TSTP Solution File: SET583+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET583+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 : n031.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 14:30:13 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET583+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
% 0.18/0.34 % Computer : n031.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Sat Aug 26 08:45:52 EDT 2023
% 0.18/0.34 % CPUTime :
% 0.20/0.55 start to proof:theBenchmark
% 0.20/0.60 %-------------------------------------------
% 0.20/0.60 % File :CSE---1.6
% 0.20/0.60 % Problem :theBenchmark
% 0.20/0.60 % Transform :cnf
% 0.20/0.60 % Format :tptp:raw
% 0.20/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.60
% 0.20/0.60 % Result :Theorem 0.000000s
% 0.20/0.60 % Output :CNFRefutation 0.000000s
% 0.20/0.60 %-------------------------------------------
% 0.20/0.60 %--------------------------------------------------------------------------
% 0.20/0.60 % File : SET583+3 : TPTP v8.1.2. Released v2.2.0.
% 0.20/0.60 % Domain : Set Theory
% 0.20/0.60 % Problem : Extensionality
% 0.20/0.60 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.20/0.60 % English :
% 0.20/0.60
% 0.20/0.60 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.20/0.60 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.60 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.20/0.60 % Source : [ILF]
% 0.20/0.60 % Names : BOOLE (28) [TS89]
% 0.20/0.60
% 0.20/0.60 % Status : Theorem
% 0.20/0.60 % Rating : 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
% 0.20/0.60 % Syntax : Number of formulae : 4 ( 1 unt; 0 def)
% 0.20/0.60 % Number of atoms : 10 ( 2 equ)
% 0.20/0.60 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.60 % Number of connectives : 6 ( 0 ~; 0 |; 2 &)
% 0.20/0.60 % ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.60 % Maximal formula depth : 6 ( 5 avg)
% 0.20/0.60 % Maximal term depth : 1 ( 1 avg)
% 0.20/0.60 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.20/0.60 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.60 % Number of variables : 8 ( 8 !; 0 ?)
% 0.20/0.60 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.60
% 0.20/0.60 % Comments :
% 0.20/0.60 %--------------------------------------------------------------------------
% 0.20/0.60 %---- line(boole - df(8),1833103)
% 0.20/0.60 fof(equal_defn,axiom,
% 0.20/0.60 ! [B,C] :
% 0.20/0.60 ( B = C
% 0.20/0.60 <=> ( subset(B,C)
% 0.20/0.60 & subset(C,B) ) ) ).
% 0.20/0.60
% 0.20/0.60 %---- line(tarski - df(3),1832749)
% 0.20/0.60 fof(subset_defn,axiom,
% 0.20/0.60 ! [B,C] :
% 0.20/0.60 ( subset(B,C)
% 0.20/0.60 <=> ! [D] :
% 0.20/0.60 ( member(D,B)
% 0.20/0.60 => member(D,C) ) ) ).
% 0.20/0.60
% 0.20/0.60 %---- property(reflexivity,op(subset,2,predicate))
% 0.20/0.60 fof(reflexivity_of_subset,axiom,
% 0.20/0.60 ! [B] : subset(B,B) ).
% 0.20/0.60
% 0.20/0.60 %---- line(boole - th(28),1833154)
% 0.20/0.60 fof(prove_extensionality,conjecture,
% 0.20/0.60 ! [B,C] :
% 0.20/0.60 ( ( subset(B,C)
% 0.20/0.60 & subset(C,B) )
% 0.20/0.60 => B = C ) ).
% 0.20/0.60
% 0.20/0.60 %--------------------------------------------------------------------------
% 0.20/0.60 %-------------------------------------------
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark
% 0.20/0.60 % SZS output start Proof
% 0.20/0.60 %ClaNum:19(EqnAxiom:9)
% 0.20/0.60 %VarNum:28(SingletonVarNum:12)
% 0.20/0.60 %MaxLitNum:3
% 0.20/0.60 %MaxfuncDepth:1
% 0.20/0.60 %SharedTerms:5
% 0.20/0.60 %goalClause: 10 11 13
% 0.20/0.60 %singleGoalClaCount:3
% 0.20/0.60 [10]P1(a1,a3)
% 0.20/0.60 [11]P1(a3,a1)
% 0.20/0.60 [13]~E(a3,a1)
% 0.20/0.60 [12]P1(x121,x121)
% 0.20/0.60 [15]~E(x151,x152)+P1(x151,x152)
% 0.20/0.60 [17]P1(x171,x172)+P2(f2(x171,x172),x171)
% 0.20/0.60 [19]P1(x191,x192)+~P2(f2(x191,x192),x192)
% 0.20/0.60 [16]~P1(x162,x161)+~P1(x161,x162)+E(x161,x162)
% 0.20/0.60 [18]~P2(x181,x183)+P2(x181,x182)+~P1(x183,x182)
% 0.20/0.60 %EqnAxiom
% 0.20/0.60 [1]E(x11,x11)
% 0.20/0.60 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.60 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.20/0.60 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.20/0.60 [6]P1(x62,x63)+~E(x61,x62)+~P1(x61,x63)
% 0.20/0.60 [7]P1(x73,x72)+~E(x71,x72)+~P1(x73,x71)
% 0.20/0.60 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83)
% 0.20/0.60 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91)
% 0.20/0.60
% 0.20/0.60 %-------------------------------------------
% 0.20/0.61 cnf(20,plain,
% 0.20/0.61 ($false),
% 0.20/0.61 inference(scs_inference,[],[10,11,13,16]),
% 0.20/0.61 ['proof']).
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time :0.000000s
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