TSTP Solution File: SET200+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n016.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 14:29:12 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 14:48:12 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.54 start to proof:theBenchmark
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % File :CSE---1.6
% 0.20/0.62 % Problem :theBenchmark
% 0.20/0.62 % Transform :cnf
% 0.20/0.62 % Format :tptp:raw
% 0.20/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.62
% 0.20/0.62 % Result :Theorem 0.000000s
% 0.20/0.62 % Output :CNFRefutation 0.000000s
% 0.20/0.62 %-------------------------------------------
% 0.20/0.63 %--------------------------------------------------------------------------
% 0.20/0.63 % File : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% 0.20/0.63 % Domain : Set Theory
% 0.20/0.63 % Problem : Union is monotonic
% 0.20/0.63 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.20/0.63 % English : If X is a subset of Y and Z is a subset of V, then the union of
% 0.20/0.63 % X and Z is a subset of the union of Y and V.
% 0.20/0.63
% 0.20/0.63 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.20/0.63 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.20/0.63 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.63 % Source : [ILF]
% 0.20/0.63 % Names : BOOLE (34) [TS89]
% 0.20/0.63
% 0.20/0.63 % Status : Theorem
% 0.20/0.63 % Rating : 0.14 v8.1.0, 0.08 v7.5.0, 0.12 v7.4.0, 0.13 v7.3.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.13 v6.4.0, 0.15 v6.3.0, 0.08 v6.2.0, 0.04 v6.1.0, 0.17 v6.0.0, 0.13 v5.5.0, 0.33 v5.4.0, 0.39 v5.3.0, 0.41 v5.2.0, 0.30 v5.1.0, 0.33 v5.0.0, 0.38 v4.1.0, 0.35 v4.0.0, 0.29 v3.7.0, 0.30 v3.5.0, 0.26 v3.4.0, 0.32 v3.3.0, 0.29 v3.2.0, 0.36 v3.1.0, 0.44 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.25 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1
% 0.20/0.63 % Syntax : Number of formulae : 6 ( 2 unt; 0 def)
% 0.20/0.63 % Number of atoms : 14 ( 2 equ)
% 0.20/0.63 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.63 % Number of connectives : 8 ( 0 ~; 1 |; 1 &)
% 0.20/0.63 % ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.63 % Maximal formula depth : 7 ( 5 avg)
% 0.20/0.63 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.63 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.20/0.63 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.20/0.63 % Number of variables : 16 ( 16 !; 0 ?)
% 0.20/0.63 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.63
% 0.20/0.63 % Comments :
% 0.20/0.63 %--------------------------------------------------------------------------
% 0.20/0.63 %---- line(boole - df(2),1833042)
% 0.20/0.63 fof(union_defn,axiom,
% 0.20/0.63 ! [B,C,D] :
% 0.20/0.63 ( member(D,union(B,C))
% 0.20/0.63 <=> ( member(D,B)
% 0.20/0.63 | member(D,C) ) ) ).
% 0.20/0.63
% 0.20/0.63 %---- line(tarski - df(3),1832749)
% 0.20/0.63 fof(subset_defn,axiom,
% 0.20/0.63 ! [B,C] :
% 0.20/0.63 ( subset(B,C)
% 0.20/0.63 <=> ! [D] :
% 0.20/0.63 ( member(D,B)
% 0.20/0.63 => member(D,C) ) ) ).
% 0.20/0.63
% 0.20/0.63 %---- property(commutativity,op(union,2,function))
% 0.20/0.63 fof(commutativity_of_union,axiom,
% 0.20/0.63 ! [B,C] : union(B,C) = union(C,B) ).
% 0.20/0.63
% 0.20/0.63 %---- property(reflexivity,op(subset,2,predicate))
% 0.20/0.63 fof(reflexivity_of_subset,axiom,
% 0.20/0.63 ! [B] : subset(B,B) ).
% 0.20/0.63
% 0.20/0.63 %---- line(hidden - axiom41,1832615)
% 0.20/0.63 fof(equal_member_defn,axiom,
% 0.20/0.63 ! [B,C] :
% 0.20/0.63 ( B = C
% 0.20/0.63 <=> ! [D] :
% 0.20/0.63 ( member(D,B)
% 0.20/0.63 <=> member(D,C) ) ) ).
% 0.20/0.63
% 0.20/0.63 %---- line(boole - th(34),1833242)
% 0.20/0.63 fof(prove_th34,conjecture,
% 0.20/0.63 ! [B,C,D,E] :
% 0.20/0.63 ( ( subset(B,C)
% 0.20/0.63 & subset(D,E) )
% 0.20/0.63 => subset(union(B,D),union(C,E)) ) ).
% 0.20/0.63
% 0.20/0.63 %--------------------------------------------------------------------------
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 %ClaNum:26(EqnAxiom:13)
% 0.20/0.63 %VarNum:55(SingletonVarNum:23)
% 0.20/0.63 %MaxLitNum:3
% 0.20/0.63 %MaxfuncDepth:1
% 0.20/0.63 %SharedTerms:9
% 0.20/0.63 %goalClause: 14 15 18
% 0.20/0.63 %singleGoalClaCount:3
% 0.20/0.63 [14]P1(a1,a4)
% 0.20/0.63 [15]P1(a5,a6)
% 0.20/0.63 [18]~P1(f7(a1,a5),f7(a4,a6))
% 0.20/0.63 [16]P1(x161,x161)
% 0.20/0.63 [17]E(f7(x171,x172),f7(x172,x171))
% 0.20/0.63 [19]P1(x191,x192)+P2(f2(x191,x192),x191)
% 0.20/0.63 [23]P1(x231,x232)+~P2(f2(x231,x232),x232)
% 0.20/0.63 [21]~P2(x211,x213)+P2(x211,f7(x212,x213))
% 0.20/0.63 [22]~P2(x221,x222)+P2(x221,f7(x222,x223))
% 0.20/0.63 [24]E(x241,x242)+P2(f3(x241,x242),x242)+P2(f3(x241,x242),x241)
% 0.20/0.63 [26]E(x261,x262)+~P2(f3(x261,x262),x262)+~P2(f3(x261,x262),x261)
% 0.20/0.63 [20]~P1(x203,x202)+P2(x201,x202)+~P2(x201,x203)
% 0.20/0.63 [25]P2(x251,x252)+P2(x251,x253)+~P2(x251,f7(x253,x252))
% 0.20/0.63 %EqnAxiom
% 0.20/0.63 [1]E(x11,x11)
% 0.20/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.63 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43))
% 0.20/0.63 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52))
% 0.20/0.63 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.20/0.63 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.20/0.63 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83))
% 0.20/0.63 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92))
% 0.20/0.63 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 0.20/0.63 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 0.20/0.63 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 0.20/0.63 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 0.20/0.63
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 cnf(27,plain,
% 0.20/0.63 (~E(f7(a1,a5),f7(a4,a6))),
% 0.20/0.63 inference(scs_inference,[],[16,18,11])).
% 0.20/0.63 cnf(28,plain,
% 0.20/0.63 (P1(x281,x281)),
% 0.20/0.63 inference(rename_variables,[],[16])).
% 0.20/0.63 cnf(32,plain,
% 0.20/0.63 (E(f7(x321,x322),f7(x322,x321))),
% 0.20/0.63 inference(rename_variables,[],[17])).
% 0.20/0.63 cnf(36,plain,
% 0.20/0.64 (P2(f2(f7(a1,a5),f7(a4,a6)),f7(a1,a5))),
% 0.20/0.64 inference(scs_inference,[],[16,28,18,17,11,10,3,2,23,19])).
% 0.20/0.64 cnf(41,plain,
% 0.20/0.64 (~P2(f2(f7(a1,a5),f7(a4,a6)),a4)),
% 0.20/0.64 inference(scs_inference,[],[16,28,18,17,32,11,10,3,2,23,19,13,12,22])).
% 0.20/0.64 cnf(43,plain,
% 0.20/0.64 (~P2(f2(f7(a1,a5),f7(a4,a6)),a6)),
% 0.20/0.64 inference(scs_inference,[],[16,28,18,17,32,11,10,3,2,23,19,13,12,22,21])).
% 0.20/0.64 cnf(55,plain,
% 0.20/0.64 (E(f7(x551,x552),f7(x552,x551))),
% 0.20/0.64 inference(rename_variables,[],[17])).
% 0.20/0.64 cnf(56,plain,
% 0.20/0.64 (P2(f2(f7(a1,a5),f7(a4,a6)),f7(a5,a1))),
% 0.20/0.64 inference(scs_inference,[],[17,55,18,36,10,13])).
% 0.20/0.64 cnf(57,plain,
% 0.20/0.64 (E(f7(x571,x572),f7(x572,x571))),
% 0.20/0.64 inference(rename_variables,[],[17])).
% 0.20/0.64 cnf(59,plain,
% 0.20/0.64 (E(f7(x591,x592),f7(x592,x591))),
% 0.20/0.64 inference(rename_variables,[],[17])).
% 0.20/0.64 cnf(62,plain,
% 0.20/0.64 (~P2(f2(f7(a1,a5),f7(a4,a6)),a1)),
% 0.20/0.64 inference(scs_inference,[],[14,17,55,57,59,18,27,36,41,10,13,11,3,20])).
% 0.20/0.64 cnf(74,plain,
% 0.20/0.64 (P2(f2(f7(a1,a5),f7(a4,a6)),a5)),
% 0.20/0.64 inference(scs_inference,[],[56,62,25])).
% 0.20/0.64 cnf(82,plain,
% 0.20/0.64 ($false),
% 0.20/0.64 inference(scs_inference,[],[15,74,43,20]),
% 0.20/0.64 ['proof']).
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time :0.000000s
%------------------------------------------------------------------------------