TSTP Solution File: SET581+3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET581+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 : n021.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 14:30:12 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET581+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 08:29:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof:theBenchmark
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % File :CSE---1.6
% 0.20/0.65 % Problem :theBenchmark
% 0.20/0.65 % Transform :cnf
% 0.20/0.65 % Format :tptp:raw
% 0.20/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.65
% 0.20/0.65 % Result :Theorem 0.010000s
% 0.20/0.65 % Output :CNFRefutation 0.010000s
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 % File : SET581+3 : TPTP v8.1.2. Released v2.2.0.
% 0.20/0.65 % Domain : Set Theory
% 0.20/0.65 % Problem : Trybulec's 24th Boolean property of sets
% 0.20/0.65 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.20/0.65 % English :
% 0.20/0.65
% 0.20/0.65 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.20/0.65 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.20/0.65 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.65 % Source : [ILF]
% 0.20/0.65 % Names : BOOLE (24) [TS89]
% 0.20/0.65
% 0.20/0.65 % Status : Theorem
% 0.20/0.65 % Rating : 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.14 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, 0.05 v3.3.0, 0.07 v3.2.0, 0.09 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 0.20/0.65 % Syntax : Number of formulae : 7 ( 2 unt; 0 def)
% 0.20/0.65 % Number of atoms : 15 ( 3 equ)
% 0.20/0.65 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.65 % Number of connectives : 11 ( 3 ~; 0 |; 2 &)
% 0.20/0.65 % ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.65 % Maximal formula depth : 6 ( 5 avg)
% 0.20/0.65 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.65 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.20/0.65 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.20/0.65 % Number of variables : 16 ( 16 !; 0 ?)
% 0.20/0.65 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.65
% 0.20/0.65 % Comments :
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 %---- line(boole - df(3),1833060)
% 0.20/0.65 fof(intersection_defn,axiom,
% 0.20/0.65 ! [B,C,D] :
% 0.20/0.65 ( member(D,intersection(B,C))
% 0.20/0.65 <=> ( member(D,B)
% 0.20/0.65 & member(D,C) ) ) ).
% 0.20/0.65
% 0.20/0.65 %---- line(hidden - axiom19,1832636)
% 0.20/0.65 fof(empty_set_defn,axiom,
% 0.20/0.65 ! [B] : ~ member(B,empty_set) ).
% 0.20/0.65
% 0.20/0.65 %---- line(hidden - axiom20,1832615)
% 0.20/0.65 fof(equal_member_defn,axiom,
% 0.20/0.65 ! [B,C] :
% 0.20/0.65 ( B = C
% 0.20/0.65 <=> ! [D] :
% 0.20/0.65 ( member(D,B)
% 0.20/0.65 <=> member(D,C) ) ) ).
% 0.20/0.65
% 0.20/0.65 %---- line(hidden - axiom21,1832619)
% 0.20/0.65 fof(not_equal_defn,axiom,
% 0.20/0.65 ! [B,C] :
% 0.20/0.65 ( not_equal(B,C)
% 0.20/0.65 <=> B != C ) ).
% 0.20/0.65
% 0.20/0.65 %---- property(commutativity,op(intersection,2,function))
% 0.20/0.65 fof(commutativity_of_intersection,axiom,
% 0.20/0.65 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.20/0.65
% 0.20/0.65 %---- line(hidden - axiom23,1832628)
% 0.20/0.65 fof(empty_defn,axiom,
% 0.20/0.65 ! [B] :
% 0.20/0.65 ( empty(B)
% 0.20/0.65 <=> ! [C] : ~ member(C,B) ) ).
% 0.20/0.65
% 0.20/0.65 %---- line(boole - th(24),1833127)
% 0.20/0.65 fof(prove_th24,conjecture,
% 0.20/0.65 ! [B,C,D] :
% 0.20/0.65 ( ( member(B,C)
% 0.20/0.65 & member(B,D) )
% 0.20/0.65 => not_equal(intersection(C,D),empty_set) ) ).
% 0.20/0.65
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % Proof found
% 0.20/0.65 % SZS status Theorem for theBenchmark
% 0.20/0.65 % SZS output start Proof
% 0.20/0.66 %ClaNum:27(EqnAxiom:13)
% 0.20/0.66 %VarNum:52(SingletonVarNum:23)
% 0.20/0.66 %MaxLitNum:3
% 0.20/0.66 %MaxfuncDepth:1
% 0.20/0.66 %SharedTerms:8
% 0.20/0.66 %goalClause: 14 15 18
% 0.20/0.66 %singleGoalClaCount:3
% 0.20/0.66 [14]P1(a1,a5)
% 0.20/0.66 [15]P1(a1,a6)
% 0.20/0.66 [18]~P3(f7(a5,a6),a2)
% 0.20/0.66 [17]~P1(x171,a2)
% 0.20/0.66 [16]E(f7(x161,x162),f7(x162,x161))
% 0.20/0.66 [20]P2(x201)+P1(f3(x201),x201)
% 0.20/0.66 [19]P3(x191,x192)+E(x191,x192)
% 0.20/0.66 [21]~P3(x211,x212)+~E(x211,x212)
% 0.20/0.66 [22]~P2(x221)+~P1(x222,x221)
% 0.20/0.66 [23]P1(x231,x232)+~P1(x231,f7(x233,x232))
% 0.20/0.66 [24]P1(x241,x242)+~P1(x241,f7(x242,x243))
% 0.20/0.66 [25]E(x251,x252)+P1(f4(x251,x252),x252)+P1(f4(x251,x252),x251)
% 0.20/0.66 [27]E(x271,x272)+~P1(f4(x271,x272),x272)+~P1(f4(x271,x272),x271)
% 0.20/0.66 [26]~P1(x261,x263)+~P1(x261,x262)+P1(x261,f7(x262,x263))
% 0.20/0.66 %EqnAxiom
% 0.20/0.66 [1]E(x11,x11)
% 0.20/0.66 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.66 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43))
% 0.20/0.66 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52))
% 0.20/0.66 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.20/0.66 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.20/0.66 [8]~E(x81,x82)+E(f3(x81),f3(x82))
% 0.20/0.66 [9]P1(x92,x93)+~E(x91,x92)+~P1(x91,x93)
% 0.20/0.66 [10]P1(x103,x102)+~E(x101,x102)+~P1(x103,x101)
% 0.20/0.66 [11]~P2(x111)+P2(x112)+~E(x111,x112)
% 0.20/0.66 [12]P3(x122,x123)+~E(x121,x122)+~P3(x121,x123)
% 0.20/0.66 [13]P3(x133,x132)+~E(x131,x132)+~P3(x133,x131)
% 0.20/0.66
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 cnf(28,plain,
% 0.20/0.66 (~P3(f7(x281,x282),f7(x282,x281))),
% 0.20/0.66 inference(scs_inference,[],[16,21])).
% 0.20/0.66 cnf(30,plain,
% 0.20/0.66 (~P1(x301,a2)),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(32,plain,
% 0.20/0.66 (~E(a5,a2)),
% 0.20/0.66 inference(scs_inference,[],[14,17,30,16,21,20,10])).
% 0.20/0.66 cnf(33,plain,
% 0.20/0.66 (~P1(x331,a2)),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(34,plain,
% 0.20/0.66 (~E(a2,a5)),
% 0.20/0.66 inference(scs_inference,[],[14,17,30,16,21,20,10,2])).
% 0.20/0.66 cnf(35,plain,
% 0.20/0.66 (~P2(a5)),
% 0.20/0.66 inference(scs_inference,[],[14,17,30,16,21,20,10,2,22])).
% 0.20/0.66 cnf(37,plain,
% 0.20/0.66 (E(f7(a5,a6),a2)),
% 0.20/0.66 inference(scs_inference,[],[14,17,30,18,16,21,20,10,2,22,19])).
% 0.20/0.66 cnf(44,plain,
% 0.20/0.66 (E(f4(x441,f7(a5,a6)),f4(x441,a2))),
% 0.20/0.66 inference(scs_inference,[],[14,17,30,33,18,16,21,20,10,2,22,19,24,23,8,7])).
% 0.20/0.66 cnf(45,plain,
% 0.20/0.66 (E(f4(f7(a5,a6),x451),f4(a2,x451))),
% 0.20/0.66 inference(scs_inference,[],[14,17,30,33,18,16,21,20,10,2,22,19,24,23,8,7,6])).
% 0.20/0.66 cnf(46,plain,
% 0.20/0.66 (E(f7(x461,f7(a5,a6)),f7(x461,a2))),
% 0.20/0.66 inference(scs_inference,[],[14,17,30,33,18,16,21,20,10,2,22,19,24,23,8,7,6,5])).
% 0.20/0.66 cnf(65,plain,
% 0.20/0.66 (~P3(f7(x651,x652),f7(x652,x651))),
% 0.20/0.66 inference(rename_variables,[],[28])).
% 0.20/0.66 cnf(67,plain,
% 0.20/0.66 (~P1(x671,a2)),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(72,plain,
% 0.20/0.66 (E(f4(x721,f7(a5,a6)),f4(x721,a2))),
% 0.20/0.66 inference(rename_variables,[],[44])).
% 0.20/0.66 cnf(76,plain,
% 0.20/0.66 ($false),
% 0.20/0.66 inference(scs_inference,[],[14,15,17,67,16,28,65,44,72,45,46,34,37,32,35,20,19,12,25,13,3,2,10,26]),
% 0.20/0.66 ['proof']).
% 0.20/0.66 % SZS output end Proof
% 0.20/0.66 % Total time :0.010000s
%------------------------------------------------------------------------------