TSTP Solution File: SET592+3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET592+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 : n009.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 14:30:16 EDT 2023
% Result : Theorem 0.56s 0.68s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET592+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:40:35 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 0.56/0.67 %-------------------------------------------
% 0.56/0.67 % File :CSE---1.6
% 0.56/0.67 % Problem :theBenchmark
% 0.56/0.67 % Transform :cnf
% 0.56/0.67 % Format :tptp:raw
% 0.56/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.56/0.67
% 0.56/0.67 % Result :Theorem 0.030000s
% 0.56/0.67 % Output :CNFRefutation 0.030000s
% 0.56/0.67 %-------------------------------------------
% 0.56/0.67 %--------------------------------------------------------------------------
% 0.56/0.67 % File : SET592+3 : TPTP v8.1.2. Released v2.2.0.
% 0.56/0.67 % Domain : Set Theory
% 0.56/0.67 % Problem : If X (= Y and X (= Z and Y ^ Z = empty set, then X = empty set
% 0.56/0.67 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.56/0.67 % English : If X is a subset of Y and X is a subset of Z and the
% 0.56/0.67 % intersection of Y and Z is the empty set, then X is the empty
% 0.56/0.67 % set.
% 0.56/0.67
% 0.56/0.67 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.56/0.67 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.56/0.67 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.56/0.67 % Source : [ILF]
% 0.56/0.67 % Names : BOOLE (51) [TS89]
% 0.56/0.67
% 0.56/0.67 % Status : Theorem
% 0.56/0.67 % Rating : 0.06 v8.1.0, 0.03 v7.4.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.3.0, 0.19 v5.2.0, 0.00 v5.0.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.05 v3.3.0, 0.07 v3.2.0, 0.09 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 0.56/0.67 % Syntax : Number of formulae : 11 ( 3 unt; 0 def)
% 0.56/0.67 % Number of atoms : 26 ( 6 equ)
% 0.56/0.67 % Maximal formula atoms : 4 ( 2 avg)
% 0.56/0.67 % Number of connectives : 17 ( 2 ~; 0 |; 5 &)
% 0.56/0.67 % ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% 0.56/0.67 % Maximal formula depth : 7 ( 5 avg)
% 0.56/0.67 % Maximal term depth : 2 ( 1 avg)
% 0.56/0.67 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.56/0.67 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.56/0.67 % Number of variables : 24 ( 24 !; 0 ?)
% 0.56/0.67 % SPC : FOF_THM_RFO_SEQ
% 0.56/0.67
% 0.56/0.67 % Comments :
% 0.56/0.67 %--------------------------------------------------------------------------
% 0.56/0.67 %---- line(boole - th(30),1833179)
% 0.56/0.67 fof(subset_of_empty_set_is_empty_set,axiom,
% 0.56/0.67 ! [B] :
% 0.56/0.67 ( subset(B,empty_set)
% 0.56/0.67 => B = empty_set ) ).
% 0.56/0.67
% 0.56/0.67 %---- line(boole - th(39),1833302)
% 0.56/0.67 fof(intersection_of_subsets,axiom,
% 0.56/0.67 ! [B,C,D] :
% 0.56/0.67 ( ( subset(B,C)
% 0.56/0.67 & subset(B,D) )
% 0.56/0.67 => subset(B,intersection(C,D)) ) ).
% 0.56/0.67
% 0.56/0.67 %---- line(hidden - axiom69,1832636)
% 0.56/0.67 fof(empty_set_defn,axiom,
% 0.56/0.67 ! [B] : ~ member(B,empty_set) ).
% 0.56/0.67
% 0.56/0.67 %---- line(boole - df(3),1833060)
% 0.56/0.67 fof(intersection_defn,axiom,
% 0.56/0.67 ! [B,C,D] :
% 0.56/0.67 ( member(D,intersection(B,C))
% 0.56/0.67 <=> ( member(D,B)
% 0.56/0.67 & member(D,C) ) ) ).
% 0.56/0.67
% 0.56/0.67 %---- line(tarski - df(3),1832749)
% 0.56/0.67 fof(subset_defn,axiom,
% 0.56/0.67 ! [B,C] :
% 0.56/0.67 ( subset(B,C)
% 0.56/0.67 <=> ! [D] :
% 0.56/0.68 ( member(D,B)
% 0.56/0.68 => member(D,C) ) ) ).
% 0.56/0.68
% 0.56/0.68 %---- line(boole - df(8),1833103)
% 0.56/0.68 fof(equal_defn,axiom,
% 0.56/0.68 ! [B,C] :
% 0.56/0.68 ( B = C
% 0.56/0.68 <=> ( subset(B,C)
% 0.56/0.68 & subset(C,B) ) ) ).
% 0.56/0.68
% 0.56/0.68 %---- property(commutativity,op(intersection,2,function))
% 0.56/0.68 fof(commutativity_of_intersection,axiom,
% 0.56/0.68 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.56/0.68
% 0.56/0.68 %---- property(reflexivity,op(subset,2,predicate))
% 0.56/0.68 fof(reflexivity_of_subset,axiom,
% 0.56/0.68 ! [B] : subset(B,B) ).
% 0.56/0.68
% 0.56/0.68 %---- line(hidden - axiom71,1832628)
% 0.56/0.68 fof(empty_defn,axiom,
% 0.56/0.68 ! [B] :
% 0.56/0.68 ( empty(B)
% 0.56/0.68 <=> ! [C] : ~ member(C,B) ) ).
% 0.56/0.68
% 0.56/0.68 %---- line(hidden - axiom72,1832615)
% 0.56/0.68 fof(equal_member_defn,axiom,
% 0.56/0.68 ! [B,C] :
% 0.56/0.68 ( B = C
% 0.56/0.68 <=> ! [D] :
% 0.56/0.68 ( member(D,B)
% 0.56/0.68 <=> member(D,C) ) ) ).
% 0.56/0.68
% 0.56/0.68 %---- line(boole - th(51),1833491)
% 0.56/0.68 fof(prove_th51,conjecture,
% 0.56/0.68 ! [B,C,D] :
% 0.56/0.68 ( ( subset(B,C)
% 0.56/0.68 & subset(B,D)
% 0.56/0.68 & intersection(C,D) = empty_set )
% 0.56/0.68 => B = empty_set ) ).
% 0.56/0.68
% 0.56/0.68 %--------------------------------------------------------------------------
% 0.56/0.68 %-------------------------------------------
% 0.56/0.68 % Proof found
% 0.56/0.68 % SZS status Theorem for theBenchmark
% 0.56/0.68 % SZS output start Proof
% 0.56/0.68 %ClaNum:37(EqnAxiom:15)
% 0.56/0.68 %VarNum:81(SingletonVarNum:35)
% 0.56/0.68 %MaxLitNum:3
% 0.56/0.68 %MaxfuncDepth:1
% 0.56/0.68 %SharedTerms:9
% 0.56/0.68 %goalClause: 16 17 18 21
% 0.56/0.68 %singleGoalClaCount:4
% 0.56/0.68 [17]P1(a3,a1)
% 0.56/0.68 [18]P1(a3,a7)
% 0.56/0.68 [21]~E(a3,a2)
% 0.56/0.68 [16]E(f8(a1,a7),a2)
% 0.56/0.68 [19]P1(x191,x191)
% 0.56/0.68 [22]~P2(x221,a2)
% 0.56/0.68 [20]E(f8(x201,x202),f8(x202,x201))
% 0.56/0.68 [25]~P1(x251,a2)+E(x251,a2)
% 0.56/0.68 [26]P3(x261)+P2(f4(x261),x261)
% 0.56/0.68 [24]~E(x241,x242)+P1(x241,x242)
% 0.56/0.68 [27]~P3(x271)+~P2(x272,x271)
% 0.56/0.68 [29]P1(x291,x292)+P2(f5(x291,x292),x291)
% 0.56/0.68 [33]P1(x331,x332)+~P2(f5(x331,x332),x332)
% 0.56/0.68 [31]P2(x311,x312)+~P2(x311,f8(x313,x312))
% 0.56/0.68 [32]P2(x321,x322)+~P2(x321,f8(x322,x323))
% 0.56/0.68 [28]~P1(x282,x281)+~P1(x281,x282)+E(x281,x282)
% 0.56/0.68 [34]E(x341,x342)+P2(f6(x341,x342),x342)+P2(f6(x341,x342),x341)
% 0.56/0.68 [37]E(x371,x372)+~P2(f6(x371,x372),x372)+~P2(f6(x371,x372),x371)
% 0.56/0.68 [30]~P2(x301,x303)+P2(x301,x302)+~P1(x303,x302)
% 0.56/0.68 [35]~P1(x351,x353)+~P1(x351,x352)+P1(x351,f8(x352,x353))
% 0.56/0.68 [36]~P2(x361,x363)+~P2(x361,x362)+P2(x361,f8(x362,x363))
% 0.56/0.68 %EqnAxiom
% 0.56/0.68 [1]E(x11,x11)
% 0.56/0.68 [2]E(x22,x21)+~E(x21,x22)
% 0.56/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.56/0.68 [4]~E(x41,x42)+E(f8(x41,x43),f8(x42,x43))
% 0.56/0.68 [5]~E(x51,x52)+E(f8(x53,x51),f8(x53,x52))
% 0.56/0.68 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 0.56/0.68 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 0.56/0.68 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83))
% 0.56/0.68 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92))
% 0.56/0.68 [10]~E(x101,x102)+E(f4(x101),f4(x102))
% 0.56/0.68 [11]P1(x112,x113)+~E(x111,x112)+~P1(x111,x113)
% 0.56/0.68 [12]P1(x123,x122)+~E(x121,x122)+~P1(x123,x121)
% 0.56/0.68 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133)
% 0.56/0.68 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141)
% 0.56/0.68 [15]~P3(x151)+P3(x152)+~E(x151,x152)
% 0.56/0.68
% 0.56/0.68 %-------------------------------------------
% 0.56/0.68 cnf(39,plain,
% 0.56/0.68 (~P1(a3,a2)),
% 0.56/0.68 inference(scs_inference,[],[16,21,2,25])).
% 0.56/0.68 cnf(42,plain,
% 0.56/0.68 (~P2(x421,a2)),
% 0.56/0.68 inference(rename_variables,[],[22])).
% 0.56/0.68 cnf(45,plain,
% 0.56/0.68 (~P2(x451,a2)),
% 0.56/0.68 inference(rename_variables,[],[22])).
% 0.56/0.68 cnf(47,plain,
% 0.56/0.68 (P3(f8(a1,a7))),
% 0.56/0.68 inference(scs_inference,[],[16,22,42,21,2,25,26,29,15])).
% 0.56/0.68 cnf(50,plain,
% 0.56/0.68 (P1(x501,x501)),
% 0.56/0.68 inference(rename_variables,[],[19])).
% 0.56/0.68 cnf(51,plain,
% 0.56/0.68 (~E(a3,f8(a1,a7))),
% 0.56/0.68 inference(scs_inference,[],[16,19,22,42,17,21,2,25,26,29,15,12,11,3])).
% 0.56/0.68 cnf(54,plain,
% 0.56/0.68 (~P2(x541,f8(a2,x542))),
% 0.56/0.68 inference(scs_inference,[],[16,19,22,42,45,17,21,2,25,26,29,15,12,11,3,24,32])).
% 0.56/0.68 cnf(56,plain,
% 0.56/0.68 (~P2(x561,f8(x562,a2))),
% 0.56/0.68 inference(scs_inference,[],[16,19,22,42,45,17,21,2,25,26,29,15,12,11,3,24,32,31])).
% 0.56/0.68 cnf(64,plain,
% 0.56/0.68 (E(f8(f8(a1,a7),x641),f8(a2,x641))),
% 0.56/0.68 inference(scs_inference,[],[16,19,22,42,45,17,21,2,25,26,29,15,12,11,3,24,32,31,10,9,8,7,6,5,4])).
% 0.56/0.68 cnf(66,plain,
% 0.56/0.68 (~P1(a1,a2)),
% 0.56/0.68 inference(scs_inference,[],[16,19,22,42,45,17,21,2,25,26,29,15,12,11,3,24,32,31,10,9,8,7,6,5,4,14,28])).
% 0.56/0.68 cnf(70,plain,
% 0.56/0.68 (P2(f6(a2,a3),a3)),
% 0.56/0.68 inference(scs_inference,[],[16,19,50,22,42,45,17,21,2,25,26,29,15,12,11,3,24,32,31,10,9,8,7,6,5,4,14,28,35,34])).
% 0.56/0.68 cnf(73,plain,
% 0.56/0.68 (~P3(a3)),
% 0.56/0.68 inference(scs_inference,[],[16,19,50,22,42,45,17,21,2,25,26,29,15,12,11,3,24,32,31,10,9,8,7,6,5,4,14,28,35,34,27])).
% 0.56/0.68 cnf(89,plain,
% 0.56/0.68 (~P1(a3,f8(a1,a7))),
% 0.56/0.68 inference(scs_inference,[],[16,18,19,22,21,39,47,70,66,73,30,29,26,15,11,35,34,12])).
% 0.56/0.68 cnf(94,plain,
% 0.56/0.68 (P2(f6(a2,a3),f8(a3,a3))),
% 0.56/0.68 inference(scs_inference,[],[16,18,20,19,22,21,54,64,39,47,51,70,66,73,30,29,26,15,11,35,34,12,14,3,36])).
% 0.56/0.68 cnf(112,plain,
% 0.56/0.68 ($false),
% 0.56/0.68 inference(scs_inference,[],[17,22,18,56,94,89,30,24,29,35]),
% 0.56/0.68 ['proof']).
% 0.56/0.68 % SZS output end Proof
% 0.56/0.68 % Total time :0.030000s
%------------------------------------------------------------------------------