of clauses : 9 ( 3 unt; 0 nHn; 6 RR)
% 0.19/0.63 % Number of literals : 17 ( 1 equ; 9 neg)
% 0.19/0.63 % Maximal clause size : 4 ( 1 avg)
% 0.19/0.63 % Maximal term depth : 7 ( 2 avg)
% 0.19/0.63 % Number of predicates : 6 ( 5 usr; 0 prp; 1-3 aty)
% 0.19/0.63 % Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% 0.19/0.63 % Number of variables : 15 ( 1 sgn)
% 0.19/0.63 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.19/0.63
% 0.19/0.63 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.19/0.63 % of which only a small selection are required for the refutation.
% 0.19/0.63 % The mission is to find those few axioms, after which a refutation
% 0.19/0.63 % can be quite easily found. This version has only the necessary
% 0.19/0.63 % axioms.
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 cnf(cls_conjecture_0,negated_conjecture,
% 0.19/0.63 c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_conjecture_1,negated_conjecture,
% 0.19/0.63 ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b) ).
% 0.19/0.63
% 0.19/0.63 cnf(tfree_tcs,negated_conjecture,
% 0.19/0.63 class_Ring__and__Field_Oordered__idom(t_b) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
% 0.19/0.63 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
% 0.19/0.63 | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_OrderedGroup_Omult__left__commute_0,axiom,
% 0.19/0.63 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
% 0.19/0.63 | c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
% 0.19/0.63 ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
% 0.19/0.63 | ~ c_lessequals(V_a,V_b,T_a)
% 0.19/0.63 | ~ c_lessequals(c_0,V_c,T_a)
% 0.19/0.63 | c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
% 0.19/0.63 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.19/0.63 | class_OrderedGroup_Oab__semigroup__mult(T) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
% 0.19/0.63 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.19/0.63 | class_Ring__and__Field_Opordered__semiring(T) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
% 0.19/0.63 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.19/0.63 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ).
% 0.19/0.63
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 %ClaNum:32(EqnAxiom:23)
% 0.19/0.63 %VarNum:45(SingletonVarNum:15)
% 0.19/0.63 %MaxLitNum:4
% 0.19/0.64 %MaxfuncDepth:6
% 0.19/0.64 %SharedTerms:4
% 0.19/0.64 %goalClause: 24 25 26
% 0.19/0.64 %singleGoalClaCount:3
% 0.19/0.64 [24]P1(a1)
% 0.19/0.64 [25]P2(f2(f5(x251),a1),f4(a6,f2(f7(x251),a1),a1),a1)
% 0.19/0.64 [26]~P2(f4(f2(f9(f8(x261),f11(x261)),a1),f2(f5(f10(f8(x261),f11(x261))),a1),a1),f4(x261,f4(f2(f9(f8(x261),f11(x261)),a1),f2(f7(f10(f8(x261),f11(x261))),a1),a1),a1),a1)
% 0.19/0.64 [27]~P1(x271)+P3(x271)
% 0.19/0.64 [28]~P1(x281)+P4(x281)
% 0.19/0.64 [29]~P1(x291)+P5(x291)
% 0.19/0.64 [30]~P3(x302)+P2(a3,f2(x301,x302),x302)
% 0.19/0.64 [31]~P4(x314)+E(f4(x311,f4(x312,x313,x314),x314),f4(x312,f4(x311,x313,x314),x314))
% 0.19/0.64 [32]~P5(x323)+~P2(x322,x324,x323)+~P2(a3,x321,x323)+P2(f4(x321,x322,x323),f4(x321,x324,x323),x323)
% 0.19/0.64 %EqnAxiom
% 0.19/0.64 [1]E(x11,x11)
% 0.19/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.64 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.19/0.64 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53))
% 0.19/0.64 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62))
% 0.19/0.64 [7]~E(x71,x72)+E(f7(x71),f7(x72))
% 0.19/0.64 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84))
% 0.19/0.64 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94))
% 0.19/0.64 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102))
% 0.19/0.64 [11]~E(x111,x112)+E(f10(x111,x113),f10(x112,x113))
% 0.19/0.64 [12]~E(x121,x122)+E(f10(x123,x121),f10(x123,x122))
% 0.19/0.64 [13]~E(x131,x132)+E(f8(x131),f8(x132))
% 0.19/0.64 [14]~E(x141,x142)+E(f11(x141),f11(x142))
% 0.19/0.64 [15]~E(x151,x152)+E(f9(x151,x153),f9(x152,x153))
% 0.19/0.64 [16]~E(x161,x162)+E(f9(x163,x161),f9(x163,x162))
% 0.19/0.64 [17]~P1(x171)+P1(x172)+~E(x171,x172)
% 0.19/0.64 [18]P2(x182,x183,x184)+~E(x181,x182)+~P2(x181,x183,x184)
% 0.19/0.64 [19]P2(x193,x192,x194)+~E(x191,x192)+~P2(x193,x191,x194)
% 0.19/0.64 [20]P2(x203,x204,x202)+~E(x201,x202)+~P2(x203,x204,x201)
% 0.19/0.64 [21]~P4(x211)+P4(x212)+~E(x211,x212)
% 0.19/0.64 [22]~P3(x221)+P3(x222)+~E(x221,x222)
% 0.19/0.64 [23]~P5(x231)+P5(x232)+~E(x231,x232)
% 0.19/0.64
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 cnf(33,plain,
% 0.19/0.64 (P5(a1)),
% 0.19/0.64 inference(scs_inference,[],[24,29])).
% 0.19/0.64 cnf(37,plain,
% 0.19/0.64 (P2(a3,f2(x371,a1),a1)),
% 0.19/0.64 inference(scs_inference,[],[24,29,28,27,30])).
% 0.19/0.64 cnf(39,plain,
% 0.19/0.64 (E(f4(x391,f4(x392,x393,a1),a1),f4(x392,f4(x391,x393,a1),a1))),
% 0.19/0.64 inference(scs_inference,[],[24,29,28,27,30,31])).
% 0.19/0.64 cnf(42,plain,
% 0.19/0.64 (~P2(f4(f2(f9(f8(x421),f11(x421)),a1),f2(f5(f10(f8(x421),f11(x421))),a1),a1),f4(f2(f9(f8(x421),f11(x421)),a1),f4(x421,f2(f7(f10(f8(x421),f11(x421))),a1),a1),a1),a1)),
% 0.19/0.64 inference(scs_inference,[],[24,26,29,28,27,30,31,23,19])).
% 0.19/0.64 cnf(63,plain,
% 0.19/0.64 ($false),
% 0.19/0.64 inference(scs_inference,[],[25,39,42,37,33,16,15,14,13,12,11,10,9,8,7,6,5,4,32]),
% 0.19/0.64 ['proof']).
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64 % Total time :0.010000s
%------------------------------------------------------------------------------