TSTP Solution File: SET183+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET183+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 : n031.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 14:29:06 EDT 2023
% Result : Theorem 0.18s 0.65s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET183+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n031.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 14:31:38 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.59 start to proof:theBenchmark
% 0.18/0.65 %-------------------------------------------
% 0.18/0.65 % File :CSE---1.6
% 0.18/0.65 % Problem :theBenchmark
% 0.18/0.65 % Transform :cnf
% 0.18/0.65 % Format :tptp:raw
% 0.18/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.65
% 0.18/0.65 % Result :Theorem 0.000000s
% 0.18/0.65 % Output :CNFRefutation 0.000000s
% 0.18/0.65 %-------------------------------------------
% 0.18/0.65 %--------------------------------------------------------------------------
% 0.18/0.65 % File : SET183+3 : TPTP v8.1.2. Released v2.2.0.
% 0.18/0.65 % Domain : Set Theory
% 0.18/0.65 % Problem : If X is a subset of Y, then the intersection of X and Y is X
% 0.18/0.65 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.18/0.65 % English :
% 0.18/0.65
% 0.18/0.65 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.18/0.65 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.18/0.65 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.18/0.65 % Source : [ILF]
% 0.18/0.65 % Names : BOOLE (42) [TS89]
% 0.18/0.65
% 0.18/0.65 % Status : Theorem
% 0.18/0.65 % Rating : 0.08 v8.1.0, 0.06 v7.4.0, 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.2.0, 0.04 v6.1.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 0.18/0.65 % Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% 0.18/0.65 % Number of atoms : 17 ( 4 equ)
% 0.18/0.65 % Maximal formula atoms : 3 ( 2 avg)
% 0.18/0.65 % Number of connectives : 9 ( 0 ~; 0 |; 2 &)
% 0.18/0.65 % ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.65 % Maximal formula depth : 6 ( 4 avg)
% 0.18/0.65 % Maximal term depth : 2 ( 1 avg)
% 0.18/0.65 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.18/0.65 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.18/0.65 % Number of variables : 18 ( 18 !; 0 ?)
% 0.18/0.65 % SPC : FOF_THM_RFO_SEQ
% 0.18/0.65
% 0.18/0.65 % Comments :
% 0.18/0.65 %--------------------------------------------------------------------------
% 0.18/0.65 %---- line(boole - df(3),1833060)
% 0.18/0.65 fof(intersection_defn,axiom,
% 0.18/0.65 ! [B,C,D] :
% 0.18/0.65 ( member(D,intersection(B,C))
% 0.18/0.65 <=> ( member(D,B)
% 0.18/0.65 & member(D,C) ) ) ).
% 0.18/0.65
% 0.18/0.65 %---- line(boole - th(37),1833277)
% 0.18/0.65 fof(intersection_is_subset,axiom,
% 0.18/0.65 ! [B,C] : subset(intersection(B,C),B) ).
% 0.18/0.65
% 0.18/0.65 %---- line(tarski - df(3),1832749)
% 0.18/0.65 fof(subset_defn,axiom,
% 0.18/0.65 ! [B,C] :
% 0.18/0.65 ( subset(B,C)
% 0.18/0.65 <=> ! [D] :
% 0.18/0.65 ( member(D,B)
% 0.18/0.65 => member(D,C) ) ) ).
% 0.18/0.65
% 0.18/0.65 %---- line(boole - df(8),1833103)
% 0.18/0.65 fof(equal_defn,axiom,
% 0.18/0.65 ! [B,C] :
% 0.18/0.65 ( B = C
% 0.18/0.65 <=> ( subset(B,C)
% 0.18/0.65 & subset(C,B) ) ) ).
% 0.18/0.65
% 0.18/0.65 %---- property(commutativity,op(intersection,2,function))
% 0.18/0.65 fof(commutativity_of_intersection,axiom,
% 0.18/0.65 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.18/0.65
% 0.18/0.65 %---- property(reflexivity,op(subset,2,predicate))
% 0.18/0.65 fof(reflexivity_of_subset,axiom,
% 0.18/0.65 ! [B] : subset(B,B) ).
% 0.18/0.65
% 0.18/0.65 %---- line(hidden - axiom55,1832615)
% 0.18/0.65 fof(equal_member_defn,axiom,
% 0.18/0.65 ! [B,C] :
% 0.18/0.65 ( B = C
% 0.18/0.65 <=> ! [D] :
% 0.18/0.65 ( member(D,B)
% 0.18/0.65 <=> member(D,C) ) ) ).
% 0.18/0.65
% 0.18/0.65 %---- line(boole - th(42),1833351)
% 0.18/0.65 fof(prove_subset_intersection,conjecture,
% 0.18/0.65 ! [B,C] :
% 0.18/0.65 ( subset(B,C)
% 0.18/0.65 => intersection(B,C) = B ) ).
% 0.18/0.65
% 0.18/0.65 %--------------------------------------------------------------------------
% 0.18/0.65 %-------------------------------------------
% 0.18/0.65 % Proof found
% 0.18/0.65 % SZS status Theorem for theBenchmark
% 0.18/0.65 % SZS output start Proof
% 0.18/0.65 %ClaNum:29(EqnAxiom:13)
% 0.18/0.65 %VarNum:68(SingletonVarNum:29)
% 0.18/0.65 %MaxLitNum:3
% 0.18/0.65 %MaxfuncDepth:1
% 0.18/0.65 %SharedTerms:5
% 0.18/0.65 %goalClause: 14 18
% 0.18/0.65 %singleGoalClaCount:2
% 0.18/0.65 [14]P1(a1,a4)
% 0.18/0.65 [18]~E(f5(a1,a4),a1)
% 0.18/0.65 [15]P1(x151,x151)
% 0.18/0.65 [16]E(f5(x161,x162),f5(x162,x161))
% 0.18/0.65 [17]P1(f5(x171,x172),x171)
% 0.18/0.65 [20]~E(x201,x202)+P1(x201,x202)
% 0.18/0.65 [22]P1(x221,x222)+P2(f2(x221,x222),x221)
% 0.18/0.65 [26]P1(x261,x262)+~P2(f2(x261,x262),x262)
% 0.18/0.65 [24]P2(x241,x242)+~P2(x241,f5(x243,x242))
% 0.18/0.65 [25]P2(x251,x252)+~P2(x251,f5(x252,x253))
% 0.18/0.65 [21]~P1(x212,x211)+~P1(x211,x212)+E(x211,x212)
% 0.18/0.65 [27]E(x271,x272)+P2(f3(x271,x272),x272)+P2(f3(x271,x272),x271)
% 0.18/0.65 [29]E(x291,x292)+~P2(f3(x291,x292),x292)+~P2(f3(x291,x292),x291)
% 0.18/0.65 [23]~P1(x233,x232)+P2(x231,x232)+~P2(x231,x233)
% 0.18/0.65 [28]~P2(x281,x283)+~P2(x281,x282)+P2(x281,f5(x282,x283))
% 0.18/0.65 %EqnAxiom
% 0.18/0.65 [1]E(x11,x11)
% 0.18/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.65 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 0.18/0.66 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 0.18/0.66 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.18/0.66 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.18/0.66 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83))
% 0.18/0.66 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92))
% 0.18/0.66 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 0.18/0.66 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 0.18/0.66 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 0.18/0.66 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 0.18/0.66
% 0.18/0.66 %-------------------------------------------
% 0.18/0.66 cnf(33,plain,
% 0.18/0.66 (P1(f5(x331,x332),x331)),
% 0.18/0.66 inference(rename_variables,[],[17])).
% 0.18/0.66 cnf(38,plain,
% 0.18/0.66 (~P2(f2(a1,f5(a1,a4)),f5(a1,a4))),
% 0.18/0.66 inference(scs_inference,[],[15,18,17,33,16,11,10,21,2,26])).
% 0.18/0.66 cnf(40,plain,
% 0.18/0.66 (P2(f2(a1,f5(a1,a4)),a1)),
% 0.18/0.66 inference(scs_inference,[],[15,18,17,33,16,11,10,21,2,26,22])).
% 0.18/0.66 cnf(42,plain,
% 0.18/0.66 (~P2(f2(a1,f5(a1,a4)),f5(a4,a1))),
% 0.18/0.66 inference(scs_inference,[],[15,18,17,33,16,11,10,21,2,26,22,13])).
% 0.18/0.66 cnf(43,plain,
% 0.18/0.66 (E(f5(x431,x432),f5(x432,x431))),
% 0.18/0.66 inference(rename_variables,[],[16])).
% 0.18/0.66 cnf(47,plain,
% 0.18/0.66 (P2(f2(a1,f5(a1,a4)),a4)),
% 0.18/0.66 inference(scs_inference,[],[14,15,18,17,33,16,43,11,10,21,2,26,22,13,12,3,23])).
% 0.18/0.66 cnf(58,plain,
% 0.18/0.66 ($false),
% 0.18/0.66 inference(scs_inference,[],[38,40,42,47,23,28]),
% 0.18/0.66 ['proof']).
% 0.18/0.66 % SZS output end Proof
% 0.18/0.66 % Total time :0.000000s
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