TSTP Solution File: SET578+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET578+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 : n018.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 14:30:11 EDT 2023
% Result : Theorem 1.01s 1.26s
% Output : CNFRefutation 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.10/0.33 % Computer : n018.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Sat Aug 26 10:58:44 EDT 2023
% 0.10/0.33 % CPUTime :
% 0.13/0.59 start to proof:theBenchmark
% 1.01/1.25 %-------------------------------------------
% 1.01/1.25 % File :CSE---1.6
% 1.01/1.25 % Problem :theBenchmark
% 1.01/1.25 % Transform :cnf
% 1.01/1.25 % Format :tptp:raw
% 1.01/1.25 % Command :java -jar mcs_scs.jar %d %s
% 1.01/1.25
% 1.01/1.25 % Result :Theorem 0.620000s
% 1.01/1.25 % Output :CNFRefutation 0.620000s
% 1.01/1.26 %-------------------------------------------
% 1.01/1.26 %--------------------------------------------------------------------------
% 1.01/1.26 % File : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% 1.01/1.26 % Domain : Set Theory
% 1.01/1.26 % Problem : Trybulec's 19th Boolean property of sets
% 1.01/1.26 % Version : [Try90] axioms : Reduced > Incomplete.
% 1.01/1.26 % English :
% 1.01/1.26
% 1.01/1.26 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 1.01/1.26 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 1.01/1.26 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 1.01/1.26 % Source : [ILF]
% 1.01/1.26 % Names : BOOLE (19) [TS89]
% 1.01/1.26
% 1.01/1.26 % Status : Theorem
% 1.01/1.26 % Rating : 0.19 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.04 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.20 v6.0.0, 0.26 v5.5.0, 0.15 v5.4.0, 0.21 v5.3.0, 0.30 v5.2.0, 0.05 v5.0.0, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 1.01/1.26 % Syntax : Number of formulae : 7 ( 2 unt; 0 def)
% 1.01/1.26 % Number of atoms : 18 ( 4 equ)
% 1.01/1.26 % Maximal formula atoms : 4 ( 2 avg)
% 1.01/1.26 % Number of connectives : 11 ( 0 ~; 0 |; 3 &)
% 1.01/1.26 % ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% 1.01/1.26 % Maximal formula depth : 8 ( 5 avg)
% 1.01/1.26 % Maximal term depth : 2 ( 1 avg)
% 1.01/1.26 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 1.01/1.26 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 1.01/1.26 % Number of variables : 18 ( 18 !; 0 ?)
% 1.01/1.26 % SPC : FOF_THM_RFO_SEQ
% 1.01/1.26
% 1.01/1.26 % Comments :
% 1.01/1.26 %--------------------------------------------------------------------------
% 1.01/1.26 %---- line(boole - df(3),1833060)
% 1.01/1.26 fof(intersection_defn,axiom,
% 1.01/1.26 ! [B,C,D] :
% 1.01/1.26 ( member(D,intersection(B,C))
% 1.01/1.26 <=> ( member(D,B)
% 1.01/1.26 & member(D,C) ) ) ).
% 1.01/1.26
% 1.01/1.26 %---- line(boole - df(8),1833103)
% 1.01/1.26 fof(equal_defn,axiom,
% 1.01/1.26 ! [B,C] :
% 1.01/1.26 ( B = C
% 1.01/1.26 <=> ( subset(B,C)
% 1.01/1.26 & subset(C,B) ) ) ).
% 1.01/1.26
% 1.01/1.26 %---- property(commutativity,op(intersection,2,function))
% 1.01/1.26 fof(commutativity_of_intersection,axiom,
% 1.01/1.26 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 1.01/1.26
% 1.01/1.26 %---- line(tarski - df(3),1832749)
% 1.01/1.26 fof(subset_defn,axiom,
% 1.01/1.26 ! [B,C] :
% 1.01/1.26 ( subset(B,C)
% 1.01/1.26 <=> ! [D] :
% 1.01/1.26 ( member(D,B)
% 1.01/1.26 => member(D,C) ) ) ).
% 1.01/1.26
% 1.01/1.26 %---- property(reflexivity,op(subset,2,predicate))
% 1.01/1.26 fof(reflexivity_of_subset,axiom,
% 1.01/1.26 ! [B] : subset(B,B) ).
% 1.01/1.26
% 1.01/1.26 %---- line(hidden - axiom15,1832615)
% 1.01/1.26 fof(equal_member_defn,axiom,
% 1.01/1.26 ! [B,C] :
% 1.01/1.26 ( B = C
% 1.01/1.26 <=> ! [D] :
% 1.01/1.26 ( member(D,B)
% 1.01/1.26 <=> member(D,C) ) ) ).
% 1.01/1.26
% 1.01/1.26 %---- line(boole - th(19),1833114)
% 1.01/1.26 fof(prove_th19,conjecture,
% 1.01/1.26 ! [B,C,D] :
% 1.01/1.26 ( ! [E] :
% 1.01/1.26 ( member(E,B)
% 1.01/1.26 <=> ( member(E,C)
% 1.01/1.26 & member(E,D) ) )
% 1.01/1.26 => B = intersection(C,D) ) ).
% 1.01/1.26
% 1.01/1.26 %--------------------------------------------------------------------------
% 1.01/1.26 %-------------------------------------------
% 1.01/1.26 % Proof found
% 1.01/1.26 % SZS status Theorem for theBenchmark
% 1.01/1.26 % SZS output start Proof
% 1.01/1.27 %ClaNum:30(EqnAxiom:13)
% 1.01/1.27 %VarNum:72(SingletonVarNum:30)
% 1.01/1.27 %MaxLitNum:3
% 1.01/1.27 %MaxfuncDepth:1
% 1.01/1.27 %SharedTerms:5
% 1.01/1.27 %goalClause: 16 19 20 22
% 1.01/1.27 %singleGoalClaCount:1
% 1.01/1.27 [16]~E(f1(a2,a6),a3)
% 1.01/1.27 [14]P1(x141,x141)
% 1.01/1.27 [15]E(f1(x151,x152),f1(x152,x151))
% 1.01/1.27 [19]~P2(x191,a3)+P2(x191,a2)
% 1.01/1.27 [20]~P2(x201,a3)+P2(x201,a6)
% 1.01/1.27 [18]~E(x181,x182)+P1(x181,x182)
% 1.01/1.27 [23]P1(x231,x232)+P2(f4(x231,x232),x231)
% 1.01/1.27 [27]P1(x271,x272)+~P2(f4(x271,x272),x272)
% 1.01/1.27 [25]P2(x251,x252)+~P2(x251,f1(x253,x252))
% 1.01/1.27 [26]P2(x261,x262)+~P2(x261,f1(x262,x263))
% 1.01/1.27 [22]~P2(x221,a2)+~P2(x221,a6)+P2(x221,a3)
% 1.01/1.27 [21]~P1(x212,x211)+~P1(x211,x212)+E(x211,x212)
% 1.01/1.27 [28]E(x281,x282)+P2(f5(x281,x282),x282)+P2(f5(x281,x282),x281)
% 1.01/1.27 [30]E(x301,x302)+~P2(f5(x301,x302),x302)+~P2(f5(x301,x302),x301)
% 1.01/1.27 [24]~P1(x243,x242)+P2(x241,x242)+~P2(x241,x243)
% 1.01/1.27 [29]~P2(x291,x293)+~P2(x291,x292)+P2(x291,f1(x292,x293))
% 1.01/1.27 %EqnAxiom
% 1.01/1.27 [1]E(x11,x11)
% 1.01/1.27 [2]E(x22,x21)+~E(x21,x22)
% 1.01/1.27 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.01/1.27 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 1.01/1.27 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 1.01/1.27 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 1.01/1.27 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 1.01/1.27 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83))
% 1.01/1.27 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92))
% 1.01/1.27 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 1.01/1.27 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 1.01/1.27 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 1.01/1.27 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 1.01/1.27
% 1.01/1.27 %-------------------------------------------
% 1.01/1.27 cnf(31,plain,
% 1.01/1.27 (P1(f1(x311,x312),f1(x312,x311))),
% 1.01/1.27 inference(scs_inference,[],[14,15,11])).
% 1.01/1.27 cnf(34,plain,
% 1.01/1.27 (~E(f1(a6,a2),a3)),
% 1.01/1.27 inference(scs_inference,[],[16,14,15,11,2,3])).
% 1.01/1.27 cnf(59,plain,
% 1.01/1.27 (~P2(x591,f1(x592,x593))+P2(x591,f1(x593,x592))),
% 1.01/1.27 inference(scs_inference,[],[31,24])).
% 1.01/1.27 cnf(110,plain,
% 1.01/1.27 (P2(f5(f1(a6,a2),a3),f1(a6,a2))+P2(f5(f1(a6,a2),a3),a3)),
% 1.01/1.27 inference(scs_inference,[],[34,28])).
% 1.01/1.27 cnf(142,plain,
% 1.01/1.27 (~P2(f5(f1(a6,a2),a3),a3)+~P2(f5(f1(a6,a2),a3),f1(a6,a2))),
% 1.01/1.27 inference(scs_inference,[],[34,30])).
% 1.01/1.27 cnf(145,plain,
% 1.01/1.27 (~P2(f5(f1(a6,a2),a3),a2)+~P2(f5(f1(a6,a2),a3),a6)+~P2(f5(f1(a6,a2),a3),a3)),
% 1.01/1.27 inference(scs_inference,[],[142,29])).
% 1.01/1.27 cnf(147,plain,
% 1.01/1.27 (~P2(f5(f1(a6,a2),a3),a2)+~P2(f5(f1(a6,a2),a3),a3)),
% 1.01/1.27 inference(scs_inference,[],[145,20])).
% 1.01/1.27 cnf(148,plain,
% 1.01/1.27 (~P2(f5(f1(a6,a2),a3),a2)+P2(f5(f1(a6,a2),a3),f1(a6,a2))),
% 1.01/1.27 inference(scs_inference,[],[34,147,28])).
% 1.01/1.27 cnf(149,plain,
% 1.01/1.27 (P2(f5(f1(a6,a2),a3),a6)+~P2(f5(f1(a6,a2),a3),a2)),
% 1.01/1.27 inference(scs_inference,[],[148,26])).
% 1.01/1.27 cnf(150,plain,
% 1.01/1.27 (P2(f5(f1(a6,a2),a3),a6)+~P2(f5(f1(a6,a2),a3),f1(x1501,a2))),
% 1.01/1.27 inference(scs_inference,[],[149,25])).
% 1.01/1.27 cnf(186,plain,
% 1.01/1.27 (~P2(f5(f1(a6,a2),a3),a3)),
% 1.01/1.27 inference(scs_inference,[],[19,147])).
% 1.01/1.27 cnf(187,plain,
% 1.01/1.27 (P2(f5(f1(a6,a2),a3),f1(a6,a2))),
% 1.01/1.27 inference(scs_inference,[],[186,110])).
% 1.01/1.27 cnf(193,plain,
% 1.01/1.27 (~P2(f5(f1(a6,a2),a3),a6)+~P2(f5(f1(a6,a2),a3),a2)),
% 1.01/1.27 inference(scs_inference,[],[186,25,59,22])).
% 1.01/1.27 cnf(195,plain,
% 1.01/1.27 (P2(f5(f1(a6,a2),a3),a6)),
% 1.01/1.27 inference(scs_inference,[],[187,150])).
% 1.01/1.27 cnf(196,plain,
% 1.01/1.27 (~P2(f5(f1(a6,a2),a3),a2)),
% 1.01/1.27 inference(scs_inference,[],[187,193,26])).
% 1.01/1.27 cnf(202,plain,
% 1.01/1.27 ($false),
% 1.01/1.27 inference(scs_inference,[],[196,195,187,13,59,25]),
% 1.01/1.27 ['proof']).
% 1.01/1.27 % SZS output end Proof
% 1.01/1.27 % Total time :0.620000s
%------------------------------------------------------------------------------