TSTP Solution File: SET062+3 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET062+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 : n027.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 14:28:19 EDT 2023
% Result : Theorem 0.20s 0.72s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET062+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.18/0.35 % Computer : n027.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Sat Aug 26 12:36:35 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.20/0.65 start to proof:theBenchmark
% 0.20/0.70 %-------------------------------------------
% 0.20/0.70 % File :CSE---1.6
% 0.20/0.71 % Problem :theBenchmark
% 0.20/0.71 % Transform :cnf
% 0.20/0.71 % Format :tptp:raw
% 0.20/0.71 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.71
% 0.20/0.71 % Result :Theorem 0.000000s
% 0.20/0.71 % Output :CNFRefutation 0.000000s
% 0.20/0.71 %-------------------------------------------
% 0.20/0.71 %--------------------------------------------------------------------------
% 0.20/0.71 % File : SET062+3 : TPTP v8.1.2. Released v2.2.0.
% 0.20/0.71 % Domain : Set Theory
% 0.20/0.71 % Problem : The empty set is a subset of X
% 0.20/0.71 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.20/0.71 % English :
% 0.20/0.71
% 0.20/0.71 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.20/0.71 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.20/0.71 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.71 % Source : [ILF]
% 0.20/0.71 % Names : BOOLE (27) [TS89]
% 0.20/0.71
% 0.20/0.71 % Status : Theorem
% 0.20/0.71 % Rating : 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.04 v5.3.0, 0.17 v5.2.0, 0.00 v3.2.0, 0.11 v3.1.0, 0.00 v2.2.1
% 0.20/0.71 % Syntax : Number of formulae : 5 ( 3 unt; 0 def)
% 0.20/0.71 % Number of atoms : 8 ( 0 equ)
% 0.20/0.71 % Maximal formula atoms : 3 ( 1 avg)
% 0.20/0.71 % Number of connectives : 5 ( 2 ~; 0 |; 0 &)
% 0.20/0.71 % ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.71 % Maximal formula depth : 6 ( 4 avg)
% 0.20/0.71 % Maximal term depth : 1 ( 1 avg)
% 0.20/0.71 % Number of predicates : 3 ( 3 usr; 0 prp; 1-2 aty)
% 0.20/0.71 % Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% 0.20/0.71 % Number of variables : 8 ( 8 !; 0 ?)
% 0.20/0.71 % SPC : FOF_THM_RFO_NEQ
% 0.20/0.71
% 0.20/0.71 % Comments :
% 0.20/0.71 %--------------------------------------------------------------------------
% 0.20/0.71 %---- line(hidden - axiom26,1832636)
% 0.20/0.71 fof(empty_set_defn,axiom,
% 0.20/0.71 ! [B] : ~ member(B,empty_set) ).
% 0.20/0.71
% 0.20/0.71 %---- line(tarski - df(3),1832749)
% 0.20/0.71 fof(subset_defn,axiom,
% 0.20/0.72 ! [B,C] :
% 0.20/0.72 ( subset(B,C)
% 0.20/0.72 <=> ! [D] :
% 0.20/0.72 ( member(D,B)
% 0.20/0.72 => member(D,C) ) ) ).
% 0.20/0.72
% 0.20/0.72 %---- property(reflexivity,op(subset,2,predicate))
% 0.20/0.72 fof(reflexivity_of_subset,axiom,
% 0.20/0.72 ! [B] : subset(B,B) ).
% 0.20/0.72
% 0.20/0.72 %---- line(hidden - axiom28,1832628)
% 0.20/0.72 fof(empty_defn,axiom,
% 0.20/0.72 ! [B] :
% 0.20/0.72 ( empty(B)
% 0.20/0.72 <=> ! [C] : ~ member(C,B) ) ).
% 0.20/0.72
% 0.20/0.72 %---- line(boole - th(27),1833153)
% 0.20/0.72 fof(prove_empty_set_subset,conjecture,
% 0.20/0.72 ! [B] : subset(empty_set,B) ).
% 0.20/0.72
% 0.20/0.72 %--------------------------------------------------------------------------
% 0.20/0.72 %-------------------------------------------
% 0.20/0.72 % Proof found
% 0.20/0.72 % SZS status Theorem for theBenchmark
% 0.20/0.72 % SZS output start Proof
% 0.20/0.72 %ClaNum:8(EqnAxiom:0)
% 0.20/0.72 %VarNum:25(SingletonVarNum:12)
% 0.20/0.72 %MaxLitNum:3
% 0.20/0.72 %MaxfuncDepth:1
% 0.20/0.72 %SharedTerms:3
% 0.20/0.72 %goalClause: 2
% 0.20/0.72 %singleGoalClaCount:1
% 0.20/0.72 [2]~P1(a1,a2)
% 0.20/0.72 [1]P1(x11,x11)
% 0.20/0.72 [3]~P2(x31,a1)
% 0.20/0.72 [4]P3(x41)+P2(f3(x41),x41)
% 0.20/0.72 [5]~P3(x51)+~P2(x52,x51)
% 0.20/0.72 [6]P1(x61,x62)+P2(f4(x61,x62),x61)
% 0.20/0.72 [8]P1(x81,x82)+~P2(f4(x81,x82),x82)
% 0.20/0.72 [7]~P1(x73,x72)+P2(x71,x72)+~P2(x71,x73)
% 0.20/0.72 %EqnAxiom
% 0.20/0.72
% 0.20/0.72 %-------------------------------------------
% 0.20/0.72 cnf(9,plain,
% 0.20/0.72 ($false),
% 0.20/0.72 inference(scs_inference,[],[2,3,6]),
% 0.20/0.72 ['proof']).
% 0.20/0.72 % SZS output end Proof
% 0.20/0.72 % Total time :0.000000s
%------------------------------------------------------------------------------