TSTP Solution File: SET594+3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET594+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 : n013.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 14:30:17 EDT 2023
% Result : Theorem 0.16s 0.73s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.10/0.31 % Computer : n013.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Aug 26 09:10:17 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.57 start to proof:theBenchmark
% 0.16/0.72 %-------------------------------------------
% 0.16/0.72 % File :CSE---1.6
% 0.16/0.72 % Problem :theBenchmark
% 0.16/0.72 % Transform :cnf
% 0.16/0.72 % Format :tptp:raw
% 0.16/0.72 % Command :java -jar mcs_scs.jar %d %s
% 0.16/0.72
% 0.16/0.72 % Result :Theorem 0.080000s
% 0.16/0.72 % Output :CNFRefutation 0.080000s
% 0.16/0.72 %-------------------------------------------
% 0.16/0.73 %--------------------------------------------------------------------------
% 0.16/0.73 % File : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% 0.16/0.73 % Domain : Set Theory
% 0.16/0.73 % Problem : If X ^ Y U X ^ Z = X, then X (= Y U Z
% 0.16/0.73 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.16/0.73 % English : If the intersection of X and the union of Y and the
% 0.16/0.73 % intersection of X and Z is X, then X is a subset of the union
% 0.16/0.73 % of Y and Z.
% 0.16/0.73
% 0.16/0.73 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.16/0.73 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.16/0.73 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.16/0.73 % Source : [ILF]
% 0.16/0.73 % Names : BOOLE (53) [TS89]
% 0.16/0.73
% 0.16/0.73 % Status : Theorem
% 0.16/0.73 % Rating : 0.19 v8.1.0, 0.28 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.23 v6.3.0, 0.12 v6.1.0, 0.30 v6.0.0, 0.26 v5.5.0, 0.37 v5.4.0, 0.43 v5.3.0, 0.44 v5.2.0, 0.30 v5.1.0, 0.29 v5.0.0, 0.33 v4.1.0, 0.35 v4.0.0, 0.33 v3.7.0, 0.35 v3.5.0, 0.32 v3.4.0, 0.37 v3.3.0, 0.43 v3.2.0, 0.55 v3.1.0, 0.56 v2.7.0, 0.33 v2.6.0, 0.14 v2.5.0, 0.12 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1
% 0.16/0.73 % Syntax : Number of formulae : 9 ( 3 unt; 0 def)
% 0.16/0.73 % Number of atoms : 20 ( 5 equ)
% 0.16/0.73 % Maximal formula atoms : 3 ( 2 avg)
% 0.16/0.73 % Number of connectives : 11 ( 0 ~; 1 |; 2 &)
% 0.16/0.73 % ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.73 % Maximal formula depth : 6 ( 5 avg)
% 0.16/0.73 % Maximal term depth : 3 ( 1 avg)
% 0.16/0.73 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.16/0.73 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.16/0.73 % Number of variables : 22 ( 22 !; 0 ?)
% 0.16/0.73 % SPC : FOF_THM_RFO_SEQ
% 0.16/0.73
% 0.16/0.73 % Comments :
% 0.16/0.73 %--------------------------------------------------------------------------
% 0.16/0.73 %---- line(tarski - df(3),1832749)
% 0.16/0.73 fof(subset_defn,axiom,
% 0.16/0.73 ! [B,C] :
% 0.16/0.73 ( subset(B,C)
% 0.16/0.73 <=> ! [D] :
% 0.16/0.73 ( member(D,B)
% 0.16/0.73 => member(D,C) ) ) ).
% 0.16/0.73
% 0.16/0.73 %---- line(boole - df(2),1833042)
% 0.16/0.73 fof(union_defn,axiom,
% 0.16/0.73 ! [B,C,D] :
% 0.16/0.73 ( member(D,union(B,C))
% 0.16/0.73 <=> ( member(D,B)
% 0.16/0.73 | member(D,C) ) ) ).
% 0.16/0.73
% 0.16/0.73 %---- line(boole - df(3),1833060)
% 0.16/0.73 fof(intersection_defn,axiom,
% 0.16/0.73 ! [B,C,D] :
% 0.16/0.73 ( member(D,intersection(B,C))
% 0.16/0.73 <=> ( member(D,B)
% 0.16/0.73 & member(D,C) ) ) ).
% 0.16/0.73
% 0.16/0.73 %---- line(boole - df(8),1833103)
% 0.16/0.73 fof(equal_defn,axiom,
% 0.16/0.73 ! [B,C] :
% 0.16/0.73 ( B = C
% 0.16/0.73 <=> ( subset(B,C)
% 0.16/0.73 & subset(C,B) ) ) ).
% 0.16/0.73
% 0.16/0.73 %---- property(commutativity,op(union,2,function))
% 0.16/0.73 fof(commutativity_of_union,axiom,
% 0.16/0.73 ! [B,C] : union(B,C) = union(C,B) ).
% 0.16/0.73
% 0.16/0.73 %---- property(commutativity,op(intersection,2,function))
% 0.16/0.73 fof(commutativity_of_intersection,axiom,
% 0.16/0.73 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.16/0.73
% 0.16/0.73 %---- property(reflexivity,op(subset,2,predicate))
% 0.16/0.73 fof(reflexivity_of_subset,axiom,
% 0.16/0.73 ! [B] : subset(B,B) ).
% 0.16/0.73
% 0.16/0.73 %---- line(hidden - axiom76,1832615)
% 0.16/0.73 fof(equal_member_defn,axiom,
% 0.16/0.73 ! [B,C] :
% 0.16/0.73 ( B = C
% 0.16/0.73 <=> ! [D] :
% 0.16/0.73 ( member(D,B)
% 0.16/0.73 <=> member(D,C) ) ) ).
% 0.16/0.73
% 0.16/0.73 %---- line(boole - th(53),1833539)
% 0.16/0.73 fof(prove_th53,conjecture,
% 0.16/0.73 ! [B,C,D] :
% 0.16/0.73 ( union(intersection(B,C),intersection(B,D)) = B
% 0.16/0.73 => subset(B,union(C,D)) ) ).
% 0.16/0.73
% 0.16/0.73 %--------------------------------------------------------------------------
% 0.16/0.73 %-------------------------------------------
% 0.16/0.73 % Proof found
% 0.16/0.73 % SZS status Theorem for theBenchmark
% 0.16/0.73 % SZS output start Proof
% 0.16/0.73 %ClaNum:34(EqnAxiom:15)
% 0.16/0.73 %VarNum:86(SingletonVarNum:38)
% 0.16/0.73 %MaxLitNum:3
% 0.16/0.73 %MaxfuncDepth:2
% 0.16/0.73 %SharedTerms:9
% 0.16/0.73 %goalClause: 19 20
% 0.16/0.73 %singleGoalClaCount:2
% 0.16/0.73 [20]~P1(a3,f1(a6,a7))
% 0.16/0.73 [19]E(f1(f2(a3,a6),f2(a3,a7)),a3)
% 0.16/0.73 [16]P1(x161,x161)
% 0.16/0.73 [17]E(f1(x171,x172),f1(x172,x171))
% 0.16/0.73 [18]E(f2(x181,x182),f2(x182,x181))
% 0.16/0.73 [22]~E(x221,x222)+P1(x221,x222)
% 0.16/0.73 [24]P1(x241,x242)+P2(f4(x241,x242),x241)
% 0.16/0.73 [30]P1(x301,x302)+~P2(f4(x301,x302),x302)
% 0.16/0.73 [26]~P2(x261,x263)+P2(x261,f1(x262,x263))
% 0.16/0.73 [27]~P2(x271,x272)+P2(x271,f1(x272,x273))
% 0.16/0.73 [28]P2(x281,x282)+~P2(x281,f2(x283,x282))
% 0.16/0.73 [29]P2(x291,x292)+~P2(x291,f2(x292,x293))
% 0.16/0.73 [23]~P1(x232,x231)+~P1(x231,x232)+E(x231,x232)
% 0.16/0.73 [31]E(x311,x312)+P2(f5(x311,x312),x312)+P2(f5(x311,x312),x311)
% 0.16/0.73 [34]E(x341,x342)+~P2(f5(x341,x342),x342)+~P2(f5(x341,x342),x341)
% 0.16/0.73 [25]~P2(x251,x253)+P2(x251,x252)+~P1(x253,x252)
% 0.16/0.73 [32]~P2(x321,x323)+~P2(x321,x322)+P2(x321,f2(x322,x323))
% 0.16/0.73 [33]P2(x331,x332)+P2(x331,x333)+~P2(x331,f1(x333,x332))
% 0.16/0.73 %EqnAxiom
% 0.16/0.73 [1]E(x11,x11)
% 0.16/0.73 [2]E(x22,x21)+~E(x21,x22)
% 0.16/0.73 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.16/0.73 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.16/0.73 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.16/0.73 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 0.16/0.73 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 0.16/0.73 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83))
% 0.16/0.73 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92))
% 0.16/0.73 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103))
% 0.16/0.73 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112))
% 0.16/0.73 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123)
% 0.16/0.73 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131)
% 0.16/0.73 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143)
% 0.16/0.73 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151)
% 0.16/0.73
% 0.16/0.73 %-------------------------------------------
% 0.16/0.73 cnf(35,plain,
% 0.16/0.74 (E(a3,f1(f2(a3,a6),f2(a3,a7)))),
% 0.16/0.74 inference(scs_inference,[],[19,2])).
% 0.16/0.74 cnf(36,plain,
% 0.16/0.74 (~E(a3,f1(a6,a7))),
% 0.16/0.74 inference(scs_inference,[],[19,20,2,22])).
% 0.16/0.74 cnf(40,plain,
% 0.16/0.74 (~E(f1(a6,a7),f1(f2(a3,a6),f2(a3,a7)))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,2,22,12,3])).
% 0.16/0.74 cnf(41,plain,
% 0.16/0.74 (E(f4(x411,f1(x412,x413)),f4(x411,f1(x413,x412)))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,2,22,12,3,11])).
% 0.16/0.74 cnf(42,plain,
% 0.16/0.74 (E(f4(f1(x421,x422),x423),f4(f1(x422,x421),x423))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,2,22,12,3,11,10])).
% 0.16/0.74 cnf(44,plain,
% 0.16/0.74 (E(f2(f1(x441,x442),x443),f2(f1(x442,x441),x443))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,2,22,12,3,11,10,9,8])).
% 0.16/0.74 cnf(47,plain,
% 0.16/0.74 (E(f1(x471,f1(x472,x473)),f1(x471,f1(x473,x472)))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,2,22,12,3,11,10,9,8,7,6,5])).
% 0.16/0.74 cnf(49,plain,
% 0.16/0.74 (~P2(f4(a3,f1(a6,a7)),f1(a6,a7))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,2,22,12,3,11,10,9,8,7,6,5,4,30])).
% 0.16/0.74 cnf(51,plain,
% 0.16/0.74 (P2(f4(a3,f1(a6,a7)),a3)),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,2,22,12,3,11,10,9,8,7,6,5,4,30,24])).
% 0.16/0.74 cnf(53,plain,
% 0.16/0.74 (~P2(f4(a3,f1(a6,a7)),f1(a7,a6))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,2,22,12,3,11,10,9,8,7,6,5,4,30,24,15])).
% 0.16/0.74 cnf(54,plain,
% 0.16/0.74 (E(f1(x541,x542),f1(x542,x541))),
% 0.16/0.74 inference(rename_variables,[],[17])).
% 0.16/0.74 cnf(55,plain,
% 0.16/0.74 (~P2(f4(a3,f1(a7,a6)),f1(a6,a7))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,2,22,12,3,11,10,9,8,7,6,5,4,30,24,15,14])).
% 0.16/0.74 cnf(56,plain,
% 0.16/0.74 (~P1(a3,f1(a7,a6))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,54,2,22,12,3,11,10,9,8,7,6,5,4,30,24,15,14,13])).
% 0.16/0.74 cnf(60,plain,
% 0.16/0.74 (~P2(f4(a3,f1(a6,a7)),f1(f1(a6,a7),f1(a6,a7)))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,54,2,22,12,3,11,10,9,8,7,6,5,4,30,24,15,14,13,23,33])).
% 0.16/0.74 cnf(62,plain,
% 0.16/0.74 (P2(f4(a3,f1(a6,a7)),f2(a3,a3))),
% 0.16/0.74 inference(scs_inference,[],[19,16,20,17,54,2,22,12,3,11,10,9,8,7,6,5,4,30,24,15,14,13,23,33,32])).
% 0.16/0.74 cnf(76,plain,
% 0.16/0.74 (P2(f4(a3,f1(a6,a7)),f1(x761,a3))),
% 0.16/0.74 inference(scs_inference,[],[51,53,29,28,26])).
% 0.16/0.74 cnf(78,plain,
% 0.16/0.74 (~P2(f4(a3,f1(a7,a6)),f1(f1(a6,a7),f1(a6,a7)))),
% 0.16/0.74 inference(scs_inference,[],[51,53,55,29,28,26,33])).
% 0.16/0.74 cnf(85,plain,
% 0.16/0.74 (P1(f1(f2(a3,a6),f2(a3,a7)),a3)),
% 0.16/0.74 inference(scs_inference,[],[19,44,51,53,36,55,35,29,28,26,33,27,15,3,22])).
% 0.16/0.74 cnf(89,plain,
% 0.16/0.74 (P2(f4(a3,f1(a7,a6)),a3)),
% 0.16/0.74 inference(scs_inference,[],[19,18,16,41,44,51,53,36,55,35,29,28,26,33,27,15,3,22,13,14])).
% 0.16/0.74 cnf(91,plain,
% 0.16/0.74 (~P1(f1(f2(a3,a6),f2(a3,a7)),f1(a6,a7))),
% 0.16/0.74 inference(scs_inference,[],[19,18,16,20,41,44,51,53,36,55,35,29,28,26,33,27,15,3,22,13,14,12])).
% 0.16/0.74 cnf(92,plain,
% 0.16/0.74 (~P1(a3,f1(f1(a6,a7),f1(a6,a7)))),
% 0.16/0.74 inference(scs_inference,[],[19,18,16,20,41,44,51,60,53,36,55,35,29,28,26,33,27,15,3,22,13,14,12,25])).
% 0.16/0.74 cnf(94,plain,
% 0.16/0.74 (P2(f4(a3,f1(a7,a6)),f2(a3,a3))),
% 0.16/0.74 inference(scs_inference,[],[19,18,16,20,41,44,51,60,53,36,55,35,29,28,26,33,27,15,3,22,13,14,12,25,32])).
% 0.16/0.74 cnf(96,plain,
% 0.16/0.74 (~P2(f4(a3,f1(a7,a6)),a6)),
% 0.16/0.74 inference(scs_inference,[],[55,27])).
% 0.16/0.74 cnf(98,plain,
% 0.16/0.74 (~P2(f4(a3,f1(a7,a6)),a7)),
% 0.16/0.74 inference(scs_inference,[],[55,27,26])).
% 0.16/0.74 cnf(102,plain,
% 0.16/0.74 (E(a3,f1(f2(a3,a7),f2(a3,a6)))),
% 0.16/0.74 inference(scs_inference,[],[35,17,56,55,27,26,22,3])).
% 0.16/0.74 cnf(103,plain,
% 0.16/0.74 (E(f1(x1031,x1032),f1(x1032,x1031))),
% 0.16/0.74 inference(rename_variables,[],[17])).
% 0.16/0.74 cnf(104,plain,
% 0.16/0.74 (P1(f1(x1041,x1042),f1(x1042,x1041))),
% 0.16/0.74 inference(scs_inference,[],[35,16,17,103,56,55,27,26,22,3,12])).
% 0.16/0.74 cnf(106,plain,
% 0.16/0.74 (~E(f2(a3,a3),f1(f1(a6,a7),f1(a6,a7)))),
% 0.16/0.74 inference(scs_inference,[],[35,16,17,103,94,78,56,55,27,26,22,3,12,15])).
% 0.16/0.74 cnf(107,plain,
% 0.16/0.74 (P2(f4(a3,f1(a7,a6)),f1(x1071,a3))),
% 0.16/0.74 inference(scs_inference,[],[35,16,17,103,94,76,78,56,41,55,27,26,22,3,12,15,14])).
% 0.16/0.74 cnf(116,plain,
% 0.16/0.74 (~P2(f4(f1(f2(a3,a6),f2(a3,a7)),f1(a6,a7)),f1(a6,a7))),
% 0.16/0.74 inference(scs_inference,[],[91,30])).
% 0.16/0.74 cnf(118,plain,
% 0.16/0.74 (~P1(f2(a3,a3),f1(a6,a7))),
% 0.16/0.74 inference(scs_inference,[],[49,62,91,30,25])).
% 0.16/0.74 cnf(120,plain,
% 0.16/0.74 (P2(f4(a3,f1(a7,a6)),f1(a3,x1201))),
% 0.16/0.74 inference(scs_inference,[],[89,49,62,91,30,25,27])).
% 0.16/0.74 cnf(122,plain,
% 0.16/0.74 (P2(f4(a3,f1(a7,a6)),f1(x1221,f1(x1222,a3)))),
% 0.16/0.74 inference(scs_inference,[],[89,49,107,62,91,30,25,27,26])).
% 0.16/0.74 cnf(124,plain,
% 0.16/0.74 (E(f1(f2(a3,a7),f2(a3,a6)),a3)),
% 0.16/0.74 inference(scs_inference,[],[89,49,107,102,62,91,30,25,27,26,2])).
% 0.16/0.74 cnf(127,plain,
% 0.16/0.74 (~E(f2(a3,a3),f1(f1(a6,a7),f1(a7,a6)))),
% 0.16/0.74 inference(scs_inference,[],[35,47,89,49,106,107,102,62,91,30,25,27,26,2,22,3])).
% 0.16/0.74 cnf(130,plain,
% 0.16/0.74 (E(f1(x1301,x1302),f1(x1302,x1301))),
% 0.16/0.74 inference(rename_variables,[],[17])).
% 0.16/0.74 cnf(131,plain,
% 0.16/0.74 (~P1(f1(f2(a3,a6),f2(a3,a7)),f1(a7,a6))),
% 0.16/0.74 inference(scs_inference,[],[35,17,130,47,89,49,106,107,102,62,91,85,30,25,27,26,2,22,3,12,13])).
% 0.16/0.74 cnf(172,plain,
% 0.16/0.74 (P2(f4(a3,f1(a7,a6)),f2(a3,a6))),
% 0.16/0.74 inference(scs_inference,[],[16,18,35,17,42,104,131,122,127,116,118,120,124,98,92,40,89,32,26,27,2,22,13,3,12,15,14,24,11,7,5,29,33,10,9,8,6,4,25,28])).
% 0.16/0.74 cnf(199,plain,
% 0.16/0.74 ($false),
% 0.16/0.74 inference(scs_inference,[],[172,96,28]),
% 0.16/0.74 ['proof']).
% 0.16/0.74 % SZS output end Proof
% 0.16/0.74 % Total time :0.080000s
%------------------------------------------------------------------------------