TSTP Solution File: ANA017-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ANA017-2 : 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 17:13:18 EDT 2023
% Result : Unsatisfiable 0.19s 0.71s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA017-2 : 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 : n001.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
% 0.13/0.34 % DateTime : Fri Aug 25 18:52:59 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 % File :CSE---1.6
% 0.19/0.70 % Problem :theBenchmark
% 0.19/0.70 % Transform :cnf
% 0.19/0.70 % Format :tptp:raw
% 0.19/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.70
% 0.19/0.70 % Result :Theorem 0.080000s
% 0.19/0.70 % Output :CNFRefutation 0.080000s
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 %------------------------------------------------------------------------------
% 0.19/0.70 % File : ANA017-2 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.70 % Domain : Analysis
% 0.19/0.70 % Problem : Problem about Big-O notation
% 0.19/0.70 % Version : [Pau06] axioms : Reduced > Especial.
% 0.19/0.70 % English :
% 0.19/0.70
% 0.19/0.70 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.19/0.70 % Source : [Pau06]
% 0.19/0.70 % Names :
% 0.19/0.70
% 0.19/0.70 % Status : Unsatisfiable
% 0.19/0.70 % Rating : 0.08 v8.1.0, 0.11 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
% 0.19/0.70 % Syntax : Number of clauses : 10 ( 3 unt; 0 nHn; 6 RR)
% 0.19/0.70 % Number of literals : 19 ( 2 equ; 10 neg)
% 0.19/0.70 % Maximal clause size : 4 ( 1 avg)
% 0.19/0.70 % Maximal term depth : 5 ( 2 avg)
% 0.19/0.70 % Number of predicates : 6 ( 5 usr; 0 prp; 1-3 aty)
% 0.19/0.70 % Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% 0.19/0.70 % Number of variables : 18 ( 1 sgn)
% 0.19/0.71 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.19/0.71
% 0.19/0.71 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.19/0.71 % of which only a small selection are required for the refutation.
% 0.19/0.71 % The mission is to find those few axioms, after which a refutation
% 0.19/0.71 % can be quite easily found. This version has only the necessary
% 0.19/0.71 % axioms.
% 0.19/0.71 %------------------------------------------------------------------------------
% 0.19/0.71 cnf(cls_conjecture_0,negated_conjecture,
% 0.19/0.71 c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b) ).
% 0.19/0.71
% 0.19/0.71 cnf(cls_conjecture_1,negated_conjecture,
% 0.19/0.71 ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(V_U)),t_b),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b) ).
% 0.19/0.71
% 0.19/0.71 cnf(tfree_tcs,negated_conjecture,
% 0.19/0.71 class_Ring__and__Field_Oordered__idom(t_b) ).
% 0.19/0.71
% 0.19/0.71 cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
% 0.19/0.71 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
% 0.19/0.71 | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ).
% 0.19/0.71
% 0.19/0.71 cnf(cls_OrderedGroup_Omult__ac__1_0,axiom,
% 0.19/0.71 ( ~ class_OrderedGroup_Osemigroup__mult(T_a)
% 0.19/0.71 | 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) ) ).
% 0.19/0.71
% 0.19/0.71 cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
% 0.19/0.71 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.19/0.71 | 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) ) ).
% 0.19/0.71
% 0.19/0.71 cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
% 0.19/0.71 ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
% 0.19/0.71 | ~ c_lessequals(V_a,V_b,T_a)
% 0.19/0.71 | ~ c_lessequals(c_0,V_c,T_a)
% 0.19/0.71 | c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) ).
% 0.19/0.71
% 0.19/0.71 cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
% 0.19/0.71 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.19/0.71 | class_OrderedGroup_Osemigroup__mult(T) ) ).
% 0.19/0.71
% 0.19/0.71 cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
% 0.19/0.71 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.19/0.71 | class_Ring__and__Field_Opordered__semiring(T) ) ).
% 0.19/0.71
% 0.19/0.71 cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
% 0.19/0.71 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.19/0.71 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ).
% 0.19/0.71
% 0.19/0.71 %------------------------------------------------------------------------------
% 0.19/0.71 %-------------------------------------------
% 0.19/0.71 % Proof found
% 0.19/0.71 % SZS status Theorem for theBenchmark
% 0.19/0.71 % SZS output start Proof
% 0.19/0.71 %ClaNum:28(EqnAxiom:18)
% 0.19/0.71 %VarNum:49(SingletonVarNum:18)
% 0.19/0.71 %MaxLitNum:4
% 0.19/0.71 %MaxfuncDepth:4
% 0.19/0.71 %SharedTerms:5
% 0.19/0.71 %goalClause: 19 20 21
% 0.19/0.71 %singleGoalClaCount:3
% 0.19/0.71 [19]P1(a1)
% 0.19/0.71 [20]P2(f2(f5(x201),a1),f4(a6,f2(f8(x201),a1),a1),a1)
% 0.19/0.71 [21]~P2(f2(f4(a7,f5(f9(x211)),a1),a1),f4(x211,f2(f8(f9(x211)),a1),a1),a1)
% 0.19/0.71 [22]~P1(x221)+P3(x221)
% 0.19/0.71 [23]~P1(x231)+P4(x231)
% 0.19/0.71 [24]~P1(x241)+P5(x241)
% 0.19/0.71 [25]~P3(x252)+P2(a3,f2(x251,x252),x252)
% 0.19/0.71 [26]~P1(x262)+E(f4(f2(x261,x262),f2(x263,x262),x262),f2(f4(x261,x263,x262),x262))
% 0.19/0.71 [27]~P4(x273)+E(f4(f4(x271,x272,x273),x274,x273),f4(x271,f4(x272,x274,x273),x273))
% 0.19/0.71 [28]~P5(x283)+~P2(x282,x284,x283)+~P2(a3,x281,x283)+P2(f4(x281,x282,x283),f4(x281,x284,x283),x283)
% 0.19/0.71 %EqnAxiom
% 0.19/0.71 [1]E(x11,x11)
% 0.19/0.71 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.71 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.19/0.71 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53))
% 0.19/0.71 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62))
% 0.19/0.71 [7]~E(x71,x72)+E(f8(x71),f8(x72))
% 0.19/0.71 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84))
% 0.19/0.71 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94))
% 0.19/0.71 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102))
% 0.19/0.71 [11]~E(x111,x112)+E(f9(x111),f9(x112))
% 0.19/0.71 [12]~P1(x121)+P1(x122)+~E(x121,x122)
% 0.19/0.71 [13]P2(x132,x133,x134)+~E(x131,x132)+~P2(x131,x133,x134)
% 0.19/0.71 [14]P2(x143,x142,x144)+~E(x141,x142)+~P2(x143,x141,x144)
% 0.19/0.71 [15]P2(x153,x154,x152)+~E(x151,x152)+~P2(x153,x154,x151)
% 0.19/0.71 [16]~P4(x161)+P4(x162)+~E(x161,x162)
% 0.19/0.71 [17]~P3(x171)+P3(x172)+~E(x171,x172)
% 0.19/0.71 [18]~P5(x181)+P5(x182)+~E(x181,x182)
% 0.19/0.71
% 0.19/0.71 %-------------------------------------------
% 0.19/0.71 cnf(33,plain,
% 0.19/0.71 (P5(a1)),
% 0.19/0.71 inference(scs_inference,[],[19,20,21,13,2,24])).
% 0.19/0.71 cnf(39,plain,
% 0.19/0.71 (P2(a3,f2(x391,a1),a1)),
% 0.19/0.71 inference(scs_inference,[],[19,20,21,13,2,24,23,22,25])).
% 0.19/0.71 cnf(41,plain,
% 0.19/0.71 (E(f4(f4(x411,x412,a1),x413,a1),f4(x411,f4(x412,x413,a1),a1))),
% 0.19/0.71 inference(scs_inference,[],[19,20,21,13,2,24,23,22,25,27])).
% 0.19/0.71 cnf(43,plain,
% 0.19/0.71 (E(f4(f2(x431,a1),f2(x432,a1),a1),f2(f4(x431,x432,a1),a1))),
% 0.19/0.71 inference(scs_inference,[],[19,20,21,13,2,24,23,22,25,27,26])).
% 0.19/0.71 cnf(61,plain,
% 0.19/0.71 (~P2(f4(f2(a7,a1),f2(f5(f9(x611)),a1),a1),f4(x611,f2(f8(f9(x611)),a1),a1),a1)),
% 0.19/0.71 inference(scs_inference,[],[21,41,43,11,10,9,8,7,6,4,5,13])).
% 0.19/0.71 cnf(62,plain,
% 0.19/0.71 (E(f4(f2(x621,a1),f2(x622,a1),a1),f2(f4(x621,x622,a1),a1))),
% 0.19/0.71 inference(rename_variables,[],[43])).
% 0.19/0.71 cnf(65,plain,
% 0.19/0.71 (P2(f4(f2(x651,a1),f2(f5(x652),a1),a1),f4(f2(x651,a1),f4(a6,f2(f8(x652),a1),a1),a1),a1)),
% 0.19/0.71 inference(scs_inference,[],[20,21,41,43,62,39,33,11,10,9,8,7,6,4,5,13,3,28])).
% 0.19/0.71 cnf(67,plain,
% 0.19/0.71 (E(f4(x671,f4(x672,x673,a1),a1),f4(f4(x671,x672,a1),x673,a1))),
% 0.19/0.71 inference(scs_inference,[],[20,21,41,43,62,39,33,11,10,9,8,7,6,4,5,13,3,28,2])).
% 0.19/0.71 cnf(135,plain,
% 0.19/0.71 ($false),
% 0.19/0.71 inference(scs_inference,[],[67,61,65,14]),
% 0.19/0.71 ['proof']).
% 0.19/0.71 % SZS output end Proof
% 0.19/0.71 % Total time :0.080000s
%------------------------------------------------------------------------------