TSTP Solution File: SET148+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET148+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 : n032.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 14:28:58 EDT 2023
% Result : Theorem 0.16s 0.53s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET148+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Aug 26 09:29:58 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.49 start to proof:theBenchmark
% 0.16/0.52 %-------------------------------------------
% 0.16/0.52 % File :CSE---1.6
% 0.16/0.52 % Problem :theBenchmark
% 0.16/0.53 % Transform :cnf
% 0.16/0.53 % Format :tptp:raw
% 0.16/0.53 % Command :java -jar mcs_scs.jar %d %s
% 0.16/0.53
% 0.16/0.53 % Result :Theorem 0.000000s
% 0.16/0.53 % Output :CNFRefutation 0.000000s
% 0.16/0.53 %-------------------------------------------
% 0.16/0.53 %--------------------------------------------------------------------------
% 0.16/0.53 % File : SET148+3 : TPTP v8.1.2. Released v2.2.0.
% 0.16/0.53 % Domain : Set Theory
% 0.16/0.53 % Problem : Idempotency of intersection
% 0.16/0.53 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.16/0.53 % English :
% 0.16/0.53
% 0.16/0.53 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.16/0.53 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.16/0.53 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.16/0.53 % Source : [ILF]
% 0.16/0.53 % Names : BOOLE (63) [TS89]
% 0.16/0.53
% 0.16/0.53 % Status : Theorem
% 0.16/0.53 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.04 v5.3.0, 0.11 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, 0.09 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 0.16/0.53 % Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% 0.16/0.53 % Number of atoms : 17 ( 5 equ)
% 0.16/0.53 % Maximal formula atoms : 3 ( 2 avg)
% 0.16/0.53 % Number of connectives : 9 ( 0 ~; 0 |; 2 &)
% 0.16/0.53 % ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.53 % Maximal formula depth : 6 ( 4 avg)
% 0.16/0.53 % Maximal term depth : 2 ( 1 avg)
% 0.16/0.53 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.16/0.53 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.16/0.53 % Number of variables : 17 ( 17 !; 0 ?)
% 0.16/0.53 % SPC : FOF_THM_RFO_SEQ
% 0.16/0.53
% 0.16/0.53 % Comments :
% 0.16/0.53 %--------------------------------------------------------------------------
% 0.16/0.53 %---- line(boole - th(42),1833351)
% 0.16/0.53 fof(subset_intersection,axiom,
% 0.16/0.53 ! [B,C] :
% 0.16/0.53 ( subset(B,C)
% 0.16/0.53 => intersection(B,C) = B ) ).
% 0.16/0.53
% 0.16/0.53 %---- line(boole - df(3),1833060)
% 0.16/0.53 fof(intersection_defn,axiom,
% 0.16/0.53 ! [B,C,D] :
% 0.16/0.53 ( member(D,intersection(B,C))
% 0.16/0.53 <=> ( member(D,B)
% 0.16/0.53 & member(D,C) ) ) ).
% 0.16/0.53
% 0.16/0.53 %---- line(boole - df(8),1833103)
% 0.16/0.53 fof(equal_defn,axiom,
% 0.16/0.53 ! [B,C] :
% 0.16/0.53 ( B = C
% 0.16/0.53 <=> ( subset(B,C)
% 0.16/0.53 & subset(C,B) ) ) ).
% 0.16/0.53
% 0.16/0.53 %---- property(commutativity,op(intersection,2,function))
% 0.16/0.53 fof(commutativity_of_intersection,axiom,
% 0.16/0.53 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.16/0.53
% 0.16/0.53 %---- line(tarski - df(3),1832749)
% 0.16/0.53 fof(subset_defn,axiom,
% 0.16/0.53 ! [B,C] :
% 0.16/0.53 ( subset(B,C)
% 0.16/0.53 <=> ! [D] :
% 0.16/0.53 ( member(D,B)
% 0.16/0.53 => member(D,C) ) ) ).
% 0.16/0.53
% 0.16/0.53 %---- property(reflexivity,op(subset,2,predicate))
% 0.16/0.53 fof(reflexivity_of_subset,axiom,
% 0.16/0.53 ! [B] : subset(B,B) ).
% 0.16/0.53
% 0.16/0.53 %---- line(hidden - axiom106,1832615)
% 0.16/0.53 fof(equal_member_defn,axiom,
% 0.16/0.53 ! [B,C] :
% 0.16/0.53 ( B = C
% 0.16/0.53 <=> ! [D] :
% 0.16/0.53 ( member(D,B)
% 0.16/0.53 <=> member(D,C) ) ) ).
% 0.16/0.53
% 0.16/0.53 %---- line(boole - th(65),1833713)
% 0.16/0.53 fof(prove_idempotency_of_intersection,conjecture,
% 0.16/0.53 ! [B] : intersection(B,B) = B ).
% 0.16/0.53
% 0.16/0.53 %--------------------------------------------------------------------------
% 0.16/0.53 %-------------------------------------------
% 0.16/0.53 % Proof found
% 0.16/0.53 % SZS status Theorem for theBenchmark
% 0.16/0.53 % SZS output start Proof
% 0.16/0.53 %ClaNum:28(EqnAxiom:13)
% 0.16/0.53 %VarNum:70(SingletonVarNum:29)
% 0.16/0.53 %MaxLitNum:3
% 0.16/0.53 %MaxfuncDepth:1
% 0.16/0.53 %SharedTerms:3
% 0.16/0.53 %goalClause: 16
% 0.16/0.53 %singleGoalClaCount:1
% 0.16/0.53 [16]~E(f1(a2,a2),a2)
% 0.16/0.53 [14]P1(x141,x141)
% 0.16/0.53 [15]E(f1(x151,x152),f1(x152,x151))
% 0.16/0.53 [18]~E(x181,x182)+P1(x181,x182)
% 0.16/0.53 [19]~P1(x191,x192)+E(f1(x191,x192),x191)
% 0.16/0.53 [21]P1(x211,x212)+P2(f3(x211,x212),x211)
% 0.16/0.53 [25]P1(x251,x252)+~P2(f3(x251,x252),x252)
% 0.16/0.53 [23]P2(x231,x232)+~P2(x231,f1(x233,x232))
% 0.16/0.53 [24]P2(x241,x242)+~P2(x241,f1(x242,x243))
% 0.16/0.53 [20]~P1(x202,x201)+~P1(x201,x202)+E(x201,x202)
% 0.16/0.53 [26]E(x261,x262)+P2(f4(x261,x262),x262)+P2(f4(x261,x262),x261)
% 0.16/0.53 [28]E(x281,x282)+~P2(f4(x281,x282),x282)+~P2(f4(x281,x282),x281)
% 0.16/0.53 [22]~P2(x221,x223)+P2(x221,x222)+~P1(x223,x222)
% 0.16/0.53 [27]~P2(x271,x273)+~P2(x271,x272)+P2(x271,f1(x272,x273))
% 0.16/0.53 %EqnAxiom
% 0.16/0.53 [1]E(x11,x11)
% 0.16/0.53 [2]E(x22,x21)+~E(x21,x22)
% 0.16/0.53 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.16/0.53 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.16/0.53 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.16/0.53 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.16/0.53 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.16/0.53 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83))
% 0.16/0.53 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92))
% 0.16/0.53 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 0.16/0.53 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 0.16/0.53 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 0.16/0.53 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 0.16/0.53
% 0.16/0.53 %-------------------------------------------
% 0.16/0.53 cnf(29,plain,
% 0.16/0.53 ($false),
% 0.16/0.53 inference(scs_inference,[],[14,16,19]),
% 0.16/0.53 ['proof']).
% 0.16/0.53 % SZS output end Proof
% 0.16/0.53 % Total time :0.000000s
%------------------------------------------------------------------------------