TSTP Solution File: SET626+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n016.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 14:30:28 EDT 2023
% Result : Theorem 0.19s 0.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 16:44:12 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 % File :CSE---1.6
% 0.19/0.61 % Problem :theBenchmark
% 0.19/0.61 % Transform :cnf
% 0.19/0.61 % Format :tptp:raw
% 0.19/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.61
% 0.19/0.61 % Result :Theorem 0.000000s
% 0.19/0.61 % Output :CNFRefutation 0.000000s
% 0.19/0.61 %-------------------------------------------
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 % File : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% 0.19/0.62 % Domain : Set Theory
% 0.19/0.62 % Problem : If X intersects the intersection of Y and Z, then X intersects Y
% 0.19/0.62 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.19/0.62 % English :
% 0.19/0.62
% 0.19/0.62 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.19/0.62 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.19/0.62 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.62 % Source : [ILF]
% 0.19/0.62 % Names : BOOLE (102) [TS89]
% 0.19/0.62
% 0.19/0.62 % Status : Theorem
% 0.19/0.62 % Rating : 0.08 v8.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.04 v6.2.0, 0.00 v6.1.0, 0.07 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, 0.04 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
% 0.19/0.62 % Syntax : Number of formulae : 6 ( 1 unt; 0 def)
% 0.19/0.62 % Number of atoms : 14 ( 2 equ)
% 0.19/0.62 % Maximal formula atoms : 3 ( 2 avg)
% 0.19/0.62 % Number of connectives : 8 ( 0 ~; 0 |; 2 &)
% 0.19/0.62 % ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.62 % Maximal formula depth : 6 ( 5 avg)
% 0.19/0.62 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.62 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.19/0.62 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.19/0.62 % Number of variables : 16 ( 15 !; 1 ?)
% 0.19/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.62
% 0.19/0.62 % Comments :
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 %---- line(boole - df(3),1833060)
% 0.19/0.62 fof(intersection_defn,axiom,
% 0.19/0.62 ! [B,C,D] :
% 0.19/0.62 ( member(D,intersection(B,C))
% 0.19/0.62 <=> ( member(D,B)
% 0.19/0.62 & member(D,C) ) ) ).
% 0.19/0.62
% 0.19/0.62 %---- line(boole - df(5),1833080)
% 0.19/0.62 fof(intersect_defn,axiom,
% 0.19/0.62 ! [B,C] :
% 0.19/0.62 ( intersect(B,C)
% 0.19/0.62 <=> ? [D] :
% 0.19/0.62 ( member(D,B)
% 0.19/0.62 & member(D,C) ) ) ).
% 0.19/0.62
% 0.19/0.62 %---- property(commutativity,op(intersection,2,function))
% 0.19/0.62 fof(commutativity_of_intersection,axiom,
% 0.19/0.62 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.19/0.62
% 0.19/0.62 %---- property(symmetry,op(intersect,2,predicate))
% 0.19/0.62 fof(symmetry_of_intersect,axiom,
% 0.19/0.62 ! [B,C] :
% 0.19/0.62 ( intersect(B,C)
% 0.19/0.62 => intersect(C,B) ) ).
% 0.19/0.62
% 0.19/0.62 %---- line(hidden - axiom189,1832615)
% 0.19/0.62 fof(equal_member_defn,axiom,
% 0.19/0.62 ! [B,C] :
% 0.19/0.62 ( B = C
% 0.19/0.62 <=> ! [D] :
% 0.19/0.62 ( member(D,B)
% 0.19/0.62 <=> member(D,C) ) ) ).
% 0.19/0.62
% 0.19/0.62 %---- line(boole - th(102),1834325)
% 0.19/0.62 fof(prove_th102,conjecture,
% 0.19/0.62 ! [B,C,D] :
% 0.19/0.62 ( intersect(B,intersection(C,D))
% 0.19/0.62 => intersect(B,C) ) ).
% 0.19/0.62
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % Proof found
% 0.19/0.62 % SZS status Theorem for theBenchmark
% 0.19/0.62 % SZS output start Proof
% 0.19/0.62 %ClaNum:25(EqnAxiom:13)
% 0.19/0.62 %VarNum:57(SingletonVarNum:24)
% 0.19/0.62 %MaxLitNum:3
% 0.19/0.62 %MaxfuncDepth:1
% 0.19/0.62 %SharedTerms:6
% 0.19/0.62 %goalClause: 15 16
% 0.19/0.62 %singleGoalClaCount:2
% 0.19/0.62 [16]~P1(a2,a5)
% 0.19/0.62 [15]P1(a2,f1(a5,a6))
% 0.19/0.62 [14]E(f1(x141,x142),f1(x142,x141))
% 0.19/0.62 [17]~P1(x172,x171)+P1(x171,x172)
% 0.19/0.62 [19]~P1(x191,x192)+P2(f3(x191,x192),x192)
% 0.19/0.62 [20]~P1(x201,x202)+P2(f3(x201,x202),x201)
% 0.19/0.62 [21]P2(x211,x212)+~P2(x211,f1(x213,x212))
% 0.19/0.62 [22]P2(x221,x222)+~P2(x221,f1(x222,x223))
% 0.19/0.62 [23]E(x231,x232)+P2(f4(x231,x232),x232)+P2(f4(x231,x232),x231)
% 0.19/0.62 [25]E(x251,x252)+~P2(f4(x251,x252),x252)+~P2(f4(x251,x252),x251)
% 0.19/0.62 [18]~P2(x183,x181)+P1(x181,x182)+~P2(x183,x182)
% 0.19/0.62 [24]~P2(x241,x243)+~P2(x241,x242)+P2(x241,f1(x242,x243))
% 0.19/0.62 %EqnAxiom
% 0.19/0.62 [1]E(x11,x11)
% 0.19/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.62 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.19/0.62 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.19/0.62 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.19/0.62 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.19/0.62 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83))
% 0.19/0.62 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92))
% 0.19/0.62 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 0.19/0.62 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 0.19/0.62 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 0.19/0.62 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 0.19/0.62
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 cnf(31,plain,
% 0.19/0.62 (P2(f3(a2,f1(a5,a6)),f1(a5,a6))),
% 0.19/0.62 inference(scs_inference,[],[15,16,17,11,2,20,19])).
% 0.19/0.62 cnf(36,plain,
% 0.19/0.62 (~P2(f3(a2,f1(a5,a6)),a5)),
% 0.19/0.62 inference(scs_inference,[],[15,16,14,17,11,2,20,19,10,3,18])).
% 0.19/0.62 cnf(52,plain,
% 0.19/0.62 ($false),
% 0.19/0.62 inference(scs_inference,[],[15,31,36,17,22]),
% 0.19/0.62 ['proof']).
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------