TSTP Solution File: SET633+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET633+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 : n007.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 14:30:30 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET633+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n007.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 09:12:41 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 % File :CSE---1.6
% 0.20/0.61 % Problem :theBenchmark
% 0.20/0.61 % Transform :cnf
% 0.20/0.61 % Format :tptp:raw
% 0.20/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.61
% 0.20/0.61 % Result :Theorem 0.000000s
% 0.20/0.61 % Output :CNFRefutation 0.000000s
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 %--------------------------------------------------------------------------
% 0.20/0.61 % File : SET633+3 : TPTP v8.1.2. Released v2.2.0.
% 0.20/0.61 % Domain : Set Theory
% 0.20/0.61 % Problem : If X \ Y (= Z and Y \ X (= Z, then X sym\ Y (= Z
% 0.20/0.61 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.20/0.61 % English : If the difference of X and Y is a subset of Z and the
% 0.20/0.61 % difference of Y and X is a subset of Z, then the symmetric
% 0.20/0.61 % difference of X and Y is a subset of Z.
% 0.20/0.61
% 0.20/0.61 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.20/0.61 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.20/0.62 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.62 % Source : [ILF]
% 0.20/0.62 % Names : BOOLE (115) [TS89]
% 0.20/0.62
% 0.20/0.62 % Status : Theorem
% 0.20/0.62 % Rating : 0.11 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.03 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.00 v6.2.0, 0.08 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.11 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 v2.5.0, 0.12 v2.4.0, 0.25 v2.3.0, 0.33 v2.2.1
% 0.20/0.62 % Syntax : Number of formulae : 9 ( 4 unt; 0 def)
% 0.20/0.62 % Number of atoms : 19 ( 4 equ)
% 0.20/0.62 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.62 % Number of connectives : 11 ( 1 ~; 0 |; 3 &)
% 0.20/0.62 % ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.62 % Maximal formula depth : 7 ( 5 avg)
% 0.20/0.62 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.62 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.20/0.62 % Number of functors : 3 ( 3 usr; 0 con; 2-2 aty)
% 0.20/0.62 % Number of variables : 22 ( 22 !; 0 ?)
% 0.20/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.62
% 0.20/0.62 % Comments :
% 0.20/0.62 %--------------------------------------------------------------------------
% 0.20/0.62 %---- line(boole - df(7),1833089)
% 0.20/0.62 fof(symmetric_difference_defn,axiom,
% 0.20/0.62 ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ).
% 0.20/0.62
% 0.20/0.62 %---- line(boole - th(32),1833206)
% 0.20/0.62 fof(union_subset,axiom,
% 0.20/0.62 ! [B,C,D] :
% 0.20/0.62 ( ( subset(B,C)
% 0.20/0.62 & subset(D,C) )
% 0.20/0.62 => subset(union(B,D),C) ) ).
% 0.20/0.62
% 0.20/0.62 %---- line(boole - df(4),1833078)
% 0.20/0.62 fof(difference_defn,axiom,
% 0.20/0.62 ! [B,C,D] :
% 0.20/0.62 ( member(D,difference(B,C))
% 0.20/0.62 <=> ( member(D,B)
% 0.20/0.62 & ~ member(D,C) ) ) ).
% 0.20/0.62
% 0.20/0.62 %---- line(tarski - df(3),1832749)
% 0.20/0.62 fof(subset_defn,axiom,
% 0.20/0.62 ! [B,C] :
% 0.20/0.62 ( subset(B,C)
% 0.20/0.62 <=> ! [D] :
% 0.20/0.62 ( member(D,B)
% 0.20/0.62 => member(D,C) ) ) ).
% 0.20/0.62
% 0.20/0.62 %---- property(commutativity,op(union,2,function))
% 0.20/0.62 fof(commutativity_of_union,axiom,
% 0.20/0.62 ! [B,C] : union(B,C) = union(C,B) ).
% 0.20/0.62
% 0.20/0.62 %---- property(commutativity,op(symmetric_difference,2,function))
% 0.20/0.62 fof(commutativity_of_symmetric_difference,axiom,
% 0.20/0.62 ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) ).
% 0.20/0.62
% 0.20/0.62 %---- line(hidden - axiom210,1832615)
% 0.20/0.62 fof(equal_member_defn,axiom,
% 0.20/0.62 ! [B,C] :
% 0.20/0.62 ( B = C
% 0.20/0.62 <=> ! [D] :
% 0.20/0.62 ( member(D,B)
% 0.20/0.62 <=> member(D,C) ) ) ).
% 0.20/0.62
% 0.20/0.62 %---- property(reflexivity,op(subset,2,predicate))
% 0.20/0.62 fof(reflexivity_of_subset,axiom,
% 0.20/0.62 ! [B] : subset(B,B) ).
% 0.20/0.62
% 0.20/0.62 %---- line(boole - th(115),1834412)
% 0.20/0.62 fof(prove_th115,conjecture,
% 0.20/0.62 ! [B,C,D] :
% 0.20/0.62 ( ( subset(difference(B,C),D)
% 0.20/0.62 & subset(difference(C,B),D) )
% 0.20/0.62 => subset(symmetric_difference(B,C),D) ) ).
% 0.20/0.62
% 0.20/0.62 %--------------------------------------------------------------------------
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark
% 0.20/0.62 % SZS output start Proof
% 0.20/0.62 %ClaNum:30(EqnAxiom:15)
% 0.20/0.62 %VarNum:62(SingletonVarNum:26)
% 0.20/0.62 %MaxLitNum:3
% 0.20/0.62 %MaxfuncDepth:2
% 0.20/0.62 %SharedTerms:9
% 0.20/0.62 %goalClause: 18 19 21
% 0.20/0.62 %singleGoalClaCount:3
% 0.20/0.62 [18]P1(f3(a2,a6),a7)
% 0.20/0.62 [19]P1(f3(a6,a2),a7)
% 0.20/0.62 [21]~P1(f1(f3(a2,a6),f3(a6,a2)),a7)
% 0.20/0.62 [16]P1(x161,x161)
% 0.20/0.62 [17]E(f1(x171,x172),f1(x172,x171))
% 0.20/0.62 [22]P1(x221,x222)+P2(f4(x221,x222),x221)
% 0.20/0.62 [26]P1(x261,x262)+~P2(f4(x261,x262),x262)
% 0.20/0.62 [25]P2(x251,x252)+~P2(x251,f3(x252,x253))
% 0.20/0.62 [29]~P2(x291,x292)+~P2(x291,f3(x293,x292))
% 0.20/0.62 [27]E(x271,x272)+P2(f5(x271,x272),x272)+P2(f5(x271,x272),x271)
% 0.20/0.62 [30]E(x301,x302)+~P2(f5(x301,x302),x302)+~P2(f5(x301,x302),x301)
% 0.20/0.62 [23]~P2(x231,x233)+P2(x231,x232)+~P1(x233,x232)
% 0.20/0.62 [24]~P2(x241,x243)+P2(x241,x242)+P2(x241,f3(x243,x242))
% 0.20/0.62 [28]~P1(x282,x283)+~P1(x281,x283)+P1(f1(x281,x282),x283)
% 0.20/0.62 %EqnAxiom
% 0.20/0.62 [1]E(x11,x11)
% 0.20/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.62 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.20/0.62 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.20/0.62 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 0.20/0.62 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 0.20/0.62 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83))
% 0.20/0.62 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92))
% 0.20/0.62 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103))
% 0.20/0.62 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112))
% 0.20/0.62 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123)
% 0.20/0.62 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131)
% 0.20/0.62 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143)
% 0.20/0.62 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151)
% 0.20/0.62
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 cnf(36,plain,
% 0.20/0.62 ($false),
% 0.20/0.62 inference(scs_inference,[],[18,16,19,21,17,13,12,3,28]),
% 0.20/0.62 ['proof']).
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time :0.000000s
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