TSTP Solution File: SET009+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET009+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 : n025.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 14:27:47 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 : SET009+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 : n025.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 16:40:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 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 %-------------------------------------------
% 0.19/0.61 %--------------------------------------------------------------------------
% 0.19/0.61 % File : SET009+3 : TPTP v8.1.2. Released v2.2.0.
% 0.19/0.61 % Domain : Set Theory
% 0.19/0.61 % Problem : If X is a subset of Y, then Z \ Y is a subset of Z \ X
% 0.19/0.61 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.19/0.61 % English : If X is a subset of Y, then the difference of Z and Y is a
% 0.19/0.61 % subset of the difference of Z and X.
% 0.19/0.61
% 0.19/0.61 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.19/0.61 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.19/0.61 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.61 % Source : [ILF]
% 0.19/0.61 % Names : BOOLE (47) [TS89]
% 0.19/0.61
% 0.19/0.61 % Status : Theorem
% 0.19/0.61 % Rating : 0.00 v7.5.0, 0.05 v7.4.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.1.0, 0.20 v6.0.0, 0.25 v5.5.0, 0.17 v5.4.0, 0.22 v5.3.0, 0.26 v5.2.0, 0.00 v4.0.1, 0.05 v3.7.0, 0.14 v3.5.0, 0.00 v3.1.0, 0.25 v2.7.0, 0.00 v2.2.1
% 0.19/0.61 % Syntax : Number of formulae : 4 ( 1 unt; 0 def)
% 0.19/0.61 % Number of atoms : 9 ( 0 equ)
% 0.19/0.61 % Maximal formula atoms : 3 ( 2 avg)
% 0.19/0.61 % Number of connectives : 6 ( 1 ~; 0 |; 1 &)
% 0.19/0.61 % ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.61 % Maximal formula depth : 7 ( 5 avg)
% 0.19/0.61 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.61 % Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty)
% 0.19/0.61 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.19/0.61 % Number of variables : 10 ( 10 !; 0 ?)
% 0.19/0.61 % SPC : FOF_THM_RFO_NEQ
% 0.19/0.61
% 0.19/0.61 % Comments :
% 0.19/0.61 %--------------------------------------------------------------------------
% 0.19/0.61 %---- line(boole - df(4),1833078)
% 0.19/0.61 fof(difference_defn,axiom,
% 0.19/0.61 ! [B,C,D] :
% 0.19/0.61 ( member(D,difference(B,C))
% 0.19/0.61 <=> ( member(D,B)
% 0.19/0.61 & ~ member(D,C) ) ) ).
% 0.19/0.61
% 0.19/0.61 %---- line(tarski - df(3),1832749)
% 0.19/0.61 fof(subset_defn,axiom,
% 0.19/0.61 ! [B,C] :
% 0.19/0.61 ( subset(B,C)
% 0.19/0.61 <=> ! [D] :
% 0.19/0.61 ( member(D,B)
% 0.19/0.61 => member(D,C) ) ) ).
% 0.19/0.61
% 0.19/0.61 %---- property(reflexivity,op(subset,2,predicate))
% 0.19/0.61 fof(reflexivity_of_subset,axiom,
% 0.19/0.61 ! [B] : subset(B,B) ).
% 0.19/0.61
% 0.19/0.61 %---- line(boole - th(47),1833437)
% 0.19/0.61 fof(prove_subset_difference,conjecture,
% 0.19/0.61 ! [B,C,D] :
% 0.19/0.61 ( subset(B,C)
% 0.19/0.62 => subset(difference(D,C),difference(D,B)) ) ).
% 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:9(EqnAxiom:0)
% 0.19/0.62 %VarNum:35(SingletonVarNum:17)
% 0.19/0.62 %MaxLitNum:3
% 0.19/0.62 %MaxfuncDepth:1
% 0.19/0.62 %SharedTerms:7
% 0.19/0.62 %goalClause: 1 3
% 0.19/0.62 %singleGoalClaCount:2
% 0.19/0.62 [1]P1(a1,a4)
% 0.19/0.62 [3]~P1(f2(a5,a4),f2(a5,a1))
% 0.19/0.62 [2]P1(x21,x21)
% 0.19/0.62 [4]P1(x41,x42)+P2(f3(x41,x42),x41)
% 0.19/0.62 [8]P1(x81,x82)+~P2(f3(x81,x82),x82)
% 0.19/0.62 [7]P2(x71,x72)+~P2(x71,f2(x72,x73))
% 0.19/0.62 [9]~P2(x91,x92)+~P2(x91,f2(x93,x92))
% 0.19/0.62 [5]~P1(x53,x52)+P2(x51,x52)+~P2(x51,x53)
% 0.19/0.62 [6]~P2(x61,x63)+P2(x61,x62)+P2(x61,f2(x63,x62))
% 0.19/0.62 %EqnAxiom
% 0.19/0.62
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 cnf(10,plain,
% 0.19/0.62 (~P2(f3(f2(a5,a4),f2(a5,a1)),f2(a5,a1))),
% 0.19/0.62 inference(scs_inference,[],[3,8])).
% 0.19/0.62 cnf(11,plain,
% 0.19/0.62 (P2(f3(f2(a5,a4),f2(a5,a1)),f2(a5,a4))),
% 0.19/0.62 inference(scs_inference,[],[3,8,4])).
% 0.19/0.62 cnf(12,plain,
% 0.19/0.62 (~P2(x121,a1)+P2(x121,a4)),
% 0.19/0.62 inference(scs_inference,[],[1,3,8,4,5])).
% 0.19/0.62 cnf(16,plain,
% 0.19/0.62 (~P2(f3(f2(a5,a4),f2(a5,a1)),a1)),
% 0.19/0.62 inference(scs_inference,[],[11,12,9])).
% 0.19/0.62 cnf(17,plain,
% 0.19/0.62 (~P2(f3(f2(a5,a4),f2(a5,a1)),a5)),
% 0.19/0.62 inference(scs_inference,[],[10,16,6])).
% 0.19/0.62 cnf(21,plain,
% 0.19/0.62 (~P1(f2(a5,a4),a1)),
% 0.19/0.62 inference(scs_inference,[],[10,11,16,6,7,5])).
% 0.19/0.62 cnf(28,plain,
% 0.19/0.62 ($false),
% 0.19/0.62 inference(scs_inference,[],[11,21,17,4,9,7]),
% 0.19/0.62 ['proof']).
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time :0.000000s
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