TSTP Solution File: ANA029-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ANA029-2 : 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 : n010.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 0.21s 0.65s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA029-2 : 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
% 0.14/0.35 % Computer : n010.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 18:08:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 % File :CSE---1.6
% 0.21/0.65 % Problem :theBenchmark
% 0.21/0.65 % Transform :cnf
% 0.21/0.65 % Format :tptp:raw
% 0.21/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.65
% 0.21/0.65 % Result :Theorem 0.010000s
% 0.21/0.65 % Output :CNFRefutation 0.010000s
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 % File : ANA029-2 : TPTP v8.1.2. Released v3.2.0.
% 0.21/0.65 % Domain : Analysis
% 0.21/0.65 % Problem : Problem about Big-O notation
% 0.21/0.65 % Version : [Pau06] axioms : Reduced > Especial.
% 0.21/0.65 % English :
% 0.21/0.65
% 0.21/0.65 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.21/0.65 % Source : [Pau06]
% 0.21/0.65 % Names :
% 0.21/0.65
% 0.21/0.65 % Status : Unsatisfiable
% 0.21/0.65 % Rating : 0.00 v6.0.0, 0.14 v5.5.0, 0.12 v5.4.0, 0.10 v5.1.0, 0.09 v5.0.0, 0.07 v4.1.0, 0.12 v4.0.1, 0.00 v3.2.0
% 0.21/0.65 % Syntax : Number of clauses : 14 ( 3 unt; 1 nHn; 12 RR)
% 0.21/0.65 % Number of literals : 33 ( 0 equ; 20 neg)
% 0.21/0.65 % Maximal clause size : 4 ( 2 avg)
% 0.21/0.65 % Maximal term depth : 4 ( 1 avg)
% 0.21/0.65 % Number of predicates : 7 ( 7 usr; 0 prp; 1-3 aty)
% 0.21/0.65 % Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% 0.21/0.65 % Number of variables : 26 ( 1 sgn)
% 0.21/0.65 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.21/0.65
% 0.21/0.65 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.21/0.65 % of which only a small selection are required for the refutation.
% 0.21/0.65 % The mission is to find those few axioms, after which a refutation
% 0.21/0.65 % can be quite easily found. This version has only the necessary
% 0.21/0.65 % axioms.
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 cnf(cls_conjecture_2,negated_conjecture,
% 0.21/0.65 ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ).
% 0.21/0.65
% 0.21/0.65 cnf(cls_conjecture_3,negated_conjecture,
% 0.21/0.65 ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ).
% 0.21/0.65
% 0.21/0.65 cnf(tfree_tcs,negated_conjecture,
% 0.21/0.65 class_Ring__and__Field_Oordered__idom(t_b) ).
% 0.21/0.65
% 0.21/0.65 cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
% 0.21/0.65 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
% 0.21/0.65 | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ).
% 0.21/0.65
% 0.21/0.65 cnf(cls_OrderedGroup_Odiff__le__0__iff__le_0,axiom,
% 0.21/0.65 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.21/0.65 | ~ c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
% 0.21/0.65 | c_lessequals(V_a,V_b,T_a) ) ).
% 0.21/0.65
% 0.21/0.65 cnf(cls_OrderedGroup_Odiff__le__0__iff__le_1,axiom,
% 0.21/0.65 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.21/0.65 | ~ c_lessequals(V_a,V_b,T_a)
% 0.21/0.65 | c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a) ) ).
% 0.21/0.65
% 0.21/0.65 cnf(cls_Orderings_Olinorder__not__le_0,axiom,
% 0.21/0.65 ( ~ class_Orderings_Olinorder(T_a)
% 0.21/0.65 | c_less(V_y,V_x,T_a)
% 0.21/0.65 | c_lessequals(V_x,V_y,T_a) ) ).
% 0.21/0.65
% 0.21/0.65 cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
% 0.21/0.65 ( ~ class_Orderings_Olinorder(T_b)
% 0.21/0.65 | ~ c_lessequals(V_y,V_z,T_b)
% 0.21/0.65 | ~ c_lessequals(V_x,V_z,T_b)
% 0.21/0.65 | c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) ).
% 0.21/0.65
% 0.21/0.65 cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
% 0.21/0.65 ( ~ class_Orderings_Oorder(T_a)
% 0.21/0.65 | ~ c_lessequals(V_y,V_z,T_a)
% 0.21/0.65 | ~ c_lessequals(V_x,V_y,T_a)
% 0.21/0.65 | c_lessequals(V_x,V_z,T_a) ) ).
% 0.21/0.65
% 0.21/0.65 cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
% 0.21/0.65 ( ~ class_Orderings_Oorder(T_a)
% 0.21/0.65 | ~ c_less(V_x,V_y,T_a)
% 0.21/0.65 | c_lessequals(V_x,V_y,T_a) ) ).
% 0.21/0.65
% 0.21/0.65 cnf(clsrel_OrderedGroup_Opordered__ab__group__add_10,axiom,
% 0.21/0.65 ( ~ class_OrderedGroup_Opordered__ab__group__add(T)
% 0.21/0.65 | class_Orderings_Oorder(T) ) ).
% 0.21/0.65
% 0.21/0.65 cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
% 0.21/0.65 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.21/0.65 | class_Orderings_Olinorder(T) ) ).
% 0.21/0.65
% 0.21/0.65 cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
% 0.21/0.65 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.21/0.65 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ).
% 0.21/0.65
% 0.21/0.65 cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
% 0.21/0.65 ( ~ class_Ring__and__Field_Oordered__idom(T)
% 0.21/0.65 | class_OrderedGroup_Opordered__ab__group__add(T) ) ).
% 0.21/0.65
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 % Proof found
% 0.21/0.65 % SZS status Theorem for theBenchmark
% 0.21/0.65 % SZS output start Proof
% 0.21/0.66 %ClaNum:14(EqnAxiom:0)
% 0.21/0.66 %VarNum:64(SingletonVarNum:26)
% 0.21/0.66 %MaxLitNum:4
% 0.21/0.66 %MaxfuncDepth:3
% 0.21/0.66 %SharedTerms:13
% 0.21/0.66 %goalClause: 1 2 3
% 0.21/0.66 %singleGoalClaCount:3
% 0.21/0.66 [1]P1(a1)
% 0.21/0.66 [2]~P2(a2,f3(f7(a6),f8(a6),a1),a1)
% 0.21/0.66 [3]~P2(f4(f3(f7(a6),f8(a6),a1),a2,a1),f5(f3(f7(a6),f9(a6),a1),a1),a1)
% 0.21/0.66 [4]~P1(x41)+P4(x41)
% 0.21/0.66 [5]~P1(x51)+P5(x51)
% 0.21/0.66 [6]~P1(x61)+P6(x61)
% 0.21/0.66 [7]~P5(x71)+P7(x71)
% 0.21/0.66 [8]~P4(x82)+P2(a2,f5(x81,x82),x82)
% 0.21/0.66 [9]P3(x92,x91,x93)+~P6(x93)+P2(x91,x92,x93)
% 0.21/0.66 [10]~P7(x103)+~P3(x101,x102,x103)+P2(x101,x102,x103)
% 0.21/0.66 [12]~P5(x123)+~P2(x121,x122,x123)+P2(f3(x121,x122,x123),a2,x123)
% 0.21/0.66 [13]~P5(x133)+P2(x131,x132,x133)+~P2(f3(x131,x132,x133),a2,x133)
% 0.21/0.66 [11]~P7(x113)+~P2(x114,x112,x113)+P2(x111,x112,x113)+~P2(x111,x114,x113)
% 0.21/0.66 [14]~P6(x143)+~P2(x141,x144,x143)+~P2(x142,x144,x143)+P2(f4(x141,x142,x143),x144,x143)
% 0.21/0.66 %EqnAxiom
% 0.21/0.66
% 0.21/0.66 %-------------------------------------------
% 0.21/0.66 cnf(15,plain,
% 0.21/0.66 (P6(a1)),
% 0.21/0.66 inference(scs_inference,[],[1,6])).
% 0.21/0.66 cnf(16,plain,
% 0.21/0.66 (P5(a1)),
% 0.21/0.66 inference(scs_inference,[],[1,6,5])).
% 0.21/0.66 cnf(19,plain,
% 0.21/0.66 (P2(a2,f5(x191,a1),a1)),
% 0.21/0.66 inference(scs_inference,[],[1,6,5,4,8])).
% 0.21/0.66 cnf(23,plain,
% 0.21/0.66 (~P2(f3(a2,f3(f7(a6),f8(a6),a1),a1),a2,a1)),
% 0.21/0.66 inference(scs_inference,[],[1,2,6,5,4,8,9,13])).
% 0.21/0.66 cnf(27,plain,
% 0.21/0.66 (P2(f4(a2,a2,a1),f5(x271,a1),a1)),
% 0.21/0.66 inference(scs_inference,[],[1,2,6,5,4,8,9,13,12,14])).
% 0.21/0.66 cnf(29,plain,
% 0.21/0.66 (P2(f3(f7(a6),f8(a6),a1),a2,a1)+~P7(a1)),
% 0.21/0.66 inference(scs_inference,[],[1,2,6,5,4,8,9,13,12,14,10])).
% 0.21/0.66 cnf(31,plain,
% 0.21/0.66 (~P2(f4(f3(f7(a6),f8(a6),a1),a2,a1),a2,a1)+~P7(a1)),
% 0.21/0.66 inference(scs_inference,[],[1,2,3,6,5,4,8,9,13,12,14,10,11])).
% 0.21/0.66 cnf(33,plain,
% 0.21/0.66 (P7(a1)),
% 0.21/0.66 inference(scs_inference,[],[16,7])).
% 0.21/0.66 cnf(49,plain,
% 0.21/0.66 (P2(f3(f7(a6),f8(a6),a1),a2,a1)),
% 0.21/0.66 inference(scs_inference,[],[3,27,23,15,16,7,10,13,12,14,9,11,31,29])).
% 0.21/0.66 cnf(57,plain,
% 0.21/0.66 (~P2(f3(f7(a6),f8(a6),a1),f5(f3(f7(a6),f9(a6),a1),a1),a1)),
% 0.21/0.66 inference(scs_inference,[],[15,3,19,14])).
% 0.21/0.66 cnf(73,plain,
% 0.21/0.66 ($false),
% 0.21/0.66 inference(scs_inference,[],[15,57,49,19,33,9,11]),
% 0.21/0.66 ['proof']).
% 0.21/0.66 % SZS output end Proof
% 0.21/0.66 % Total time :0.010000s
%------------------------------------------------------------------------------