TSTP Solution File: SET027+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET027+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 : n010.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 14:28:02 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET027+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n010.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 10:34:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 % File :CSE---1.6
% 0.19/0.60 % Problem :theBenchmark
% 0.19/0.60 % Transform :cnf
% 0.19/0.60 % Format :tptp:raw
% 0.19/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.60
% 0.19/0.60 % Result :Theorem 0.000000s
% 0.19/0.60 % Output :CNFRefutation 0.000000s
% 0.19/0.60 %-------------------------------------------
% 0.19/0.61 %--------------------------------------------------------------------------
% 0.19/0.61 % File : SET027+3 : TPTP v8.1.2. Released v2.2.0.
% 0.19/0.61 % Domain : Set Theory
% 0.19/0.61 % Problem : Transitivity of subset
% 0.19/0.61 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.19/0.61 % English : If X is a subset of Y and Y is a subset of Z, then X is a
% 0.19/0.61 % subset of Z.
% 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 (29) [TS89]
% 0.19/0.61
% 0.19/0.61 % Status : Theorem
% 0.19/0.61 % 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, 0.13 v5.2.0, 0.00 v3.2.0, 0.11 v3.1.0, 0.00 v2.2.1
% 0.19/0.61 % Syntax : Number of formulae : 3 ( 1 unt; 0 def)
% 0.19/0.61 % Number of atoms : 7 ( 0 equ)
% 0.19/0.61 % Maximal formula atoms : 3 ( 2 avg)
% 0.19/0.61 % Number of connectives : 4 ( 0 ~; 0 |; 1 &)
% 0.19/0.61 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.61 % Maximal formula depth : 6 ( 5 avg)
% 0.19/0.61 % Maximal term depth : 1 ( 1 avg)
% 0.19/0.61 % Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty)
% 0.19/0.61 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.61 % Number of variables : 7 ( 7 !; 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(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(29),1833172)
% 0.19/0.61 fof(prove_transitivity_of_subset,conjecture,
% 0.19/0.61 ! [B,C,D] :
% 0.19/0.61 ( ( subset(B,C)
% 0.19/0.61 & subset(C,D) )
% 0.19/0.61 => subset(B,D) ) ).
% 0.19/0.61
% 0.19/0.61 %--------------------------------------------------------------------------
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark
% 0.19/0.61 % SZS output start Proof
% 0.19/0.61 %ClaNum:7(EqnAxiom:0)
% 0.19/0.61 %VarNum:18(SingletonVarNum:8)
% 0.19/0.61 %MaxLitNum:3
% 0.19/0.61 %MaxfuncDepth:1
% 0.19/0.61 %SharedTerms:6
% 0.19/0.61 %goalClause: 1 2 4
% 0.19/0.61 %singleGoalClaCount:3
% 0.19/0.61 [1]P1(a1,a3)
% 0.19/0.61 [2]P1(a3,a4)
% 0.19/0.61 [4]~P1(a1,a4)
% 0.19/0.61 [3]P1(x31,x31)
% 0.19/0.61 [5]P1(x51,x52)+P2(f2(x51,x52),x51)
% 0.19/0.61 [7]P1(x71,x72)+~P2(f2(x71,x72),x72)
% 0.19/0.61 [6]~P2(x61,x63)+P2(x61,x62)+~P1(x63,x62)
% 0.19/0.61 %EqnAxiom
% 0.19/0.61
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 cnf(8,plain,
% 0.19/0.61 (~P2(f2(a1,a4),a4)),
% 0.19/0.61 inference(scs_inference,[],[4,7])).
% 0.19/0.61 cnf(9,plain,
% 0.19/0.61 (P2(f2(a1,a4),a1)),
% 0.19/0.61 inference(scs_inference,[],[4,7,5])).
% 0.19/0.61 cnf(10,plain,
% 0.19/0.61 (P2(f2(a1,a4),a3)),
% 0.19/0.61 inference(scs_inference,[],[1,9,6])).
% 0.19/0.61 cnf(12,plain,
% 0.19/0.61 ($false),
% 0.19/0.61 inference(scs_inference,[],[2,8,10,6]),
% 0.19/0.61 ['proof']).
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time :0.000000s
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