TSTP Solution File: SET063+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET063+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 : n024.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 14:28:20 EDT 2023
% Result : Theorem 0.18s 0.60s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET063+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 14:03:24 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.55 start to proof:theBenchmark
% 0.18/0.60 %-------------------------------------------
% 0.18/0.60 % File :CSE---1.6
% 0.18/0.60 % Problem :theBenchmark
% 0.18/0.60 % Transform :cnf
% 0.18/0.60 % Format :tptp:raw
% 0.18/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.60
% 0.18/0.60 % Result :Theorem 0.000000s
% 0.18/0.60 % Output :CNFRefutation 0.000000s
% 0.18/0.60 %-------------------------------------------
% 0.18/0.60 %--------------------------------------------------------------------------
% 0.18/0.60 % File : SET063+3 : TPTP v8.1.2. Released v2.2.0.
% 0.18/0.60 % Domain : Set Theory
% 0.18/0.60 % Problem : If X is a subset of the empty set, then X is the empty set
% 0.18/0.60 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.18/0.60 % English :
% 0.18/0.60
% 0.18/0.60 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.18/0.60 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.18/0.60 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.18/0.60 % Source : [ILF]
% 0.18/0.60 % Names : BOOLE (30) [TS89]
% 0.18/0.60
% 0.18/0.60 % Status : Theorem
% 0.18/0.60 % Rating : 0.00 v6.1.0, 0.03 v6.0.0, 0.00 v5.3.0, 0.07 v5.2.0, 0.00 v2.5.0, 0.33 v2.4.0, 0.33 v2.2.1
% 0.18/0.60 % Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% 0.18/0.60 % Number of atoms : 13 ( 2 equ)
% 0.18/0.60 % Maximal formula atoms : 3 ( 1 avg)
% 0.18/0.60 % Number of connectives : 8 ( 2 ~; 0 |; 1 &)
% 0.18/0.60 % ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.60 % Maximal formula depth : 6 ( 4 avg)
% 0.18/0.60 % Maximal term depth : 1 ( 1 avg)
% 0.18/0.60 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.18/0.60 % Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% 0.18/0.60 % Number of variables : 11 ( 11 !; 0 ?)
% 0.18/0.60 % SPC : FOF_THM_RFO_SEQ
% 0.18/0.60
% 0.18/0.60 % Comments :
% 0.18/0.60 %--------------------------------------------------------------------------
% 0.18/0.60 %---- line(boole - th(27),1833153)
% 0.18/0.60 fof(empty_set_subset,axiom,
% 0.18/0.60 ! [B] : subset(empty_set,B) ).
% 0.18/0.60
% 0.18/0.60 %---- line(hidden - axiom31,1832636)
% 0.18/0.60 fof(empty_set_defn,axiom,
% 0.18/0.60 ! [B] : ~ member(B,empty_set) ).
% 0.18/0.60
% 0.18/0.60 %---- line(tarski - df(3),1832749)
% 0.18/0.60 fof(subset_defn,axiom,
% 0.18/0.60 ! [B,C] :
% 0.18/0.60 ( subset(B,C)
% 0.18/0.60 <=> ! [D] :
% 0.18/0.60 ( member(D,B)
% 0.18/0.60 => member(D,C) ) ) ).
% 0.18/0.60
% 0.18/0.60 %---- line(boole - df(8),1833103)
% 0.18/0.60 fof(equal_defn,axiom,
% 0.18/0.60 ! [B,C] :
% 0.18/0.60 ( B = C
% 0.18/0.60 <=> ( subset(B,C)
% 0.18/0.60 & subset(C,B) ) ) ).
% 0.18/0.60
% 0.18/0.60 %---- property(reflexivity,op(subset,2,predicate))
% 0.18/0.60 fof(reflexivity_of_subset,axiom,
% 0.18/0.60 ! [B] : subset(B,B) ).
% 0.18/0.60
% 0.18/0.60 %---- line(hidden - axiom33,1832628)
% 0.18/0.60 fof(empty_defn,axiom,
% 0.18/0.60 ! [B] :
% 0.18/0.60 ( empty(B)
% 0.18/0.60 <=> ! [C] : ~ member(C,B) ) ).
% 0.18/0.60
% 0.18/0.60 %---- line(boole - th(30),1833179)
% 0.18/0.60 fof(prove_subset_of_empty_set_is_empty_set,conjecture,
% 0.18/0.60 ! [B] :
% 0.18/0.60 ( subset(B,empty_set)
% 0.18/0.60 => B = empty_set ) ).
% 0.18/0.60
% 0.18/0.60 %--------------------------------------------------------------------------
% 0.18/0.60 %-------------------------------------------
% 0.18/0.60 % Proof found
% 0.18/0.60 % SZS status Theorem for theBenchmark
% 0.18/0.60 % SZS output start Proof
% 0.18/0.60 %ClaNum:24(EqnAxiom:11)
% 0.18/0.60 %VarNum:36(SingletonVarNum:17)
% 0.18/0.60 %MaxLitNum:3
% 0.18/0.60 %MaxfuncDepth:1
% 0.18/0.60 %SharedTerms:4
% 0.18/0.60 %goalClause: 12 15
% 0.18/0.60 %singleGoalClaCount:2
% 0.18/0.60 [12]P1(a1,a2)
% 0.18/0.60 [15]~E(a1,a2)
% 0.18/0.60 [13]P1(a2,x131)
% 0.18/0.60 [14]P1(x141,x141)
% 0.18/0.60 [16]~P2(x161,a2)
% 0.18/0.60 [19]P3(x191)+P2(f3(x191),x191)
% 0.18/0.60 [18]~E(x181,x182)+P1(x181,x182)
% 0.18/0.60 [20]~P3(x201)+~P2(x202,x201)
% 0.18/0.60 [22]P1(x221,x222)+P2(f4(x221,x222),x221)
% 0.18/0.60 [24]P1(x241,x242)+~P2(f4(x241,x242),x242)
% 0.18/0.60 [21]~P1(x212,x211)+~P1(x211,x212)+E(x211,x212)
% 0.18/0.60 [23]~P2(x231,x233)+P2(x231,x232)+~P1(x233,x232)
% 0.18/0.60 %EqnAxiom
% 0.18/0.60 [1]E(x11,x11)
% 0.18/0.60 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.60 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.18/0.60 [5]~E(x51,x52)+E(f4(x51,x53),f4(x52,x53))
% 0.18/0.60 [6]~E(x61,x62)+E(f4(x63,x61),f4(x63,x62))
% 0.18/0.60 [7]P1(x72,x73)+~E(x71,x72)+~P1(x71,x73)
% 0.18/0.60 [8]P1(x83,x82)+~E(x81,x82)+~P1(x83,x81)
% 0.18/0.60 [9]P2(x92,x93)+~E(x91,x92)+~P2(x91,x93)
% 0.18/0.60 [10]P2(x103,x102)+~E(x101,x102)+~P2(x103,x101)
% 0.18/0.60 [11]~P3(x111)+P3(x112)+~E(x111,x112)
% 0.18/0.60
% 0.18/0.60 %-------------------------------------------
% 0.18/0.61 cnf(26,plain,
% 0.18/0.61 (~P2(x261,a2)),
% 0.18/0.61 inference(rename_variables,[],[16])).
% 0.18/0.61 cnf(29,plain,
% 0.18/0.61 ($false),
% 0.18/0.61 inference(scs_inference,[],[12,13,16,26,15,19,23,21]),
% 0.18/0.61 ['proof']).
% 0.18/0.61 % SZS output end Proof
% 0.18/0.61 % Total time :0.000000s
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