TSTP Solution File: SET618+3 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET618+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 : n020.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 14:30:25 EDT 2023
% Result : Theorem 0.21s 0.62s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET618+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 11:06:30 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.55 start to proof:theBenchmark
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 % File :CSE---1.6
% 0.21/0.62 % Problem :theBenchmark
% 0.21/0.62 % Transform :cnf
% 0.21/0.62 % Format :tptp:raw
% 0.21/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.62
% 0.21/0.62 % Result :Theorem 0.010000s
% 0.21/0.62 % Output :CNFRefutation 0.010000s
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 %--------------------------------------------------------------------------
% 0.21/0.62 % File : SET618+3 : TPTP v8.1.2. Released v2.2.0.
% 0.21/0.62 % Domain : Set Theory
% 0.21/0.62 % Problem : The symmetric difference of X and X is the empty set
% 0.21/0.62 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.21/0.62 % English :
% 0.21/0.62
% 0.21/0.62 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.21/0.62 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.21/0.62 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.21/0.62 % Source : [ILF]
% 0.21/0.62 % Names : BOOLE (93) [TS89]
% 0.21/0.62
% 0.21/0.62 % Status : Theorem
% 0.21/0.62 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.13 v5.5.0, 0.07 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 v2.5.0, 0.12 v2.4.0, 0.25 v2.3.0, 0.33 v2.2.1
% 0.21/0.62 % Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% 0.21/0.62 % Number of atoms : 19 ( 8 equ)
% 0.21/0.62 % Maximal formula atoms : 3 ( 1 avg)
% 0.21/0.62 % Number of connectives : 9 ( 2 ~; 0 |; 1 &)
% 0.21/0.62 % ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% 0.21/0.62 % Maximal formula depth : 6 ( 4 avg)
% 0.21/0.62 % Maximal term depth : 3 ( 1 avg)
% 0.21/0.62 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.21/0.62 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.21/0.62 % Number of variables : 21 ( 21 !; 0 ?)
% 0.21/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.62
% 0.21/0.62 % Comments :
% 0.21/0.62 %--------------------------------------------------------------------------
% 0.21/0.62 %---- line(boole - df(7),1833089)
% 0.21/0.62 fof(symmetric_difference_defn,axiom,
% 0.21/0.62 ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ).
% 0.21/0.62
% 0.21/0.62 %---- line(boole - th(62),1833685)
% 0.21/0.62 fof(idempotency_of_union,axiom,
% 0.21/0.62 ! [B] : union(B,B) = B ).
% 0.21/0.62
% 0.21/0.62 %---- line(boole - th(73),1833852)
% 0.21/0.62 fof(self_difference_is_empty_set,axiom,
% 0.21/0.62 ! [B] : difference(B,B) = empty_set ).
% 0.21/0.62
% 0.21/0.62 %---- line(hidden - axiom171,1832636)
% 0.21/0.62 fof(empty_set_defn,axiom,
% 0.21/0.62 ! [B] : ~ member(B,empty_set) ).
% 0.21/0.62
% 0.21/0.62 %---- line(boole - df(8),1833103)
% 0.21/0.62 fof(equal_defn,axiom,
% 0.21/0.62 ! [B,C] :
% 0.21/0.62 ( B = C
% 0.21/0.62 <=> ( subset(B,C)
% 0.21/0.62 & subset(C,B) ) ) ).
% 0.21/0.62
% 0.21/0.62 %---- property(commutativity,op(union,2,function))
% 0.21/0.62 fof(commutativity_of_union,axiom,
% 0.21/0.62 ! [B,C] : union(B,C) = union(C,B) ).
% 0.21/0.62
% 0.21/0.62 %---- property(commutativity,op(symmetric_difference,2,function))
% 0.21/0.62 fof(commutativity_of_symmetric_difference,axiom,
% 0.21/0.62 ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) ).
% 0.21/0.62
% 0.21/0.62 %---- line(hidden - axiom172,1832615)
% 0.21/0.62 fof(equal_member_defn,axiom,
% 0.21/0.62 ! [B,C] :
% 0.21/0.62 ( B = C
% 0.21/0.62 <=> ! [D] :
% 0.21/0.62 ( member(D,B)
% 0.21/0.62 <=> member(D,C) ) ) ).
% 0.21/0.62
% 0.21/0.62 %---- line(tarski - df(3),1832749)
% 0.21/0.62 fof(subset_defn,axiom,
% 0.21/0.62 ! [B,C] :
% 0.21/0.62 ( subset(B,C)
% 0.21/0.62 <=> ! [D] :
% 0.21/0.62 ( member(D,B)
% 0.21/0.62 => member(D,C) ) ) ).
% 0.21/0.62
% 0.21/0.62 %---- property(reflexivity,op(subset,2,predicate))
% 0.21/0.62 fof(reflexivity_of_subset,axiom,
% 0.21/0.62 ! [B] : subset(B,B) ).
% 0.21/0.62
% 0.21/0.62 %---- line(hidden - axiom174,1832628)
% 0.21/0.62 fof(empty_defn,axiom,
% 0.21/0.62 ! [B] :
% 0.21/0.62 ( empty(B)
% 0.21/0.62 <=> ! [C] : ~ member(C,B) ) ).
% 0.21/0.62
% 0.21/0.62 %---- line(boole - th(93),1834213)
% 0.21/0.62 fof(prove_th93,conjecture,
% 0.21/0.62 ! [B] : symmetric_difference(B,B) = empty_set ).
% 0.21/0.62
% 0.21/0.62 %--------------------------------------------------------------------------
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 % Proof found
% 0.21/0.62 % SZS status Theorem for theBenchmark
% 0.21/0.62 % SZS output start Proof
% 0.21/0.62 %ClaNum:34(EqnAxiom:17)
% 0.21/0.62 %VarNum:60(SingletonVarNum:24)
% 0.21/0.62 %MaxLitNum:3
% 0.21/0.62 %MaxfuncDepth:2
% 0.21/0.62 %SharedTerms:5
% 0.21/0.62 %goalClause: 24
% 0.21/0.62 %singleGoalClaCount:1
% 0.21/0.62 [24]~E(f3(f1(a4,a4),f1(a4,a4)),a2)
% 0.21/0.62 [19]P1(x191,x191)
% 0.21/0.62 [23]~P2(x231,a2)
% 0.21/0.62 [18]E(f1(x181,x181),a2)
% 0.21/0.62 [20]E(f3(x201,x201),x201)
% 0.21/0.62 [21]E(f3(x211,x212),f3(x212,x211))
% 0.21/0.62 [27]P3(x271)+P2(f5(x271),x271)
% 0.21/0.62 [26]~E(x261,x262)+P1(x261,x262)
% 0.21/0.62 [28]~P3(x281)+~P2(x282,x281)
% 0.21/0.62 [30]P1(x301,x302)+P2(f6(x301,x302),x301)
% 0.21/0.62 [32]P1(x321,x322)+~P2(f6(x321,x322),x322)
% 0.21/0.62 [29]~P1(x292,x291)+~P1(x291,x292)+E(x291,x292)
% 0.21/0.62 [33]E(x331,x332)+P2(f7(x331,x332),x332)+P2(f7(x331,x332),x331)
% 0.21/0.62 [34]E(x341,x342)+~P2(f7(x341,x342),x342)+~P2(f7(x341,x342),x341)
% 0.21/0.62 [31]~P1(x313,x312)+P2(x311,x312)+~P2(x311,x313)
% 0.21/0.62 %EqnAxiom
% 0.21/0.62 [1]E(x11,x11)
% 0.21/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.62 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.21/0.62 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.21/0.63 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.21/0.63 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.21/0.63 [8]~E(x81,x82)+E(f5(x81),f5(x82))
% 0.21/0.63 [9]~E(x91,x92)+E(f6(x91,x93),f6(x92,x93))
% 0.21/0.63 [10]~E(x101,x102)+E(f6(x103,x101),f6(x103,x102))
% 0.21/0.63 [11]~E(x111,x112)+E(f7(x111,x113),f7(x112,x113))
% 0.21/0.63 [12]~E(x121,x122)+E(f7(x123,x121),f7(x123,x122))
% 0.21/0.63 [13]P1(x132,x133)+~E(x131,x132)+~P1(x131,x133)
% 0.21/0.63 [14]P1(x143,x142)+~E(x141,x142)+~P1(x143,x141)
% 0.21/0.63 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153)
% 0.21/0.63 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161)
% 0.21/0.63 [17]~P3(x171)+P3(x172)+~E(x171,x172)
% 0.21/0.63
% 0.21/0.63 %-------------------------------------------
% 0.21/0.63 cnf(37,plain,
% 0.21/0.63 (~P2(x371,a2)),
% 0.21/0.63 inference(rename_variables,[],[23])).
% 0.21/0.63 cnf(40,plain,
% 0.21/0.63 (~P2(x401,a2)),
% 0.21/0.63 inference(rename_variables,[],[23])).
% 0.21/0.63 cnf(46,plain,
% 0.21/0.63 (E(f3(x461,x461),x461)),
% 0.21/0.63 inference(rename_variables,[],[20])).
% 0.21/0.63 cnf(47,plain,
% 0.21/0.63 (P1(f3(x471,x471),x471)),
% 0.21/0.63 inference(scs_inference,[],[24,19,23,37,20,46,2,27,30,17,14,13,3,26])).
% 0.21/0.63 cnf(60,plain,
% 0.21/0.63 (~P1(f3(f1(a4,a4),f1(a4,a4)),a2)),
% 0.21/0.63 inference(scs_inference,[],[24,19,23,37,40,20,46,2,27,30,17,14,13,3,26,12,11,10,9,8,7,6,5,4,16,29])).
% 0.21/0.63 cnf(64,plain,
% 0.21/0.63 ($false),
% 0.21/0.63 inference(scs_inference,[],[24,18,23,47,60,2,16,14]),
% 0.21/0.63 ['proof']).
% 0.21/0.63 % SZS output end Proof
% 0.21/0.63 % Total time :0.010000s
%------------------------------------------------------------------------------