TSTP Solution File: ANA031-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ANA031-2 : 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 : n029.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 17:13:23 EDT 2023
% Result : Unsatisfiable 0.58s 1.01s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA031-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 18:36:09 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 0.58/1.00 %-------------------------------------------
% 0.58/1.00 % File :CSE---1.6
% 0.58/1.00 % Problem :theBenchmark
% 0.58/1.00 % Transform :cnf
% 0.58/1.00 % Format :tptp:raw
% 0.58/1.00 % Command :java -jar mcs_scs.jar %d %s
% 0.58/1.00
% 0.58/1.00 % Result :Theorem 0.330000s
% 0.58/1.00 % Output :CNFRefutation 0.330000s
% 0.58/1.00 %-------------------------------------------
% 0.58/1.01 %------------------------------------------------------------------------------
% 0.58/1.01 % File : ANA031-2 : TPTP v8.1.2. Released v3.2.0.
% 0.58/1.01 % Domain : Analysis
% 0.58/1.01 % Problem : Problem about Big-O notation
% 0.58/1.01 % Version : [Pau06] axioms : Reduced > Especial.
% 0.58/1.01 % English :
% 0.58/1.01
% 0.58/1.01 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.58/1.01 % Source : [Pau06]
% 0.58/1.01 % Names :
% 0.58/1.01
% 0.58/1.01 % Status : Unsatisfiable
% 0.58/1.01 % Rating : 0.17 v8.1.0, 0.00 v7.5.0, 0.10 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.20 v6.0.0, 0.22 v5.5.0, 0.44 v5.4.0, 0.47 v5.3.0, 0.58 v5.2.0, 0.25 v5.1.0, 0.29 v4.1.0, 0.33 v3.3.0, 0.43 v3.2.0
% 0.58/1.01 % Syntax : Number of clauses : 11 ( 3 unt; 0 nHn; 7 RR)
% 0.58/1.01 % Number of literals : 21 ( 2 equ; 11 neg)
% 0.58/1.01 % Maximal clause size : 4 ( 1 avg)
% 0.58/1.01 % Maximal term depth : 6 ( 2 avg)
% 0.58/1.01 % Number of predicates : 7 ( 6 usr; 0 prp; 1-3 aty)
% 0.58/1.01 % Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% 0.58/1.01 % Number of variables : 19 ( 1 sgn)
% 0.58/1.01 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.58/1.01
% 0.58/1.01 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.58/1.01 % of which only a small selection are required for the refutation.
% 0.58/1.01 % The mission is to find those few axioms, after which a refutation
% 0.58/1.01 % can be quite easily found. This version has only the necessary
% 0.58/1.01 % axioms.
% 0.58/1.01 %------------------------------------------------------------------------------
% 0.58/1.01 cnf(cls_conjecture_0,negated_conjecture,
% 0.58/1.01 c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b) ).
% 0.58/1.01
% 0.58/1.01 cnf(cls_conjecture_1,negated_conjecture,
% 0.58/1.01 ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b) ).
% 0.58/1.01
% 0.58/1.01 cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
% 0.58/1.01 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
% 0.58/1.01 | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ).
% 0.58/1.01
% 0.58/1.01 cnf(cls_OrderedGroup_Omult__ac__1_0,axiom,
% 0.58/1.01 ( ~ class_OrderedGroup_Osemigroup__mult(T_a)
% 0.58/1.01 | 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) ) ).
% 0.58/1.01
% 0.58/1.01 cnf(cls_OrderedGroup_Omult__ac__2_0,axiom,
% 0.58/1.01 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
% 0.58/1.01 | c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) ).
% 0.58/1.01
% 0.58/1.01 cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
% 0.58/1.01 ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
% 0.58/1.01 | ~ c_lessequals(V_a,V_b,T_a)
% 0.58/1.01 | ~ c_lessequals(c_0,V_c,T_a)
% 0.58/1.01 | c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) ).
% 0.58/1.01
% 0.58/1.01 cnf(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
% 0.58/1.01 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.58/1.01 | class_OrderedGroup_Oab__semigroup__mult(T) ) ).
% 0.58/1.01
% 0.58/1.01 cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
% 0.58/1.01 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.58/1.01 | class_OrderedGroup_Osemigroup__mult(T) ) ).
% 0.58/1.01
% 0.58/1.01 cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
% 0.58/1.01 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.58/1.01 | class_Ring__and__Field_Opordered__semiring(T) ) ).
% 0.58/1.01
% 0.58/1.01 cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
% 0.58/1.01 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.58/1.01 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ).
% 0.58/1.01
% 0.58/1.01 cnf(tfree_tcs,negated_conjecture,
% 0.58/1.01 class_Ring__and__Field_Oordered__idom(t_b) ).
% 0.58/1.01
% 0.58/1.01 %------------------------------------------------------------------------------
% 0.58/1.01 %-------------------------------------------
% 0.58/1.01 % Proof found
% 0.58/1.01 % SZS status Theorem for theBenchmark
% 0.58/1.01 % SZS output start Proof
% 0.58/1.01 %ClaNum:31(EqnAxiom:20)
% 0.58/1.01 %VarNum:50(SingletonVarNum:19)
% 0.58/1.01 %MaxLitNum:4
% 0.58/1.01 %MaxfuncDepth:5
% 0.58/1.01 %SharedTerms:4
% 0.58/1.01 %goalClause: 21 22 23
% 0.58/1.01 %singleGoalClaCount:3
% 0.58/1.01 [21]P1(a1)
% 0.58/1.01 [22]P2(f2(f5(x221),a1),f4(a6,f2(f7(x221),a1),a1),a1)
% 0.58/1.01 [23]~P2(f4(f2(f5(f9(x231)),a1),f2(f8(f9(x231)),a1),a1),f4(x231,f4(f2(f8(f9(x231)),a1),f2(f7(f9(x231)),a1),a1),a1),a1)
% 0.58/1.01 [24]~P1(x241)+P3(x241)
% 0.58/1.01 [25]~P1(x251)+P5(x251)
% 0.58/1.01 [26]~P1(x261)+P4(x261)
% 0.58/1.01 [27]~P1(x271)+P6(x271)
% 0.58/1.01 [28]~P3(x282)+P2(a3,f2(x281,x282),x282)
% 0.58/1.01 [29]~P4(x293)+E(f4(x291,x292,x293),f4(x292,x291,x293))
% 0.58/1.01 [30]~P5(x303)+E(f4(f4(x301,x302,x303),x304,x303),f4(x301,f4(x302,x304,x303),x303))
% 0.58/1.01 [31]~P6(x313)+~P2(x312,x314,x313)+~P2(a3,x311,x313)+P2(f4(x311,x312,x313),f4(x311,x314,x313),x313)
% 0.58/1.01 %EqnAxiom
% 0.58/1.01 [1]E(x11,x11)
% 0.58/1.01 [2]E(x22,x21)+~E(x21,x22)
% 0.58/1.01 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.58/1.01 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.58/1.01 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53))
% 0.58/1.01 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62))
% 0.58/1.01 [7]~E(x71,x72)+E(f7(x71),f7(x72))
% 0.58/1.01 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84))
% 0.58/1.01 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94))
% 0.58/1.01 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102))
% 0.58/1.01 [11]~E(x111,x112)+E(f9(x111),f9(x112))
% 0.58/1.01 [12]~E(x121,x122)+E(f8(x121),f8(x122))
% 0.58/1.01 [13]~P1(x131)+P1(x132)+~E(x131,x132)
% 0.58/1.01 [14]P2(x142,x143,x144)+~E(x141,x142)+~P2(x141,x143,x144)
% 0.58/1.01 [15]P2(x153,x152,x154)+~E(x151,x152)+~P2(x153,x151,x154)
% 0.58/1.01 [16]P2(x163,x164,x162)+~E(x161,x162)+~P2(x163,x164,x161)
% 0.58/1.01 [17]~P5(x171)+P5(x172)+~E(x171,x172)
% 0.58/1.01 [18]~P3(x181)+P3(x182)+~E(x181,x182)
% 0.58/1.01 [19]~P4(x191)+P4(x192)+~E(x191,x192)
% 0.58/1.01 [20]~P6(x201)+P6(x202)+~E(x201,x202)
% 0.58/1.01
% 0.58/1.01 %-------------------------------------------
% 0.58/1.02 cnf(32,plain,
% 0.58/1.02 (P6(a1)),
% 0.58/1.02 inference(scs_inference,[],[21,27])).
% 0.58/1.02 cnf(38,plain,
% 0.58/1.02 (P2(a3,f2(x381,a1),a1)),
% 0.58/1.02 inference(scs_inference,[],[21,27,26,25,24,28])).
% 0.58/1.02 cnf(40,plain,
% 0.58/1.02 (E(f4(x401,x402,a1),f4(x402,x401,a1))),
% 0.58/1.02 inference(scs_inference,[],[21,27,26,25,24,28,29])).
% 0.58/1.02 cnf(42,plain,
% 0.58/1.02 (E(f4(f4(x421,x422,a1),x423,a1),f4(x421,f4(x422,x423,a1),a1))),
% 0.58/1.02 inference(scs_inference,[],[21,27,26,25,24,28,29,30])).
% 0.58/1.02 cnf(45,plain,
% 0.58/1.02 (~P2(f4(f2(f5(f9(x451)),a1),f2(f8(f9(x451)),a1),a1),f4(f4(f2(f8(f9(x451)),a1),f2(f7(f9(x451)),a1),a1),x451,a1),a1)),
% 0.58/1.02 inference(scs_inference,[],[21,23,27,26,25,24,28,29,30,20,15])).
% 0.58/1.02 cnf(48,plain,
% 0.58/1.02 (E(f4(x481,f4(x482,x483,a1),a1),f4(f4(x481,x482,a1),x483,a1))),
% 0.58/1.02 inference(scs_inference,[],[21,23,27,26,25,24,28,29,30,20,15,31,2])).
% 0.58/1.02 cnf(55,plain,
% 0.58/1.02 (E(f4(x551,f4(x552,x553,a1),x554),f4(x551,f4(x553,x552,a1),x554))),
% 0.58/1.02 inference(scs_inference,[],[40,12,11,10,9])).
% 0.58/1.02 cnf(63,plain,
% 0.58/1.02 (E(f4(x631,x632,a1),f4(x632,x631,a1))),
% 0.58/1.02 inference(rename_variables,[],[40])).
% 0.58/1.02 cnf(66,plain,
% 0.58/1.02 (P2(f4(f2(x661,a1),f2(f5(x662),a1),a1),f4(f2(x661,a1),f4(a6,f2(f7(x662),a1),a1),a1),a1)),
% 0.58/1.02 inference(scs_inference,[],[22,40,63,42,38,32,12,11,10,9,8,7,6,5,4,3,15,31])).
% 0.58/1.02 cnf(74,plain,
% 0.58/1.02 (P2(f4(f2(x741,a1),f2(f5(x742),a1),a1),f4(f2(x741,a1),f4(f2(f7(x742),a1),a6,a1),a1),a1)),
% 0.58/1.02 inference(scs_inference,[],[55,66,15])).
% 0.58/1.02 cnf(78,plain,
% 0.58/1.02 (~P2(f4(f2(f8(f9(x781)),a1),f2(f5(f9(x781)),a1),a1),f4(x781,f4(f2(f8(f9(x781)),a1),f2(f7(f9(x781)),a1),a1),a1),a1)),
% 0.58/1.02 inference(scs_inference,[],[32,23,55,66,38,40,15,31,14])).
% 0.58/1.02 cnf(169,plain,
% 0.58/1.02 (~P2(f4(f2(f8(f9(x1691)),a1),f2(f5(f9(x1691)),a1),a1),f4(f4(f2(f8(f9(x1691)),a1),f2(f7(f9(x1691)),a1),a1),x1691,a1),a1)),
% 0.58/1.02 inference(scs_inference,[],[42,45,78,40,15,14])).
% 0.58/1.02 cnf(381,plain,
% 0.58/1.02 ($false),
% 0.58/1.02 inference(scs_inference,[],[48,169,74,15]),
% 0.58/1.02 ['proof']).
% 0.58/1.02 % SZS output end Proof
% 0.58/1.02 % Total time :0.330000s
%------------------------------------------------------------------------------