TSTP Solution File: SET014+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n025.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 14:27:51 EDT 2023
% Result : Theorem 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.15/0.34 % Computer : n025.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 12:36:52 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % File :CSE---1.6
% 0.20/0.63 % Problem :theBenchmark
% 0.20/0.63 % Transform :cnf
% 0.20/0.63 % Format :tptp:raw
% 0.20/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.63
% 0.20/0.63 % Result :Theorem 0.010000s
% 0.20/0.64 % Output :CNFRefutation 0.010000s
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 % File : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% 0.20/0.64 % Domain : Set Theory
% 0.20/0.64 % Problem : If X (= Z and Y (= Z, then X U Y (= Z
% 0.20/0.64 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.20/0.64 % English : If X is a subset of Z and Y is a subset of Z, then the union of
% 0.20/0.64 % X and Y is a subset of Z.
% 0.20/0.64
% 0.20/0.64 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.20/0.64 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.20/0.64 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.64 % Source : [ILF]
% 0.20/0.64 % Names : BOOLE (32) [TS89]
% 0.20/0.64
% 0.20/0.64 % Status : Theorem
% 0.20/0.64 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.10 v7.3.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.00 v6.1.0, 0.13 v5.5.0, 0.19 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.12 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.15 v3.5.0, 0.11 v3.4.0, 0.26 v3.3.0, 0.21 v3.2.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.14 v2.5.0, 0.12 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1
% 0.20/0.64 % Syntax : Number of formulae : 6 ( 2 unt; 0 def)
% 0.20/0.64 % Number of atoms : 14 ( 2 equ)
% 0.20/0.64 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.64 % Number of connectives : 8 ( 0 ~; 1 |; 1 &)
% 0.20/0.64 % ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.64 % Maximal formula depth : 6 ( 5 avg)
% 0.20/0.64 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.64 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.20/0.64 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.20/0.64 % Number of variables : 15 ( 15 !; 0 ?)
% 0.20/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.64
% 0.20/0.64 % Comments :
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 %---- line(boole - df(2),1833042)
% 0.20/0.64 fof(union_defn,axiom,
% 0.20/0.64 ! [B,C,D] :
% 0.20/0.64 ( member(D,union(B,C))
% 0.20/0.64 <=> ( member(D,B)
% 0.20/0.64 | member(D,C) ) ) ).
% 0.20/0.64
% 0.20/0.64 %---- line(tarski - df(3),1832749)
% 0.20/0.64 fof(subset_defn,axiom,
% 0.20/0.64 ! [B,C] :
% 0.20/0.64 ( subset(B,C)
% 0.20/0.64 <=> ! [D] :
% 0.20/0.64 ( member(D,B)
% 0.20/0.64 => member(D,C) ) ) ).
% 0.20/0.64
% 0.20/0.64 %---- property(commutativity,op(union,2,function))
% 0.20/0.64 fof(commutativity_of_union,axiom,
% 0.20/0.64 ! [B,C] : union(B,C) = union(C,B) ).
% 0.20/0.64
% 0.20/0.64 %---- property(reflexivity,op(subset,2,predicate))
% 0.20/0.64 fof(reflexivity_of_subset,axiom,
% 0.20/0.64 ! [B] : subset(B,B) ).
% 0.20/0.64
% 0.20/0.64 %---- line(hidden - axiom37,1832615)
% 0.20/0.64 fof(equal_member_defn,axiom,
% 0.20/0.64 ! [B,C] :
% 0.20/0.64 ( B = C
% 0.20/0.64 <=> ! [D] :
% 0.20/0.64 ( member(D,B)
% 0.20/0.64 <=> member(D,C) ) ) ).
% 0.20/0.64
% 0.20/0.64 %---- line(boole - th(32),1833206)
% 0.20/0.64 fof(prove_union_subset,conjecture,
% 0.20/0.64 ! [B,C,D] :
% 0.20/0.64 ( ( subset(B,C)
% 0.20/0.64 & subset(D,C) )
% 0.20/0.64 => subset(union(B,D),C) ) ).
% 0.20/0.64
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark
% 0.20/0.64 % SZS output start Proof
% 0.20/0.64 %ClaNum:26(EqnAxiom:13)
% 0.20/0.64 %VarNum:55(SingletonVarNum:23)
% 0.20/0.64 %MaxLitNum:3
% 0.20/0.64 %MaxfuncDepth:1
% 0.20/0.64 %SharedTerms:7
% 0.20/0.64 %goalClause: 14 15 18
% 0.20/0.64 %singleGoalClaCount:3
% 0.20/0.64 [14]P1(a1,a4)
% 0.20/0.64 [15]P1(a5,a4)
% 0.20/0.64 [18]~P1(f6(a1,a5),a4)
% 0.20/0.64 [16]P1(x161,x161)
% 0.20/0.64 [17]E(f6(x171,x172),f6(x172,x171))
% 0.20/0.64 [19]P1(x191,x192)+P2(f2(x191,x192),x191)
% 0.20/0.64 [23]P1(x231,x232)+~P2(f2(x231,x232),x232)
% 0.20/0.64 [21]~P2(x211,x213)+P2(x211,f6(x212,x213))
% 0.20/0.64 [22]~P2(x221,x222)+P2(x221,f6(x222,x223))
% 0.20/0.64 [24]E(x241,x242)+P2(f3(x241,x242),x242)+P2(f3(x241,x242),x241)
% 0.20/0.64 [26]E(x261,x262)+~P2(f3(x261,x262),x262)+~P2(f3(x261,x262),x261)
% 0.20/0.64 [20]~P1(x203,x202)+P2(x201,x202)+~P2(x201,x203)
% 0.20/0.64 [25]P2(x251,x252)+P2(x251,x253)+~P2(x251,f6(x253,x252))
% 0.20/0.64 %EqnAxiom
% 0.20/0.64 [1]E(x11,x11)
% 0.20/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.64 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.20/0.64 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.20/0.64 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.20/0.64 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.20/0.64 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83))
% 0.20/0.64 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92))
% 0.20/0.64 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 0.20/0.64 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 0.20/0.64 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 0.20/0.64 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 0.20/0.64
% 0.20/0.64 %-------------------------------------------
% 0.20/0.65 cnf(31,plain,
% 0.20/0.65 (E(f6(x311,x312),f6(x312,x311))),
% 0.20/0.65 inference(rename_variables,[],[17])).
% 0.20/0.65 cnf(33,plain,
% 0.20/0.65 (~P2(f2(f6(a1,a5),a4),a4)),
% 0.20/0.65 inference(scs_inference,[],[14,16,18,17,11,10,3,2,23])).
% 0.20/0.65 cnf(35,plain,
% 0.20/0.65 (P2(f2(f6(a1,a5),a4),f6(a1,a5))),
% 0.20/0.65 inference(scs_inference,[],[14,16,18,17,11,10,3,2,23,19])).
% 0.20/0.65 cnf(38,plain,
% 0.20/0.65 (~P2(f2(f6(a1,a5),a4),a1)),
% 0.20/0.65 inference(scs_inference,[],[14,16,18,17,11,10,3,2,23,19,12,20])).
% 0.20/0.65 cnf(42,plain,
% 0.20/0.65 (P2(f2(f6(a1,a5),a4),f6(a5,a1))),
% 0.20/0.65 inference(scs_inference,[],[14,16,18,17,31,11,10,3,2,23,19,12,20,25,13])).
% 0.20/0.65 cnf(53,plain,
% 0.20/0.65 (P2(f2(f6(a1,a5),a4),a5)),
% 0.20/0.65 inference(scs_inference,[],[16,33,42,38,35,20,11,25])).
% 0.20/0.65 cnf(64,plain,
% 0.20/0.65 ($false),
% 0.20/0.65 inference(scs_inference,[],[15,53,33,20]),
% 0.20/0.65 ['proof']).
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time :0.010000s
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