TSTP Solution File: SET603+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET603+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 : n005.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 14:30:20 EDT 2023
% Result : Theorem 9.12s 9.26s
% Output : CNFRefutation 9.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SET603+3 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:38:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 9.12/9.25 %-------------------------------------------
% 9.12/9.25 % File :CSE---1.6
% 9.12/9.25 % Problem :theBenchmark
% 9.12/9.25 % Transform :cnf
% 9.12/9.25 % Format :tptp:raw
% 9.12/9.25 % Command :java -jar mcs_scs.jar %d %s
% 9.12/9.25
% 9.12/9.25 % Result :Theorem 8.570000s
% 9.12/9.25 % Output :CNFRefutation 8.570000s
% 9.12/9.25 %-------------------------------------------
% 9.12/9.25 %--------------------------------------------------------------------------
% 9.12/9.25 % File : SET603+3 : TPTP v8.1.2. Released v2.2.0.
% 9.12/9.25 % Domain : Set Theory
% 9.12/9.25 % Problem : The difference of X and the empty set is X
% 9.12/9.25 % Version : [Try90] axioms : Reduced > Incomplete.
% 9.12/9.25 % English :
% 9.12/9.25
% 9.12/9.25 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 9.12/9.25 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 9.12/9.25 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 9.12/9.25 % Source : [ILF]
% 9.12/9.25 % Names : BOOLE (74) [TS89]
% 9.12/9.25
% 9.12/9.25 % Status : Theorem
% 9.12/9.25 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.12 v6.2.0, 0.08 v6.1.0, 0.17 v6.0.0, 0.26 v5.5.0, 0.15 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.05 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.15 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.21 v3.2.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.14 v2.5.0, 0.00 v2.2.1
% 9.12/9.25 % Syntax : Number of formulae : 9 ( 3 unt; 0 def)
% 9.12/9.25 % Number of atoms : 20 ( 4 equ)
% 9.12/9.25 % Maximal formula atoms : 3 ( 2 avg)
% 9.12/9.25 % Number of connectives : 14 ( 3 ~; 0 |; 2 &)
% 9.12/9.25 % ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% 9.12/9.25 % Maximal formula depth : 7 ( 5 avg)
% 9.12/9.25 % Maximal term depth : 2 ( 1 avg)
% 9.12/9.25 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 9.12/9.25 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 9.12/9.25 % Number of variables : 19 ( 19 !; 0 ?)
% 9.12/9.25 % SPC : FOF_THM_RFO_SEQ
% 9.12/9.25
% 9.12/9.25 % Comments :
% 9.12/9.25 %--------------------------------------------------------------------------
% 9.12/9.25 %---- line(tarski - th(2),1832736)
% 9.12/9.25 fof(member_equal,axiom,
% 9.12/9.25 ! [B,C] :
% 9.12/9.25 ( ! [D] :
% 9.12/9.25 ( member(D,B)
% 9.12/9.25 <=> member(D,C) )
% 9.12/9.25 => B = C ) ).
% 9.12/9.25
% 9.12/9.25 %---- line(boole - df(4),1833078)
% 9.12/9.25 fof(difference_defn,axiom,
% 9.12/9.25 ! [B,C,D] :
% 9.12/9.25 ( member(D,difference(B,C))
% 9.12/9.25 <=> ( member(D,B)
% 9.12/9.25 & ~ member(D,C) ) ) ).
% 9.12/9.25
% 9.12/9.25 %---- line(hidden - axiom122,1832636)
% 9.12/9.25 fof(empty_set_defn,axiom,
% 9.12/9.25 ! [B] : ~ member(B,empty_set) ).
% 9.12/9.25
% 9.12/9.25 %---- line(boole - df(8),1833103)
% 9.12/9.25 fof(equal_defn,axiom,
% 9.12/9.25 ! [B,C] :
% 9.12/9.25 ( B = C
% 9.12/9.25 <=> ( subset(B,C)
% 9.12/9.25 & subset(C,B) ) ) ).
% 9.12/9.25
% 9.12/9.25 %---- line(hidden - axiom123,1832615)
% 9.12/9.25 fof(equal_member_defn,axiom,
% 9.12/9.25 ! [B,C] :
% 9.12/9.25 ( B = C
% 9.12/9.25 <=> ! [D] :
% 9.12/9.25 ( member(D,B)
% 9.12/9.25 <=> member(D,C) ) ) ).
% 9.12/9.25
% 9.12/9.25 %---- line(tarski - df(3),1832749)
% 9.12/9.25 fof(subset_defn,axiom,
% 9.12/9.25 ! [B,C] :
% 9.12/9.25 ( subset(B,C)
% 9.12/9.25 <=> ! [D] :
% 9.12/9.25 ( member(D,B)
% 9.12/9.25 => member(D,C) ) ) ).
% 9.12/9.25
% 9.12/9.25 %---- property(reflexivity,op(subset,2,predicate))
% 9.12/9.25 fof(reflexivity_of_subset,axiom,
% 9.12/9.25 ! [B] : subset(B,B) ).
% 9.12/9.25
% 9.12/9.25 %---- line(hidden - axiom125,1832628)
% 9.12/9.25 fof(empty_defn,axiom,
% 9.12/9.26 ! [B] :
% 9.12/9.26 ( empty(B)
% 9.12/9.26 <=> ! [C] : ~ member(C,B) ) ).
% 9.12/9.26
% 9.12/9.26 %---- line(boole - th(74),1833858)
% 9.12/9.26 fof(prove_th74,conjecture,
% 9.12/9.26 ! [B] : difference(B,empty_set) = B ).
% 9.12/9.26
% 9.12/9.26 %--------------------------------------------------------------------------
% 9.12/9.26 %-------------------------------------------
% 9.12/9.26 % Proof found
% 9.12/9.26 % SZS status Theorem for theBenchmark
% 9.12/9.26 % SZS output start Proof
% 9.12/9.26 %ClaNum:35(EqnAxiom:17)
% 9.12/9.26 %VarNum:84(SingletonVarNum:33)
% 9.12/9.26 %MaxLitNum:3
% 9.12/9.26 %MaxfuncDepth:1
% 9.12/9.26 %SharedTerms:4
% 9.12/9.26 %goalClause: 19
% 9.12/9.26 %singleGoalClaCount:1
% 9.12/9.26 [19]~E(f3(a1,a2),a1)
% 9.12/9.26 [18]P1(x181,x181)
% 9.12/9.26 [20]~P2(x201,a2)
% 9.12/9.26 [23]P3(x231)+P2(f4(x231),x231)
% 9.12/9.26 [22]~E(x221,x222)+P1(x221,x222)
% 9.12/9.26 [24]~P3(x241)+~P2(x242,x241)
% 9.12/9.26 [26]P1(x261,x262)+P2(f5(x261,x262),x261)
% 9.12/9.26 [30]P1(x301,x302)+~P2(f5(x301,x302),x302)
% 9.12/9.26 [29]P2(x291,x292)+~P2(x291,f3(x292,x293))
% 9.12/9.26 [33]~P2(x331,x332)+~P2(x331,f3(x333,x332))
% 9.12/9.26 [25]~P1(x252,x251)+~P1(x251,x252)+E(x251,x252)
% 9.12/9.26 [31]E(x311,x312)+P2(f6(x311,x312),x312)+P2(f6(x311,x312),x311)
% 9.12/9.26 [32]E(x321,x322)+P2(f7(x321,x322),x322)+P2(f7(x321,x322),x321)
% 9.12/9.26 [34]E(x341,x342)+~P2(f6(x341,x342),x342)+~P2(f6(x341,x342),x341)
% 9.12/9.26 [35]E(x351,x352)+~P2(f7(x351,x352),x352)+~P2(f7(x351,x352),x351)
% 9.12/9.26 [27]~P1(x273,x272)+P2(x271,x272)+~P2(x271,x273)
% 9.12/9.26 [28]~P2(x281,x283)+P2(x281,x282)+P2(x281,f3(x283,x282))
% 9.12/9.26 %EqnAxiom
% 9.12/9.26 [1]E(x11,x11)
% 9.12/9.26 [2]E(x22,x21)+~E(x21,x22)
% 9.12/9.26 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 9.12/9.26 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 9.12/9.26 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 9.12/9.26 [6]~E(x61,x62)+E(f4(x61),f4(x62))
% 9.12/9.26 [7]~E(x71,x72)+E(f5(x71,x73),f5(x72,x73))
% 9.12/9.26 [8]~E(x81,x82)+E(f5(x83,x81),f5(x83,x82))
% 9.12/9.26 [9]~E(x91,x92)+E(f7(x91,x93),f7(x92,x93))
% 9.12/9.26 [10]~E(x101,x102)+E(f7(x103,x101),f7(x103,x102))
% 9.12/9.26 [11]~E(x111,x112)+E(f6(x111,x113),f6(x112,x113))
% 9.12/9.26 [12]~E(x121,x122)+E(f6(x123,x121),f6(x123,x122))
% 9.12/9.26 [13]P1(x132,x133)+~E(x131,x132)+~P1(x131,x133)
% 9.12/9.26 [14]P1(x143,x142)+~E(x141,x142)+~P1(x143,x141)
% 9.12/9.26 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153)
% 9.12/9.26 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161)
% 9.12/9.26 [17]~P3(x171)+P3(x172)+~E(x171,x172)
% 9.12/9.26
% 9.12/9.26 %-------------------------------------------
% 9.12/9.26 cnf(37,plain,
% 9.12/9.26 (~P2(x371,a2)),
% 9.12/9.26 inference(rename_variables,[],[20])).
% 9.12/9.26 cnf(38,plain,
% 9.12/9.26 (P1(a2,x381)),
% 9.12/9.26 inference(scs_inference,[],[20,37,23,26])).
% 9.12/9.26 cnf(39,plain,
% 9.12/9.26 (~P2(x391,a2)),
% 9.12/9.26 inference(rename_variables,[],[20])).
% 9.12/9.26 cnf(41,plain,
% 9.12/9.26 (~E(a1,f3(a1,a2))),
% 9.12/9.26 inference(scs_inference,[],[19,20,37,23,26,2])).
% 9.12/9.26 cnf(42,plain,
% 9.12/9.26 (~P2(x421,f3(a2,x422))),
% 9.12/9.26 inference(scs_inference,[],[19,20,37,39,23,26,2,29])).
% 9.12/9.26 cnf(44,plain,
% 9.12/9.26 (~E(a2,x441)+P3(x441)),
% 9.12/9.26 inference(scs_inference,[],[19,20,37,39,23,26,2,29,17])).
% 9.12/9.26 cnf(45,plain,
% 9.12/9.26 (E(f3(a2,x451),a2)),
% 9.12/9.26 inference(scs_inference,[],[19,20,37,39,23,26,2,29,17,32])).
% 9.12/9.26 cnf(50,plain,
% 9.12/9.26 (~E(a2,x501)+E(f3(a2,x502),x501)),
% 9.12/9.26 inference(scs_inference,[],[19,18,20,37,39,23,26,2,29,17,32,14,3])).
% 9.12/9.26 cnf(51,plain,
% 9.12/9.26 (E(a2,f3(a2,x511))),
% 9.12/9.26 inference(scs_inference,[],[19,18,20,37,39,23,26,2,29,17,32,14,3,25])).
% 9.12/9.26 cnf(53,plain,
% 9.12/9.26 (~P2(f7(f3(a1,a2),a1),f3(a1,a2))+~P2(f7(f3(a1,a2),a1),a1)),
% 9.12/9.26 inference(scs_inference,[],[19,18,20,37,39,23,26,2,29,17,32,14,3,25,35])).
% 9.12/9.26 cnf(72,plain,
% 9.12/9.26 (E(f3(x721,f3(a2,x722)),f3(x721,a2))),
% 9.12/9.26 inference(scs_inference,[],[45,51,50,44,22,12,11,10,9,8,7,6,5])).
% 9.12/9.26 cnf(84,plain,
% 9.12/9.26 (P2(f7(f3(a1,a2),a1),a1)+P2(f7(f3(a1,a2),a1),f3(a1,a2))+P2(f6(a2,x841),f3(x841,f3(a2,x842)))),
% 9.12/9.26 inference(scs_inference,[],[19,20,42,38,45,51,50,44,22,12,11,10,9,8,7,6,5,4,13,2,3,17,16,28,31,32])).
% 9.12/9.26 cnf(88,plain,
% 9.12/9.26 (P2(f7(f3(a1,a2),a1),f3(a1,a2))+P2(f7(f3(a1,a2),a1),a1)),
% 9.12/9.26 inference(scs_inference,[],[72,41,42,3,84])).
% 9.12/9.26 cnf(469,plain,
% 9.12/9.26 (~P2(f7(f3(a1,a2),a1),f3(a1,a2))+~P2(f7(f3(a1,a2),a1),f3(a1,x4691))),
% 9.12/9.26 inference(scs_inference,[],[53,29])).
% 9.12/9.26 cnf(470,plain,
% 9.12/9.26 (~P2(f7(f3(a1,a2),a1),f3(a1,a2))),
% 9.12/9.26 inference(factoring_inference,[],[469])).
% 9.12/9.26 cnf(471,plain,
% 9.12/9.26 (P2(f7(f3(a1,a2),a1),a1)),
% 9.12/9.26 inference(scs_inference,[],[470,88])).
% 9.12/9.26 cnf(472,plain,
% 9.12/9.26 (~P2(f7(f3(a1,a2),a1),a1)),
% 9.12/9.26 inference(scs_inference,[],[470,20,28])).
% 9.12/9.26 cnf(491,plain,
% 9.12/9.26 ($false),
% 9.12/9.26 inference(scs_inference,[],[471,472]),
% 9.12/9.26 ['proof']).
% 9.12/9.26 % SZS output end Proof
% 9.12/9.26 % Total time :8.570000s
%------------------------------------------------------------------------------