TSTP Solution File: SET584+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET584+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 : n011.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 0.22s 0.64s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET584+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 10:24:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.57 start to proof:theBenchmark
% 0.22/0.63 %-------------------------------------------
% 0.22/0.63 % File :CSE---1.6
% 0.22/0.63 % Problem :theBenchmark
% 0.22/0.63 % Transform :cnf
% 0.22/0.63 % Format :tptp:raw
% 0.22/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.22/0.63
% 0.22/0.63 % Result :Theorem 0.010000s
% 0.22/0.63 % Output :CNFRefutation 0.010000s
% 0.22/0.63 %-------------------------------------------
% 0.22/0.64 %--------------------------------------------------------------------------
% 0.22/0.64 % File : SET584+3 : TPTP v8.1.2. Released v2.2.0.
% 0.22/0.64 % Domain : Set Theory
% 0.22/0.64 % Problem : If X (= Y, then X U Z (= Y U Z
% 0.22/0.64 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.22/0.64 % English : If X is a subset of Y, then the union of X and Z is a subset of
% 0.22/0.64 % the union of Y and Z.
% 0.22/0.64
% 0.22/0.64 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.22/0.64 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.22/0.64 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.22/0.64 % Source : [ILF]
% 0.22/0.64 % Names : BOOLE (33) [TS89]
% 0.22/0.64
% 0.22/0.64 % Status : Theorem
% 0.22/0.64 % Rating : 0.14 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.04 v6.1.0, 0.13 v5.5.0, 0.19 v5.4.0, 0.25 v5.3.0, 0.33 v5.2.0, 0.15 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.17 v3.7.0, 0.15 v3.5.0, 0.21 v3.4.0, 0.26 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, 0.12 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1
% 0.22/0.64 % Syntax : Number of formulae : 6 ( 2 unt; 0 def)
% 0.22/0.64 % Number of atoms : 13 ( 2 equ)
% 0.22/0.64 % Maximal formula atoms : 3 ( 2 avg)
% 0.22/0.64 % Number of connectives : 7 ( 0 ~; 1 |; 0 &)
% 0.22/0.64 % ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% 0.22/0.64 % Maximal formula depth : 6 ( 5 avg)
% 0.22/0.64 % Maximal term depth : 2 ( 1 avg)
% 0.22/0.64 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.22/0.64 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.22/0.64 % Number of variables : 15 ( 15 !; 0 ?)
% 0.22/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.22/0.64
% 0.22/0.64 % Comments :
% 0.22/0.64 %--------------------------------------------------------------------------
% 0.22/0.64 %---- line(boole - df(2),1833042)
% 0.22/0.64 fof(union_defn,axiom,
% 0.22/0.64 ! [B,C,D] :
% 0.22/0.64 ( member(D,union(B,C))
% 0.22/0.64 <=> ( member(D,B)
% 0.22/0.64 | member(D,C) ) ) ).
% 0.22/0.64
% 0.22/0.64 %---- line(tarski - df(3),1832749)
% 0.22/0.64 fof(subset_defn,axiom,
% 0.22/0.64 ! [B,C] :
% 0.22/0.64 ( subset(B,C)
% 0.22/0.64 <=> ! [D] :
% 0.22/0.64 ( member(D,B)
% 0.22/0.64 => member(D,C) ) ) ).
% 0.22/0.64
% 0.22/0.64 %---- property(commutativity,op(union,2,function))
% 0.22/0.64 fof(commutativity_of_union,axiom,
% 0.22/0.64 ! [B,C] : union(B,C) = union(C,B) ).
% 0.22/0.64
% 0.22/0.64 %---- property(reflexivity,op(subset,2,predicate))
% 0.22/0.64 fof(reflexivity_of_subset,axiom,
% 0.22/0.64 ! [B] : subset(B,B) ).
% 0.22/0.64
% 0.22/0.64 %---- line(hidden - axiom39,1832615)
% 0.22/0.64 fof(equal_member_defn,axiom,
% 0.22/0.64 ! [B,C] :
% 0.22/0.64 ( B = C
% 0.22/0.64 <=> ! [D] :
% 0.22/0.64 ( member(D,B)
% 0.22/0.64 <=> member(D,C) ) ) ).
% 0.22/0.64
% 0.22/0.64 %---- line(boole - th(33),1833222) (Looks like Quaife's LA3.1, but not mine)
% 0.22/0.64 fof(prove_th33,conjecture,
% 0.22/0.64 ! [B,C,D] :
% 0.22/0.64 ( subset(B,C)
% 0.22/0.64 => subset(union(B,D),union(C,D)) ) ).
% 0.22/0.64
% 0.22/0.64 %--------------------------------------------------------------------------
% 0.22/0.64 %-------------------------------------------
% 0.22/0.64 % Proof found
% 0.22/0.64 % SZS status Theorem for theBenchmark
% 0.22/0.64 % SZS output start Proof
% 0.22/0.64 %ClaNum:25(EqnAxiom:13)
% 0.22/0.64 %VarNum:55(SingletonVarNum:23)
% 0.22/0.64 %MaxLitNum:3
% 0.22/0.64 %MaxfuncDepth:1
% 0.22/0.64 %SharedTerms:7
% 0.22/0.64 %goalClause: 14 17
% 0.22/0.64 %singleGoalClaCount:2
% 0.22/0.64 [14]P1(a1,a4)
% 0.22/0.64 [17]~P1(f5(a1,a6),f5(a4,a6))
% 0.22/0.64 [15]P1(x151,x151)
% 0.22/0.64 [16]E(f5(x161,x162),f5(x162,x161))
% 0.22/0.64 [18]P1(x181,x182)+P2(f2(x181,x182),x181)
% 0.22/0.64 [22]P1(x221,x222)+~P2(f2(x221,x222),x222)
% 0.22/0.64 [20]~P2(x201,x203)+P2(x201,f5(x202,x203))
% 0.22/0.64 [21]~P2(x211,x212)+P2(x211,f5(x212,x213))
% 0.22/0.64 [23]E(x231,x232)+P2(f3(x231,x232),x232)+P2(f3(x231,x232),x231)
% 0.22/0.64 [25]E(x251,x252)+~P2(f3(x251,x252),x252)+~P2(f3(x251,x252),x251)
% 0.22/0.64 [19]~P1(x193,x192)+P2(x191,x192)+~P2(x191,x193)
% 0.22/0.64 [24]P2(x241,x242)+P2(x241,x243)+~P2(x241,f5(x243,x242))
% 0.22/0.64 %EqnAxiom
% 0.22/0.64 [1]E(x11,x11)
% 0.22/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.22/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.22/0.64 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 0.22/0.64 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 0.22/0.64 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.22/0.64 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.22/0.64 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83))
% 0.22/0.64 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92))
% 0.22/0.64 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 0.22/0.64 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 0.22/0.64 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 0.22/0.64 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 0.22/0.64
% 0.22/0.64 %-------------------------------------------
% 0.22/0.64 cnf(26,plain,
% 0.22/0.64 (~E(f5(a1,a6),f5(a4,a6))),
% 0.22/0.64 inference(scs_inference,[],[15,17,11])).
% 0.22/0.64 cnf(27,plain,
% 0.22/0.64 (P1(x271,x271)),
% 0.22/0.64 inference(rename_variables,[],[15])).
% 0.22/0.64 cnf(31,plain,
% 0.22/0.64 (E(f5(x311,x312),f5(x312,x311))),
% 0.22/0.64 inference(rename_variables,[],[16])).
% 0.22/0.64 cnf(35,plain,
% 0.22/0.64 (P2(f2(f5(a1,a6),f5(a4,a6)),f5(a1,a6))),
% 0.22/0.64 inference(scs_inference,[],[15,27,17,16,11,10,3,2,22,18])).
% 0.22/0.64 cnf(40,plain,
% 0.22/0.64 (~P2(f2(f5(a1,a6),f5(a4,a6)),a4)),
% 0.22/0.64 inference(scs_inference,[],[15,27,17,16,31,11,10,3,2,22,18,13,12,21])).
% 0.22/0.64 cnf(42,plain,
% 0.22/0.64 (~P2(f2(f5(a1,a6),f5(a4,a6)),a6)),
% 0.22/0.64 inference(scs_inference,[],[15,27,17,16,31,11,10,3,2,22,18,13,12,21,20])).
% 0.22/0.64 cnf(57,plain,
% 0.22/0.64 (E(f5(x571,x572),f5(x572,x571))),
% 0.22/0.64 inference(rename_variables,[],[16])).
% 0.22/0.64 cnf(59,plain,
% 0.22/0.64 (E(f5(x591,x592),f5(x592,x591))),
% 0.22/0.64 inference(rename_variables,[],[16])).
% 0.22/0.64 cnf(62,plain,
% 0.22/0.64 ($false),
% 0.22/0.64 inference(scs_inference,[],[14,16,57,59,17,26,35,42,40,24,13,10,3,19]),
% 0.22/0.64 ['proof']).
% 0.22/0.64 % SZS output end Proof
% 0.22/0.64 % Total time :0.010000s
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