TSTP Solution File: SET840-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET840-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n023.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 : Thu Aug 31 14:31:18 EDT 2023
% Result : Unsatisfiable 61.52s 61.62s
% Output : CNFRefutation 61.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET840-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 11:02:11 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.45/0.55 start to proof:theBenchmark
% 61.52/61.61 %-------------------------------------------
% 61.52/61.61 % File :CSE---1.6
% 61.52/61.61 % Problem :theBenchmark
% 61.52/61.61 % Transform :cnf
% 61.52/61.61 % Format :tptp:raw
% 61.52/61.61 % Command :java -jar mcs_scs.jar %d %s
% 61.52/61.61
% 61.52/61.61 % Result :Theorem 61.020000s
% 61.52/61.62 % Output :CNFRefutation 61.020000s
% 61.52/61.62 %-------------------------------------------
% 61.52/61.62 %------------------------------------------------------------------------------
% 61.52/61.62 % File : SET840-2 : TPTP v8.1.2. Released v3.2.0.
% 61.52/61.62 % Domain : Set Theory
% 61.52/61.62 % Problem : Problem about set theory
% 61.52/61.62 % Version : [Pau06] axioms : Reduced > Especial.
% 61.52/61.62 % English :
% 61.52/61.62
% 61.52/61.62 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 61.52/61.62 % Source : [Pau06]
% 61.52/61.62 % Names :
% 61.52/61.62
% 61.52/61.62 % Status : Unsatisfiable
% 61.52/61.62 % Rating : 0.24 v8.1.0, 0.16 v7.5.0, 0.26 v7.4.0, 0.24 v7.3.0, 0.33 v7.1.0, 0.25 v7.0.0, 0.27 v6.2.0, 0.20 v6.1.0, 0.43 v6.0.0, 0.40 v5.5.0, 0.60 v5.3.0, 0.56 v5.2.0, 0.44 v5.1.0, 0.47 v5.0.0, 0.36 v4.1.0, 0.46 v4.0.1, 0.36 v3.7.0, 0.10 v3.5.0, 0.18 v3.4.0, 0.33 v3.3.0, 0.36 v3.2.0
% 61.52/61.62 % Syntax : Number of clauses : 9 ( 2 unt; 2 nHn; 6 RR)
% 61.52/61.62 % Number of literals : 19 ( 2 equ; 9 neg)
% 61.52/61.62 % Maximal clause size : 3 ( 2 avg)
% 61.52/61.62 % Maximal term depth : 3 ( 1 avg)
% 61.52/61.62 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% 61.52/61.62 % Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% 61.52/61.62 % Number of variables : 26 ( 3 sgn)
% 61.52/61.62 % SPC : CNF_UNS_RFO_SEQ_NHN
% 61.52/61.62
% 61.52/61.62 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 61.52/61.62 % of which only a small selection are required for the refutation.
% 61.52/61.62 % The mission is to find those few axioms, after which a refutation
% 61.52/61.62 % can be quite easily found. This version has only the necessary
% 61.52/61.62 % axioms.
% 61.52/61.62 %------------------------------------------------------------------------------
% 61.52/61.62 cnf(cls_conjecture_0,negated_conjecture,
% 61.52/61.62 ~ c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))) ).
% 61.52/61.62
% 61.52/61.62 cnf(cls_conjecture_1,negated_conjecture,
% 61.52/61.62 ( c_lessequals(c_Union(v_S,t_b),V_U,tc_set(t_b))
% 61.52/61.62 | ~ c_in(V_U,v_S,tc_set(t_b)) ) ).
% 61.52/61.62
% 61.52/61.62 cnf(cls_Set_OUnionI_0,axiom,
% 61.52/61.62 ( ~ c_in(V_A,V_X,T_a)
% 61.52/61.62 | ~ c_in(V_X,V_C,tc_set(T_a))
% 61.52/61.62 | c_in(V_A,c_Union(V_C,T_a),T_a) ) ).
% 61.52/61.62
% 61.52/61.62 cnf(cls_Set_OinsertCI_0,axiom,
% 61.52/61.62 ( ~ c_in(V_a,V_B,T_a)
% 61.52/61.62 | c_in(V_a,c_insert(V_b,V_B,T_a),T_a) ) ).
% 61.52/61.62
% 61.52/61.62 cnf(cls_Set_OinsertCI_1,axiom,
% 61.52/61.62 c_in(V_x,c_insert(V_x,V_B,T_a),T_a) ).
% 61.52/61.62
% 61.52/61.62 cnf(cls_Set_OinsertE_0,axiom,
% 61.52/61.62 ( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
% 61.52/61.62 | c_in(V_a,V_A,T_a)
% 61.52/61.62 | V_a = V_b ) ).
% 61.52/61.62
% 61.52/61.62 cnf(cls_Set_OsubsetI_0,axiom,
% 61.52/61.62 ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
% 61.52/61.62 | c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
% 61.52/61.62
% 61.52/61.62 cnf(cls_Set_OsubsetI_1,axiom,
% 61.52/61.62 ( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
% 61.52/61.62 | c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
% 61.52/61.62
% 61.52/61.62 cnf(cls_Set_Osubset__antisym_0,axiom,
% 61.52/61.62 ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
% 61.52/61.62 | ~ c_lessequals(V_A,V_B,tc_set(T_a))
% 61.52/61.62 | V_A = V_B ) ).
% 61.52/61.62
% 61.52/61.62 %------------------------------------------------------------------------------
% 61.52/61.62 %-------------------------------------------
% 61.52/61.62 % Proof found
% 61.52/61.62 % SZS status Theorem for theBenchmark
% 61.52/61.62 % SZS output start Proof
% 61.52/61.62 %ClaNum:27(EqnAxiom:18)
% 61.52/61.62 %VarNum:60(SingletonVarNum:26)
% 61.52/61.62 %MaxLitNum:3
% 61.52/61.62 %MaxfuncDepth:2
% 61.52/61.62 %SharedTerms:6
% 61.52/61.62 %goalClause: 20 21
% 61.52/61.62 %singleGoalClaCount:1
% 61.52/61.62 [20]~P2(a5,f1(x201,a2,f7(a6)),f7(f7(a6)))
% 61.52/61.62 [19]P1(x191,f1(x191,x192,x193),x193)
% 61.52/61.62 [21]P2(f3(a5,a6),x211,f7(a6))+~P1(x211,a5,f7(a6))
% 61.52/61.62 [23]P1(f4(x231,x232,x233),x231,x233)+P2(x231,x232,f7(x233))
% 61.52/61.62 [27]~P1(f4(x271,x272,x273),x272,x273)+P2(x271,x272,f7(x273))
% 61.52/61.62 [24]~P1(x241,x243,x244)+P1(x241,f1(x242,x243,x244),x244)
% 61.52/61.62 [22]E(x221,x222)+~P2(x222,x221,f7(x223))+~P2(x221,x222,f7(x223))
% 61.52/61.62 [25]~P1(x251,x254,x253)+~P1(x254,x252,f7(x253))+P1(x251,f3(x252,x253),x253)
% 61.52/61.62 [26]E(x261,x262)+P1(x261,x263,x264)+~P1(x261,f1(x262,x263,x264),x264)
% 61.52/61.62 %EqnAxiom
% 61.52/61.62 [1]E(x11,x11)
% 61.52/61.62 [2]E(x22,x21)+~E(x21,x22)
% 61.52/61.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 61.52/61.62 [4]~E(x41,x42)+E(f1(x41,x43,x44),f1(x42,x43,x44))
% 61.52/61.62 [5]~E(x51,x52)+E(f1(x53,x51,x54),f1(x53,x52,x54))
% 61.52/61.62 [6]~E(x61,x62)+E(f1(x63,x64,x61),f1(x63,x64,x62))
% 61.52/61.62 [7]~E(x71,x72)+E(f7(x71),f7(x72))
% 61.52/61.62 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84))
% 61.52/61.62 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94))
% 61.52/61.62 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102))
% 61.52/61.62 [11]~E(x111,x112)+E(f3(x111,x113),f3(x112,x113))
% 61.52/61.62 [12]~E(x121,x122)+E(f3(x123,x121),f3(x123,x122))
% 61.52/61.62 [13]P1(x132,x133,x134)+~E(x131,x132)+~P1(x131,x133,x134)
% 61.52/61.62 [14]P1(x143,x142,x144)+~E(x141,x142)+~P1(x143,x141,x144)
% 61.52/61.62 [15]P1(x153,x154,x152)+~E(x151,x152)+~P1(x153,x154,x151)
% 61.52/61.62 [16]P2(x162,x163,x164)+~E(x161,x162)+~P2(x161,x163,x164)
% 61.52/61.63 [17]P2(x173,x172,x174)+~E(x171,x172)+~P2(x173,x171,x174)
% 61.52/61.63 [18]P2(x183,x184,x182)+~E(x181,x182)+~P2(x183,x184,x181)
% 61.52/61.63
% 61.52/61.63 %-------------------------------------------
% 61.52/61.63 cnf(28,plain,
% 61.52/61.63 (~P1(f4(a5,f1(x281,a2,f7(a6)),f7(a6)),f1(x281,a2,f7(a6)),f7(a6))),
% 61.52/61.63 inference(scs_inference,[],[20,27])).
% 61.52/61.63 cnf(29,plain,
% 61.52/61.63 (P1(f4(a5,f1(x291,a2,f7(a6)),f7(a6)),a5,f7(a6))),
% 61.52/61.63 inference(scs_inference,[],[20,27,23])).
% 61.52/61.63 cnf(31,plain,
% 61.52/61.63 (~E(x311,f4(a5,f1(x311,a2,f7(a6)),f7(a6)))),
% 61.52/61.63 inference(scs_inference,[],[20,19,27,23,14,13])).
% 61.52/61.63 cnf(32,plain,
% 61.52/61.63 (P1(x321,f1(x321,x322,x323),x323)),
% 61.52/61.63 inference(rename_variables,[],[19])).
% 61.52/61.63 cnf(37,plain,
% 61.52/61.63 (P2(f3(a5,a6),f4(a5,f1(x371,a2,f7(a6)),f7(a6)),f7(a6))),
% 61.52/61.63 inference(scs_inference,[],[20,19,32,27,23,14,13,2,24,18,21])).
% 61.52/61.63 cnf(42,plain,
% 61.52/61.63 (P1(x421,f3(x422,x423),x423)+~P1(f1(x421,x424,x423),x422,f7(x423))),
% 61.52/61.63 inference(scs_inference,[],[20,19,32,27,23,14,13,2,24,18,21,9,22,25])).
% 61.52/61.63 cnf(47,plain,
% 61.52/61.63 (~P2(f4(a5,f1(f3(a5,a6),a2,f7(a6)),f7(a6)),f3(a5,a6),f7(a6))),
% 61.52/61.63 inference(scs_inference,[],[31,28,37,24,22])).
% 61.52/61.63 cnf(52,plain,
% 61.52/61.63 (P1(x521,f1(x521,x522,x523),x523)),
% 61.52/61.63 inference(rename_variables,[],[19])).
% 61.52/61.63 cnf(53,plain,
% 61.52/61.63 (P1(x531,f3(f1(f1(x531,x532,x533),x534,f7(x533)),x533),x533)),
% 61.52/61.63 inference(scs_inference,[],[19,52,31,28,37,24,22,14,42])).
% 61.52/61.63 cnf(279,plain,
% 61.52/61.63 (~E(f1(x2791,a2,f7(a6)),f3(f1(f1(f4(a5,f1(x2791,a2,f7(a6)),f7(a6)),x2792,f7(a6)),x2793,f7(f7(a6))),f7(a6)))),
% 61.52/61.63 inference(scs_inference,[],[28,53,2,14])).
% 61.52/61.63 cnf(1125,plain,
% 61.52/61.63 (~P1(x11251,f4(a5,f1(x11252,a2,f7(a6)),f7(a6)),a6)+P1(x11251,f3(a5,a6),a6)),
% 61.52/61.63 inference(scs_inference,[],[29,25])).
% 61.52/61.63 cnf(1134,plain,
% 61.52/61.63 (~P1(f4(f4(a5,f1(f3(a5,a6),a2,f7(a6)),f7(a6)),f3(a5,a6),a6),f4(a5,f1(x11341,a2,f7(a6)),f7(a6)),a6)),
% 61.52/61.63 inference(scs_inference,[],[47,1125,27])).
% 61.52/61.63 cnf(1180,plain,
% 61.52/61.63 ($false),
% 61.52/61.63 inference(scs_inference,[],[47,53,279,1134,2,24,42,23]),
% 61.52/61.63 ['proof']).
% 61.52/61.63 % SZS output end Proof
% 61.52/61.63 % Total time :61.020000s
%------------------------------------------------------------------------------