TSTP Solution File: SET162+3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET162+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 : 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 14:29:01 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET162+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 15:17:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.54 start to proof:theBenchmark
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % File :CSE---1.6
% 0.20/0.65 % Problem :theBenchmark
% 0.20/0.65 % Transform :cnf
% 0.20/0.65 % Format :tptp:raw
% 0.20/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.65
% 0.20/0.65 % Result :Theorem 0.050000s
% 0.20/0.65 % Output :CNFRefutation 0.050000s
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 % File : SET162+3 : TPTP v8.1.2. Released v2.2.0.
% 0.20/0.65 % Domain : Set Theory
% 0.20/0.65 % Problem : The union of X and the empty set is X
% 0.20/0.65 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.20/0.65 % English :
% 0.20/0.65
% 0.20/0.65 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.20/0.65 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.20/0.65 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.65 % Source : [ILF]
% 0.20/0.65 % Names : BOOLE (60) [TS89]
% 0.20/0.65
% 0.20/0.65 % Status : Theorem
% 0.20/0.65 % Rating : 0.08 v8.1.0, 0.03 v7.2.0, 0.00 v7.1.0, 0.04 v7.0.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.12 v6.1.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.26 v5.2.0, 0.05 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
% 0.20/0.65 % Syntax : Number of formulae : 9 ( 4 unt; 0 def)
% 0.20/0.65 % Number of atoms : 18 ( 4 equ)
% 0.20/0.65 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.65 % Number of connectives : 11 ( 2 ~; 1 |; 1 &)
% 0.20/0.65 % ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.65 % Maximal formula depth : 6 ( 4 avg)
% 0.20/0.65 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.65 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.20/0.65 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.20/0.65 % Number of variables : 18 ( 18 !; 0 ?)
% 0.20/0.65 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.65
% 0.20/0.65 % Comments :
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 %---- line(boole - df(2),1833042)
% 0.20/0.65 fof(union_defn,axiom,
% 0.20/0.65 ! [B,C,D] :
% 0.20/0.65 ( member(D,union(B,C))
% 0.20/0.65 <=> ( member(D,B)
% 0.20/0.65 | member(D,C) ) ) ).
% 0.20/0.65
% 0.20/0.65 %---- line(hidden - axiom93,1832636)
% 0.20/0.65 fof(empty_set_defn,axiom,
% 0.20/0.65 ! [B] : ~ member(B,empty_set) ).
% 0.20/0.65
% 0.20/0.65 %---- line(boole - df(8),1833103)
% 0.20/0.65 fof(equal_defn,axiom,
% 0.20/0.65 ! [B,C] :
% 0.20/0.65 ( B = C
% 0.20/0.65 <=> ( subset(B,C)
% 0.20/0.65 & subset(C,B) ) ) ).
% 0.20/0.65
% 0.20/0.65 %---- property(commutativity,op(union,2,function))
% 0.20/0.65 fof(commutativity_of_union,axiom,
% 0.20/0.65 ! [B,C] : union(B,C) = union(C,B) ).
% 0.20/0.65
% 0.20/0.65 %---- line(tarski - df(3),1832749)
% 0.20/0.65 fof(subset_defn,axiom,
% 0.20/0.65 ! [B,C] :
% 0.20/0.65 ( subset(B,C)
% 0.20/0.65 <=> ! [D] :
% 0.20/0.65 ( member(D,B)
% 0.20/0.65 => member(D,C) ) ) ).
% 0.20/0.65
% 0.20/0.65 %---- property(reflexivity,op(subset,2,predicate))
% 0.20/0.65 fof(reflexivity_of_subset,axiom,
% 0.20/0.65 ! [B] : subset(B,B) ).
% 0.20/0.65
% 0.20/0.65 %---- line(hidden - axiom95,1832628)
% 0.20/0.65 fof(empty_defn,axiom,
% 0.20/0.65 ! [B] :
% 0.20/0.65 ( empty(B)
% 0.20/0.65 <=> ! [C] : ~ member(C,B) ) ).
% 0.20/0.65
% 0.20/0.65 %---- line(hidden - axiom96,1832615)
% 0.20/0.65 fof(equal_member_defn,axiom,
% 0.20/0.65 ! [B,C] :
% 0.20/0.65 ( B = C
% 0.20/0.65 <=> ! [D] :
% 0.20/0.65 ( member(D,B)
% 0.20/0.65 <=> member(D,C) ) ) ).
% 0.20/0.65
% 0.20/0.65 %---- line(boole - th(60),1833665)
% 0.20/0.65 fof(prove_union_empty_set,conjecture,
% 0.20/0.65 ! [B] : union(B,empty_set) = B ).
% 0.20/0.65
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % Proof found
% 0.20/0.65 % SZS status Theorem for theBenchmark
% 0.20/0.65 % SZS output start Proof
% 0.20/0.65 %ClaNum:32(EqnAxiom:15)
% 0.20/0.65 %VarNum:72(SingletonVarNum:31)
% 0.20/0.65 %MaxLitNum:3
% 0.20/0.65 %MaxfuncDepth:1
% 0.20/0.65 %SharedTerms:4
% 0.20/0.65 %goalClause: 18
% 0.20/0.65 %singleGoalClaCount:1
% 0.20/0.66 [18]~E(f1(a2,a3),a2)
% 0.20/0.66 [16]P1(x161,x161)
% 0.20/0.66 [19]~P2(x191,a3)
% 0.20/0.66 [17]E(f1(x171,x172),f1(x172,x171))
% 0.20/0.66 [22]P3(x221)+P2(f4(x221),x221)
% 0.20/0.66 [21]~E(x211,x212)+P1(x211,x212)
% 0.20/0.66 [23]~P3(x231)+~P2(x232,x231)
% 0.20/0.66 [25]P1(x251,x252)+P2(f5(x251,x252),x251)
% 0.20/0.66 [29]P1(x291,x292)+~P2(f5(x291,x292),x292)
% 0.20/0.66 [27]~P2(x271,x273)+P2(x271,f1(x272,x273))
% 0.20/0.66 [28]~P2(x281,x282)+P2(x281,f1(x282,x283))
% 0.20/0.66 [24]~P1(x242,x241)+~P1(x241,x242)+E(x241,x242)
% 0.20/0.66 [30]E(x301,x302)+P2(f6(x301,x302),x302)+P2(f6(x301,x302),x301)
% 0.20/0.66 [32]E(x321,x322)+~P2(f6(x321,x322),x322)+~P2(f6(x321,x322),x321)
% 0.20/0.66 [26]~P1(x263,x262)+P2(x261,x262)+~P2(x261,x263)
% 0.20/0.66 [31]P2(x311,x312)+P2(x311,x313)+~P2(x311,f1(x313,x312))
% 0.20/0.66 %EqnAxiom
% 0.20/0.66 [1]E(x11,x11)
% 0.20/0.66 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.66 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.20/0.66 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.20/0.66 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 0.20/0.66 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 0.20/0.66 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83))
% 0.20/0.66 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92))
% 0.20/0.66 [10]~E(x101,x102)+E(f4(x101),f4(x102))
% 0.20/0.66 [11]P1(x112,x113)+~E(x111,x112)+~P1(x111,x113)
% 0.20/0.66 [12]P1(x123,x122)+~E(x121,x122)+~P1(x123,x121)
% 0.20/0.66 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133)
% 0.20/0.66 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141)
% 0.20/0.66 [15]~P3(x151)+P3(x152)+~E(x151,x152)
% 0.20/0.66
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 cnf(33,plain,
% 0.20/0.66 (P3(a3)),
% 0.20/0.66 inference(scs_inference,[],[19,22])).
% 0.20/0.66 cnf(34,plain,
% 0.20/0.66 (~P2(x341,a3)),
% 0.20/0.66 inference(rename_variables,[],[19])).
% 0.20/0.66 cnf(35,plain,
% 0.20/0.66 (P1(a3,x351)),
% 0.20/0.66 inference(scs_inference,[],[19,34,22,25])).
% 0.20/0.66 cnf(36,plain,
% 0.20/0.66 (~P2(x361,a3)),
% 0.20/0.66 inference(rename_variables,[],[19])).
% 0.20/0.66 cnf(39,plain,
% 0.20/0.66 (~E(a2,f1(a2,a3))),
% 0.20/0.66 inference(scs_inference,[],[18,16,19,34,17,22,25,12,2])).
% 0.20/0.66 cnf(41,plain,
% 0.20/0.66 (~E(f1(a3,a2),a2)),
% 0.20/0.66 inference(scs_inference,[],[18,16,19,34,17,22,25,12,2,15,3])).
% 0.20/0.66 cnf(43,plain,
% 0.20/0.66 (~P2(x431,f1(a3,a3))),
% 0.20/0.66 inference(scs_inference,[],[18,16,19,34,36,17,22,25,12,2,15,3,31])).
% 0.20/0.66 cnf(45,plain,
% 0.20/0.66 (E(f1(a3,a3),a3)),
% 0.20/0.66 inference(scs_inference,[],[18,16,19,34,36,17,22,25,12,2,15,3,31,30])).
% 0.20/0.66 cnf(51,plain,
% 0.20/0.66 (E(f4(f1(a3,a3)),f4(a3))),
% 0.20/0.66 inference(scs_inference,[],[45,10])).
% 0.20/0.66 cnf(52,plain,
% 0.20/0.66 (E(f5(x521,f1(a3,a3)),f5(x521,a3))),
% 0.20/0.66 inference(scs_inference,[],[45,10,9])).
% 0.20/0.66 cnf(56,plain,
% 0.20/0.66 (E(f1(x561,f1(a3,a3)),f1(x561,a3))),
% 0.20/0.66 inference(scs_inference,[],[45,10,9,8,7,6,5])).
% 0.20/0.66 cnf(57,plain,
% 0.20/0.66 (E(f1(f1(a3,a3),x571),f1(a3,x571))),
% 0.20/0.66 inference(scs_inference,[],[45,10,9,8,7,6,5,4])).
% 0.20/0.66 cnf(60,plain,
% 0.20/0.66 (~P2(x601,f1(f1(a3,a3),a3))),
% 0.20/0.66 inference(scs_inference,[],[19,43,45,10,9,8,7,6,5,4,21,31])).
% 0.20/0.66 cnf(64,plain,
% 0.20/0.66 (E(a3,f1(a3,a3))),
% 0.20/0.66 inference(scs_inference,[],[19,43,45,10,9,8,7,6,5,4,21,31,3,2])).
% 0.20/0.66 cnf(66,plain,
% 0.20/0.66 (E(f1(x661,x662),f1(x662,x661))),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(67,plain,
% 0.20/0.66 (E(a3,f1(f1(a3,a3),a3))),
% 0.20/0.66 inference(scs_inference,[],[19,17,43,45,10,9,8,7,6,5,4,21,31,3,2,14,30])).
% 0.20/0.66 cnf(70,plain,
% 0.20/0.66 (P1(f4(f1(a3,a3)),f4(a3))),
% 0.20/0.66 inference(scs_inference,[],[16,19,17,43,45,10,9,8,7,6,5,4,21,31,3,2,14,30,12])).
% 0.20/0.66 cnf(72,plain,
% 0.20/0.66 (~P3(f1(x721,x722))+P3(f1(x722,x721))),
% 0.20/0.66 inference(scs_inference,[],[16,19,17,66,43,45,10,9,8,7,6,5,4,21,31,3,2,14,30,12,15])).
% 0.20/0.66 cnf(80,plain,
% 0.20/0.66 (~E(a2,f1(a3,a2))),
% 0.20/0.66 inference(scs_inference,[],[17,60,64,56,35,39,14,11,3])).
% 0.20/0.66 cnf(84,plain,
% 0.20/0.66 (E(f5(x841,a3),f5(x841,f1(a3,a3)))),
% 0.20/0.66 inference(scs_inference,[],[17,60,64,52,56,70,35,39,14,11,3,26,2])).
% 0.20/0.66 cnf(95,plain,
% 0.20/0.66 (~E(f1(f1(a3,a3),a2),a2)),
% 0.20/0.66 inference(scs_inference,[],[80,57,3,2])).
% 0.20/0.66 cnf(118,plain,
% 0.20/0.66 (P2(f6(f1(a3,a2),a2),f1(a3,a2))),
% 0.20/0.66 inference(scs_inference,[],[17,33,19,41,51,84,95,67,64,15,2,3,21,8,7,6,5,4,30,14,72,23,28,27,32])).
% 0.20/0.66 cnf(120,plain,
% 0.20/0.66 (~P2(x1201,a3)),
% 0.20/0.66 inference(rename_variables,[],[19])).
% 0.20/0.66 cnf(124,plain,
% 0.20/0.66 ($false),
% 0.20/0.66 inference(scs_inference,[],[19,120,118,41,26,32,31]),
% 0.20/0.66 ['proof']).
% 0.20/0.66 % SZS output end Proof
% 0.20/0.66 % Total time :0.050000s
%------------------------------------------------------------------------------