TSTP Solution File: SET185+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET185+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 : n028.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 14:29:07 EDT 2023
% Result : Theorem 0.19s 0.75s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET185+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.35 % Computer : n028.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat Aug 26 12:10:22 EDT 2023
% 0.19/0.35 % CPUTime :
% 0.19/0.59 start to proof:theBenchmark
% 0.19/0.74 %-------------------------------------------
% 0.19/0.74 % File :CSE---1.6
% 0.19/0.74 % Problem :theBenchmark
% 0.19/0.74 % Transform :cnf
% 0.19/0.74 % Format :tptp:raw
% 0.19/0.74 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.74
% 0.19/0.74 % Result :Theorem 0.110000s
% 0.19/0.74 % Output :CNFRefutation 0.110000s
% 0.19/0.75 %-------------------------------------------
% 0.19/0.75 %--------------------------------------------------------------------------
% 0.19/0.75 % File : SET185+3 : TPTP v8.1.2. Released v2.2.0.
% 0.19/0.75 % Domain : Set Theory
% 0.19/0.75 % Problem : If X is a subset of Y, then the union of X and Y is Y
% 0.19/0.75 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.19/0.75 % English :
% 0.19/0.75
% 0.19/0.75 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.19/0.75 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.19/0.75 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.75 % Source : [ILF]
% 0.19/0.75 % Names : BOOLE (35) [TS89]
% 0.19/0.75
% 0.19/0.75 % Status : Theorem
% 0.19/0.75 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.08 v6.3.0, 0.12 v6.2.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.26 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.1, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 0.19/0.75 % Syntax : Number of formulae : 7 ( 2 unt; 0 def)
% 0.19/0.75 % Number of atoms : 16 ( 4 equ)
% 0.19/0.75 % Maximal formula atoms : 3 ( 2 avg)
% 0.19/0.75 % Number of connectives : 9 ( 0 ~; 1 |; 1 &)
% 0.19/0.75 % ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.75 % Maximal formula depth : 6 ( 5 avg)
% 0.19/0.75 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.75 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.19/0.75 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.19/0.75 % Number of variables : 16 ( 16 !; 0 ?)
% 0.19/0.75 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.75
% 0.19/0.75 % Comments :
% 0.19/0.75 %--------------------------------------------------------------------------
% 0.19/0.75 %---- line(boole - df(2),1833042)
% 0.19/0.75 fof(union_defn,axiom,
% 0.19/0.75 ! [B,C,D] :
% 0.19/0.75 ( member(D,union(B,C))
% 0.19/0.75 <=> ( member(D,B)
% 0.19/0.75 | member(D,C) ) ) ).
% 0.19/0.75
% 0.19/0.75 %---- line(tarski - df(3),1832749)
% 0.19/0.75 fof(subset_defn,axiom,
% 0.19/0.75 ! [B,C] :
% 0.19/0.75 ( subset(B,C)
% 0.19/0.75 <=> ! [D] :
% 0.19/0.75 ( member(D,B)
% 0.19/0.75 => member(D,C) ) ) ).
% 0.19/0.75
% 0.19/0.75 %---- line(boole - df(8),1833103)
% 0.19/0.75 fof(equal_defn,axiom,
% 0.19/0.75 ! [B,C] :
% 0.19/0.75 ( B = C
% 0.19/0.75 <=> ( subset(B,C)
% 0.19/0.75 & subset(C,B) ) ) ).
% 0.19/0.75
% 0.19/0.75 %---- property(commutativity,op(union,2,function))
% 0.19/0.75 fof(commutativity_of_union,axiom,
% 0.19/0.75 ! [B,C] : union(B,C) = union(C,B) ).
% 0.19/0.75
% 0.19/0.75 %---- property(reflexivity,op(subset,2,predicate))
% 0.19/0.75 fof(reflexivity_of_subset,axiom,
% 0.19/0.75 ! [B] : subset(B,B) ).
% 0.19/0.75
% 0.19/0.75 %---- line(hidden - axiom43,1832615)
% 0.19/0.75 fof(equal_member_defn,axiom,
% 0.19/0.75 ! [B,C] :
% 0.19/0.75 ( B = C
% 0.19/0.75 <=> ! [D] :
% 0.19/0.75 ( member(D,B)
% 0.19/0.75 <=> member(D,C) ) ) ).
% 0.19/0.75
% 0.19/0.75 %---- line(boole - th(35),1833266)
% 0.19/0.75 fof(prove_subset_union,conjecture,
% 0.19/0.75 ! [B,C] :
% 0.19/0.75 ( subset(B,C)
% 0.19/0.75 => union(B,C) = C ) ).
% 0.19/0.75
% 0.19/0.75 %--------------------------------------------------------------------------
% 0.19/0.75 %-------------------------------------------
% 0.19/0.75 % Proof found
% 0.19/0.75 % SZS status Theorem for theBenchmark
% 0.19/0.75 % SZS output start Proof
% 0.19/0.76 %ClaNum:28(EqnAxiom:13)
% 0.19/0.76 %VarNum:65(SingletonVarNum:27)
% 0.19/0.76 %MaxLitNum:3
% 0.19/0.76 %MaxfuncDepth:1
% 0.19/0.76 %SharedTerms:5
% 0.19/0.76 %goalClause: 14 17
% 0.19/0.76 %singleGoalClaCount:2
% 0.19/0.76 [14]P1(a1,a4)
% 0.19/0.76 [17]~E(f5(a1,a4),a4)
% 0.19/0.76 [15]P1(x151,x151)
% 0.19/0.76 [16]E(f5(x161,x162),f5(x162,x161))
% 0.19/0.76 [19]~E(x191,x192)+P1(x191,x192)
% 0.19/0.76 [21]P1(x211,x212)+P2(f2(x211,x212),x211)
% 0.19/0.76 [25]P1(x251,x252)+~P2(f2(x251,x252),x252)
% 0.19/0.76 [23]~P2(x231,x233)+P2(x231,f5(x232,x233))
% 0.19/0.76 [24]~P2(x241,x242)+P2(x241,f5(x242,x243))
% 0.19/0.76 [20]~P1(x202,x201)+~P1(x201,x202)+E(x201,x202)
% 0.19/0.76 [26]E(x261,x262)+P2(f3(x261,x262),x262)+P2(f3(x261,x262),x261)
% 0.19/0.76 [28]E(x281,x282)+~P2(f3(x281,x282),x282)+~P2(f3(x281,x282),x281)
% 0.19/0.76 [22]~P1(x223,x222)+P2(x221,x222)+~P2(x221,x223)
% 0.19/0.76 [27]P2(x271,x272)+P2(x271,x273)+~P2(x271,f5(x273,x272))
% 0.19/0.76 %EqnAxiom
% 0.19/0.76 [1]E(x11,x11)
% 0.19/0.76 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.76 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.76 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 0.19/0.76 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 0.19/0.76 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.19/0.76 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.19/0.76 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83))
% 0.19/0.76 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92))
% 0.19/0.76 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 0.19/0.76 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 0.19/0.76 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 0.19/0.76 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 0.19/0.76
% 0.19/0.76 %-------------------------------------------
% 0.19/0.76 cnf(32,plain,
% 0.19/0.76 (~E(f5(a4,a1),a4)),
% 0.19/0.76 inference(scs_inference,[],[15,17,16,11,2,3])).
% 0.19/0.76 cnf(34,plain,
% 0.19/0.76 (~P2(x341,a1)+P2(x341,a4)),
% 0.19/0.76 inference(scs_inference,[],[14,15,17,16,11,2,3,22])).
% 0.19/0.76 cnf(73,plain,
% 0.19/0.76 (~E(a4,f5(a4,a1))),
% 0.19/0.76 inference(scs_inference,[],[32,14,20,2])).
% 0.19/0.76 cnf(115,plain,
% 0.19/0.76 (P2(f3(a4,f5(a4,a1)),a4)+P2(f3(a4,f5(a4,a1)),f5(a4,a1))),
% 0.19/0.76 inference(scs_inference,[],[73,26])).
% 0.19/0.76 cnf(124,plain,
% 0.19/0.76 (~P2(f3(a4,f5(a4,a1)),a4)),
% 0.19/0.76 inference(scs_inference,[],[73,28,24])).
% 0.19/0.76 cnf(126,plain,
% 0.19/0.76 (P2(f3(a4,f5(a4,a1)),f5(a4,a1))),
% 0.19/0.76 inference(scs_inference,[],[124,115])).
% 0.19/0.76 cnf(132,plain,
% 0.19/0.76 ($false),
% 0.19/0.76 inference(scs_inference,[],[124,126,16,34,13,27]),
% 0.19/0.76 ['proof']).
% 0.19/0.76 % SZS output end Proof
% 0.19/0.76 % Total time :0.110000s
%------------------------------------------------------------------------------