TSTP Solution File: SET194+3 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET194+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n022.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 14:29:10 EDT 2023
% Result : Theorem 0.19s 0.66s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET194+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n022.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 12:22:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.65 %-------------------------------------------
% 0.19/0.65 % File :CSE---1.6
% 0.19/0.65 % Problem :theBenchmark
% 0.19/0.65 % Transform :cnf
% 0.19/0.65 % Format :tptp:raw
% 0.19/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.65
% 0.19/0.65 % Result :Theorem 0.000000s
% 0.19/0.65 % Output :CNFRefutation 0.000000s
% 0.19/0.65 %-------------------------------------------
% 0.19/0.65 %--------------------------------------------------------------------------
% 0.19/0.65 % File : SET194+3 : TPTP v8.1.2. Released v2.2.0.
% 0.19/0.65 % Domain : Set Theory
% 0.19/0.65 % Problem : X is a subset of the union of X and Y
% 0.19/0.65 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.19/0.65 % English :
% 0.19/0.65
% 0.19/0.65 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.19/0.65 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.19/0.65 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.65 % Source : [ILF]
% 0.19/0.65 % Names : BOOLE (31) [TS89]
% 0.19/0.65
% 0.19/0.65 % Status : Theorem
% 0.19/0.65 % Rating : 0.08 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.00 v6.1.0, 0.03 v6.0.0, 0.04 v5.4.0, 0.11 v5.3.0, 0.15 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, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 0.19/0.65 % Syntax : Number of formulae : 6 ( 3 unt; 0 def)
% 0.19/0.65 % Number of atoms : 12 ( 2 equ)
% 0.19/0.66 % Maximal formula atoms : 3 ( 2 avg)
% 0.19/0.66 % Number of connectives : 6 ( 0 ~; 1 |; 0 &)
% 0.19/0.66 % ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.66 % Maximal formula depth : 6 ( 4 avg)
% 0.19/0.66 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.66 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.19/0.66 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.19/0.66 % Number of variables : 14 ( 14 !; 0 ?)
% 0.19/0.66 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.66
% 0.19/0.66 % Comments :
% 0.19/0.66 %--------------------------------------------------------------------------
% 0.19/0.66 %---- line(boole - df(2),1833042)
% 0.19/0.66 fof(union_defn,axiom,
% 0.19/0.66 ! [B,C,D] :
% 0.19/0.66 ( member(D,union(B,C))
% 0.19/0.66 <=> ( member(D,B)
% 0.19/0.66 | member(D,C) ) ) ).
% 0.19/0.66
% 0.19/0.66 %---- line(tarski - df(3),1832749)
% 0.19/0.66 fof(subset_defn,axiom,
% 0.19/0.66 ! [B,C] :
% 0.19/0.66 ( subset(B,C)
% 0.19/0.66 <=> ! [D] :
% 0.19/0.66 ( member(D,B)
% 0.19/0.66 => member(D,C) ) ) ).
% 0.19/0.66
% 0.19/0.66 %---- property(commutativity,op(union,2,function))
% 0.19/0.66 fof(commutativity_of_union,axiom,
% 0.19/0.66 ! [B,C] : union(B,C) = union(C,B) ).
% 0.19/0.66
% 0.19/0.66 %---- property(reflexivity,op(subset,2,predicate))
% 0.19/0.66 fof(reflexivity_of_subset,axiom,
% 0.19/0.66 ! [B] : subset(B,B) ).
% 0.19/0.66
% 0.19/0.66 %---- line(hidden - axiom35,1832615)
% 0.19/0.66 fof(equal_member_defn,axiom,
% 0.19/0.66 ! [B,C] :
% 0.19/0.66 ( B = C
% 0.19/0.66 <=> ! [D] :
% 0.19/0.66 ( member(D,B)
% 0.19/0.66 <=> member(D,C) ) ) ).
% 0.19/0.66
% 0.19/0.66 %---- line(boole - th(31),1833190)
% 0.19/0.66 fof(prove_subset_of_union,conjecture,
% 0.19/0.66 ! [B,C] : subset(B,union(B,C)) ).
% 0.19/0.66
% 0.19/0.66 %--------------------------------------------------------------------------
% 0.19/0.66 %-------------------------------------------
% 0.19/0.66 % Proof found
% 0.19/0.66 % SZS status Theorem for theBenchmark
% 0.19/0.66 % SZS output start Proof
% 0.19/0.66 %ClaNum:24(EqnAxiom:13)
% 0.19/0.66 %VarNum:55(SingletonVarNum:23)
% 0.19/0.66 %MaxLitNum:3
% 0.19/0.66 %MaxfuncDepth:1
% 0.19/0.66 %SharedTerms:4
% 0.19/0.66 %goalClause: 16
% 0.19/0.66 %singleGoalClaCount:1
% 0.19/0.66 [16]~P1(a2,f1(a2,a5))
% 0.19/0.66 [14]P1(x141,x141)
% 0.19/0.66 [15]E(f1(x151,x152),f1(x152,x151))
% 0.19/0.66 [17]P1(x171,x172)+P2(f3(x171,x172),x171)
% 0.19/0.66 [21]P1(x211,x212)+~P2(f3(x211,x212),x212)
% 0.19/0.66 [19]~P2(x191,x193)+P2(x191,f1(x192,x193))
% 0.19/0.66 [20]~P2(x201,x202)+P2(x201,f1(x202,x203))
% 0.19/0.66 [22]E(x221,x222)+P2(f4(x221,x222),x222)+P2(f4(x221,x222),x221)
% 0.19/0.66 [24]E(x241,x242)+~P2(f4(x241,x242),x242)+~P2(f4(x241,x242),x241)
% 0.19/0.66 [18]~P1(x183,x182)+P2(x181,x182)+~P2(x181,x183)
% 0.19/0.66 [23]P2(x231,x232)+P2(x231,x233)+~P2(x231,f1(x233,x232))
% 0.19/0.66 %EqnAxiom
% 0.19/0.66 [1]E(x11,x11)
% 0.19/0.66 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.66 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.19/0.66 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.19/0.66 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.19/0.66 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.19/0.66 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83))
% 0.19/0.66 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92))
% 0.19/0.66 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 0.19/0.66 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 0.19/0.66 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 0.19/0.66 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 0.19/0.66
% 0.19/0.66 %-------------------------------------------
% 0.19/0.67 cnf(26,plain,
% 0.19/0.67 (P1(x261,x261)),
% 0.19/0.67 inference(rename_variables,[],[14])).
% 0.19/0.67 cnf(32,plain,
% 0.19/0.67 (~P2(f3(a2,f1(a2,a5)),f1(a2,a5))),
% 0.19/0.67 inference(scs_inference,[],[16,14,26,15,11,10,3,2,21])).
% 0.19/0.67 cnf(34,plain,
% 0.19/0.67 (P2(f3(a2,f1(a2,a5)),a2)),
% 0.19/0.67 inference(scs_inference,[],[16,14,26,15,11,10,3,2,21,17])).
% 0.19/0.67 cnf(51,plain,
% 0.19/0.67 ($false),
% 0.19/0.67 inference(scs_inference,[],[32,34,20]),
% 0.19/0.67 ['proof']).
% 0.19/0.67 % SZS output end Proof
% 0.19/0.67 % Total time :0.000000s
%------------------------------------------------------------------------------