TSTP Solution File: SET639+3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET639+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 : n005.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 14:30:32 EDT 2023
% Result : Theorem 0.19s 0.74s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET639+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 09:11:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.73 %-------------------------------------------
% 0.19/0.73 % File :CSE---1.6
% 0.19/0.73 % Problem :theBenchmark
% 0.19/0.73 % Transform :cnf
% 0.19/0.73 % Format :tptp:raw
% 0.19/0.73 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.73
% 0.19/0.73 % Result :Theorem 0.010000s
% 0.19/0.73 % Output :CNFRefutation 0.010000s
% 0.19/0.73 %-------------------------------------------
% 0.19/0.73 %--------------------------------------------------------------------------
% 0.19/0.73 % File : SET639+3 : TPTP v8.1.2. Released v2.2.0.
% 0.19/0.73 % Domain : Set Theory
% 0.19/0.73 % Problem : Trybulec's 121th Boolean property of sets
% 0.19/0.73 % Version : [Try89] axioms : Reduced > Incomplete.
% 0.19/0.73 % English :
% 0.19/0.73
% 0.19/0.73 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.19/0.73 % : [Try89] Trybulec (1989), Tarski Grothendieck Set Theory
% 0.19/0.74 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.74 % Source : [ILF]
% 0.19/0.74 % Names : BOOLE (121) [TS89]
% 0.19/0.74
% 0.19/0.74 % Status : Theorem
% 0.19/0.74 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.2.0, 0.04 v6.1.0, 0.07 v6.0.0, 0.09 v5.5.0, 0.04 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 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
% 0.19/0.74 % Syntax : Number of formulae : 10 ( 3 unt; 0 def)
% 0.19/0.74 % Number of atoms : 22 ( 6 equ)
% 0.19/0.74 % Maximal formula atoms : 3 ( 2 avg)
% 0.19/0.74 % Number of connectives : 14 ( 2 ~; 0 |; 3 &)
% 0.19/0.74 % ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.74 % Maximal formula depth : 6 ( 5 avg)
% 0.19/0.74 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.74 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.19/0.74 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.19/0.74 % Number of variables : 21 ( 21 !; 0 ?)
% 0.19/0.74 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.74
% 0.19/0.74 % Comments :
% 0.19/0.74 %--------------------------------------------------------------------------
% 0.19/0.74 %---- line(boole - th(42),1833351)
% 0.19/0.74 fof(subset_intersection,axiom,
% 0.19/0.74 ! [B,C] :
% 0.19/0.74 ( subset(B,C)
% 0.19/0.74 => intersection(B,C) = B ) ).
% 0.19/0.74
% 0.19/0.74 %---- line(hidden - axiom232,1832636)
% 0.19/0.74 fof(empty_set_defn,axiom,
% 0.19/0.74 ! [B] : ~ member(B,empty_set) ).
% 0.19/0.74
% 0.19/0.74 %---- line(boole - df(3),1833060)
% 0.19/0.74 fof(intersection_defn,axiom,
% 0.19/0.74 ! [B,C,D] :
% 0.19/0.74 ( member(D,intersection(B,C))
% 0.19/0.74 <=> ( member(D,B)
% 0.19/0.74 & member(D,C) ) ) ).
% 0.19/0.74
% 0.19/0.74 %---- line(tarski - df(3),1832749)
% 0.19/0.74 fof(subset_defn,axiom,
% 0.19/0.74 ! [B,C] :
% 0.19/0.74 ( subset(B,C)
% 0.19/0.74 <=> ! [D] :
% 0.19/0.74 ( member(D,B)
% 0.19/0.74 => member(D,C) ) ) ).
% 0.19/0.74
% 0.19/0.74 %---- line(boole - df(8),1833103)
% 0.19/0.74 fof(equal_defn,axiom,
% 0.19/0.74 ! [B,C] :
% 0.19/0.74 ( B = C
% 0.19/0.74 <=> ( subset(B,C)
% 0.19/0.74 & subset(C,B) ) ) ).
% 0.19/0.74
% 0.19/0.74 %---- property(commutativity,op(intersection,2,function))
% 0.19/0.74 fof(commutativity_of_intersection,axiom,
% 0.19/0.74 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.19/0.74
% 0.19/0.74 %---- property(reflexivity,op(subset,2,predicate))
% 0.19/0.74 fof(reflexivity_of_subset,axiom,
% 0.19/0.74 ! [B] : subset(B,B) ).
% 0.19/0.74
% 0.19/0.74 %---- line(hidden - axiom234,1832628)
% 0.19/0.74 fof(empty_defn,axiom,
% 0.19/0.74 ! [B] :
% 0.19/0.74 ( empty(B)
% 0.19/0.74 <=> ! [C] : ~ member(C,B) ) ).
% 0.19/0.74
% 0.19/0.74 %---- line(hidden - axiom235,1832615)
% 0.19/0.74 fof(equal_member_defn,axiom,
% 0.19/0.74 ! [B,C] :
% 0.19/0.74 ( B = C
% 0.19/0.74 <=> ! [D] :
% 0.19/0.74 ( member(D,B)
% 0.19/0.74 <=> member(D,C) ) ) ).
% 0.19/0.74
% 0.19/0.74 %---- line(boole - th(121),1834507)
% 0.19/0.74 fof(prove_th121,conjecture,
% 0.19/0.74 ! [B,C] :
% 0.19/0.74 ( ( subset(B,C)
% 0.19/0.74 & intersection(C,B) = empty_set )
% 0.19/0.74 => B = empty_set ) ).
% 0.19/0.74
% 0.19/0.74 %--------------------------------------------------------------------------
% 0.19/0.74 %-------------------------------------------
% 0.19/0.74 % Proof found
% 0.19/0.74 % SZS status Theorem for theBenchmark
% 0.19/0.74 % SZS output start Proof
% 0.19/0.74 %ClaNum:35(EqnAxiom:15)
% 0.19/0.74 %VarNum:77(SingletonVarNum:33)
% 0.19/0.74 %MaxLitNum:3
% 0.19/0.74 %MaxfuncDepth:1
% 0.19/0.74 %SharedTerms:7
% 0.19/0.74 %goalClause: 16 17 20
% 0.19/0.74 %singleGoalClaCount:3
% 0.19/0.74 [17]P1(a2,a1)
% 0.19/0.74 [20]~E(a3,a2)
% 0.19/0.74 [16]E(f7(a1,a2),a3)
% 0.19/0.74 [18]P1(x181,x181)
% 0.19/0.74 [21]~P2(x211,a3)
% 0.19/0.74 [19]E(f7(x191,x192),f7(x192,x191))
% 0.19/0.74 [24]P3(x241)+P2(f4(x241),x241)
% 0.19/0.74 [23]~E(x231,x232)+P1(x231,x232)
% 0.19/0.74 [25]~P3(x251)+~P2(x252,x251)
% 0.19/0.74 [26]~P1(x261,x262)+E(f7(x261,x262),x261)
% 0.19/0.74 [28]P1(x281,x282)+P2(f5(x281,x282),x281)
% 0.19/0.74 [32]P1(x321,x322)+~P2(f5(x321,x322),x322)
% 0.19/0.74 [30]P2(x301,x302)+~P2(x301,f7(x303,x302))
% 0.19/0.74 [31]P2(x311,x312)+~P2(x311,f7(x312,x313))
% 0.19/0.74 [27]~P1(x272,x271)+~P1(x271,x272)+E(x271,x272)
% 0.19/0.74 [33]E(x331,x332)+P2(f6(x331,x332),x332)+P2(f6(x331,x332),x331)
% 0.19/0.74 [35]E(x351,x352)+~P2(f6(x351,x352),x352)+~P2(f6(x351,x352),x351)
% 0.19/0.74 [29]~P2(x291,x293)+P2(x291,x292)+~P1(x293,x292)
% 0.19/0.74 [34]~P2(x341,x343)+~P2(x341,x342)+P2(x341,f7(x342,x343))
% 0.19/0.74 %EqnAxiom
% 0.19/0.74 [1]E(x11,x11)
% 0.19/0.74 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.74 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.74 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43))
% 0.19/0.74 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52))
% 0.19/0.74 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 0.19/0.74 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 0.19/0.74 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83))
% 0.19/0.74 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92))
% 0.19/0.74 [10]~E(x101,x102)+E(f4(x101),f4(x102))
% 0.19/0.74 [11]P1(x112,x113)+~E(x111,x112)+~P1(x111,x113)
% 0.19/0.74 [12]P1(x123,x122)+~E(x121,x122)+~P1(x123,x121)
% 0.19/0.74 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133)
% 0.19/0.74 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141)
% 0.19/0.74 [15]~P3(x151)+P3(x152)+~E(x151,x152)
% 0.19/0.74
% 0.19/0.74 %-------------------------------------------
% 0.19/0.74 cnf(38,plain,
% 0.19/0.74 (~P2(x381,a3)),
% 0.19/0.74 inference(rename_variables,[],[21])).
% 0.19/0.74 cnf(41,plain,
% 0.19/0.74 (~P2(x411,a3)),
% 0.19/0.74 inference(rename_variables,[],[21])).
% 0.19/0.74 cnf(43,plain,
% 0.19/0.74 (P3(f7(a1,a2))),
% 0.19/0.74 inference(scs_inference,[],[16,21,38,2,24,28,15])).
% 0.19/0.74 cnf(45,plain,
% 0.19/0.74 (P1(x451,x451)),
% 0.19/0.74 inference(rename_variables,[],[18])).
% 0.19/0.74 cnf(48,plain,
% 0.19/0.74 (E(f7(x481,x482),f7(x482,x481))),
% 0.19/0.74 inference(rename_variables,[],[19])).
% 0.19/0.74 cnf(49,plain,
% 0.19/0.74 (~P2(x491,f7(a1,a2))),
% 0.19/0.74 inference(scs_inference,[],[16,18,21,38,41,19,2,24,28,15,12,11,3,29])).
% 0.19/0.74 cnf(51,plain,
% 0.19/0.74 (~P1(a2,a3)),
% 0.19/0.74 inference(scs_inference,[],[16,18,21,38,41,20,19,2,24,28,15,12,11,3,29,27])).
% 0.19/0.74 cnf(57,plain,
% 0.19/0.74 (~P2(x571,f7(x572,a3))),
% 0.19/0.74 inference(scs_inference,[],[16,18,21,38,41,20,19,48,2,24,28,15,12,11,3,29,27,23,31,30])).
% 0.19/0.74 cnf(60,plain,
% 0.19/0.74 (E(f5(x601,f7(a1,a2)),f5(x601,a3))),
% 0.19/0.74 inference(scs_inference,[],[16,18,21,38,41,20,19,48,2,24,28,15,12,11,3,29,27,23,31,30,10,9])).
% 0.19/0.74 cnf(68,plain,
% 0.19/0.74 (~P2(x681,f7(a2,a1))),
% 0.19/0.74 inference(scs_inference,[],[16,18,45,21,38,41,20,19,48,2,24,28,15,12,11,3,29,27,23,31,30,10,9,8,7,6,5,4,26,14])).
% 0.19/0.74 cnf(70,plain,
% 0.19/0.74 (P2(f6(a3,a2),a2)),
% 0.19/0.74 inference(scs_inference,[],[16,18,45,21,38,41,20,19,48,2,24,28,15,12,11,3,29,27,23,31,30,10,9,8,7,6,5,4,26,14,33])).
% 0.19/0.74 cnf(73,plain,
% 0.19/0.74 (~P3(a2)),
% 0.19/0.74 inference(scs_inference,[],[16,18,45,21,38,41,20,19,48,2,24,28,15,12,11,3,29,27,23,31,30,10,9,8,7,6,5,4,26,14,33,25])).
% 0.19/0.74 cnf(85,plain,
% 0.19/0.74 (P2(f5(a2,a3),a2)),
% 0.19/0.74 inference(scs_inference,[],[21,68,70,51,73,34,23,33,24,28])).
% 0.19/0.74 cnf(87,plain,
% 0.19/0.74 (~E(f7(a1,a2),a2)),
% 0.19/0.74 inference(scs_inference,[],[21,68,43,70,51,73,34,23,33,24,28,15])).
% 0.19/0.74 cnf(104,plain,
% 0.19/0.74 (~P2(x1041,f7(x1042,a3))),
% 0.19/0.74 inference(rename_variables,[],[57])).
% 0.19/0.74 cnf(107,plain,
% 0.19/0.74 (~P2(x1071,f7(x1072,a3))),
% 0.19/0.74 inference(rename_variables,[],[57])).
% 0.19/0.74 cnf(115,plain,
% 0.19/0.74 (P2(f5(a2,a3),a1)),
% 0.19/0.74 inference(scs_inference,[],[17,21,57,104,107,60,85,34,24,28,33,23,29])).
% 0.19/0.74 cnf(132,plain,
% 0.19/0.74 (~P2(x1321,f7(a1,a2))),
% 0.19/0.74 inference(rename_variables,[],[49])).
% 0.19/0.74 cnf(134,plain,
% 0.19/0.74 ($false),
% 0.19/0.74 inference(scs_inference,[],[49,132,115,87,85,33,34]),
% 0.19/0.74 ['proof']).
% 0.19/0.74 % SZS output end Proof
% 0.19/0.74 % Total time :0.010000s
%------------------------------------------------------------------------------