TSTP Solution File: SET597+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET597+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 : n013.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 14:30:18 EDT 2023
% Result : Theorem 101.56s 101.60s
% Output : CNFRefutation 101.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET597+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
% 0.14/0.35 % Computer : n013.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 12:49:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.65 start to proof:theBenchmark
% 101.56/101.58 %-------------------------------------------
% 101.56/101.58 % File :CSE---1.6
% 101.56/101.58 % Problem :theBenchmark
% 101.56/101.58 % Transform :cnf
% 101.56/101.58 % Format :tptp:raw
% 101.56/101.58 % Command :java -jar mcs_scs.jar %d %s
% 101.56/101.58
% 101.56/101.58 % Result :Theorem 100.880000s
% 101.56/101.58 % Output :CNFRefutation 100.880000s
% 101.56/101.58 %-------------------------------------------
% 101.56/101.59 %--------------------------------------------------------------------------
% 101.56/101.59 % File : SET597+3 : TPTP v8.1.2. Released v2.2.0.
% 101.56/101.59 % Domain : Set Theory
% 101.56/101.59 % Problem : X = Y U Z iff Y (= X, Z (= X, !V: Y (= V & Z (= V, X (= V
% 101.56/101.59 % Version : [Try90] axioms : Reduced > Incomplete.
% 101.56/101.59 % English : X is the union of Y and Z if and only if the following
% 101.56/101.59 % conditions are satisfied: 1. Y is a subset of X, 2. Z is a
% 101.56/101.59 % subset of X, and 3. for every V such that Y is a subset of V
% 101.56/101.59 % and Z is a subset of V : X is a subset of V.
% 101.56/101.59
% 101.56/101.59 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 101.56/101.59 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 101.56/101.59 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 101.56/101.59 % Source : [ILF]
% 101.56/101.59 % Names : BOOLE (56) [TS89]
% 101.56/101.59
% 101.56/101.59 % Status : Theorem
% 101.56/101.59 % Rating : 0.14 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.1.0, 0.17 v6.0.0, 0.13 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.30 v5.2.0, 0.00 v5.0.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.10 v3.5.0, 0.16 v3.3.0, 0.14 v3.2.0, 0.18 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.14 v2.5.0, 0.12 v2.4.0, 0.00 v2.2.1
% 101.56/101.59 % Syntax : Number of formulae : 9 ( 3 unt; 0 def)
% 101.56/101.59 % Number of atoms : 24 ( 4 equ)
% 101.56/101.59 % Maximal formula atoms : 6 ( 2 avg)
% 101.56/101.59 % Number of connectives : 15 ( 0 ~; 1 |; 5 &)
% 101.56/101.59 % ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% 101.56/101.59 % Maximal formula depth : 10 ( 5 avg)
% 101.56/101.59 % Maximal term depth : 2 ( 1 avg)
% 101.56/101.59 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 101.56/101.59 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 101.56/101.59 % Number of variables : 23 ( 23 !; 0 ?)
% 101.56/101.59 % SPC : FOF_THM_RFO_SEQ
% 101.56/101.59
% 101.56/101.59 % Comments :
% 101.56/101.59 %--------------------------------------------------------------------------
% 101.56/101.59 %---- line(boole - th(31),1833190)
% 101.56/101.59 fof(subset_of_union,axiom,
% 101.56/101.59 ! [B,C] : subset(B,union(B,C)) ).
% 101.56/101.59
% 101.56/101.59 %---- line(boole - th(32),1833206)
% 101.56/101.59 fof(union_subset,axiom,
% 101.56/101.59 ! [B,C,D] :
% 101.56/101.59 ( ( subset(B,C)
% 101.56/101.59 & subset(D,C) )
% 101.56/101.59 => subset(union(B,D),C) ) ).
% 101.56/101.59
% 101.56/101.59 %---- line(boole - df(2),1833042)
% 101.56/101.59 fof(union_defn,axiom,
% 101.56/101.59 ! [B,C,D] :
% 101.56/101.59 ( member(D,union(B,C))
% 101.56/101.59 <=> ( member(D,B)
% 101.56/101.59 | member(D,C) ) ) ).
% 101.56/101.59
% 101.56/101.59 %---- line(tarski - df(3),1832749)
% 101.56/101.59 fof(subset_defn,axiom,
% 101.56/101.59 ! [B,C] :
% 101.56/101.59 ( subset(B,C)
% 101.56/101.59 <=> ! [D] :
% 101.56/101.59 ( member(D,B)
% 101.56/101.59 => member(D,C) ) ) ).
% 101.56/101.59
% 101.56/101.59 %---- line(boole - df(8),1833103)
% 101.56/101.59 fof(equal_defn,axiom,
% 101.56/101.59 ! [B,C] :
% 101.56/101.59 ( B = C
% 101.56/101.59 <=> ( subset(B,C)
% 101.56/101.59 & subset(C,B) ) ) ).
% 101.56/101.59
% 101.56/101.59 %---- property(commutativity,op(union,2,function))
% 101.56/101.59 fof(commutativity_of_union,axiom,
% 101.56/101.59 ! [B,C] : union(B,C) = union(C,B) ).
% 101.56/101.59
% 101.56/101.59 %---- property(reflexivity,op(subset,2,predicate))
% 101.56/101.59 fof(reflexivity_of_subset,axiom,
% 101.56/101.59 ! [B] : subset(B,B) ).
% 101.56/101.59
% 101.56/101.59 %---- line(hidden - axiom84,1832615)
% 101.56/101.59 fof(equal_member_defn,axiom,
% 101.56/101.59 ! [B,C] :
% 101.56/101.59 ( B = C
% 101.56/101.59 <=> ! [D] :
% 101.56/101.59 ( member(D,B)
% 101.56/101.59 <=> member(D,C) ) ) ).
% 101.56/101.59
% 101.56/101.59 %---- line(boole - th(56),1833583)
% 101.56/101.59 fof(prove_th56,conjecture,
% 101.56/101.59 ! [B,C,D] :
% 101.56/101.59 ( B = union(C,D)
% 101.56/101.59 <=> ( subset(C,B)
% 101.56/101.59 & subset(D,B)
% 101.56/101.59 & ! [E] :
% 101.56/101.59 ( ( subset(C,E)
% 101.56/101.59 & subset(D,E) )
% 101.56/101.59 => subset(B,E) ) ) ) ).
% 101.56/101.59
% 101.56/101.59 %--------------------------------------------------------------------------
% 101.56/101.59 %-------------------------------------------
% 101.56/101.60 % Proof found
% 101.56/101.60 % SZS status Theorem for theBenchmark
% 101.56/101.60 % SZS output start Proof
% 101.56/101.60 %ClaNum:34(EqnAxiom:13)
% 101.56/101.60 %VarNum:78(SingletonVarNum:33)
% 101.56/101.60 %MaxLitNum:4
% 101.56/101.60 %MaxfuncDepth:1
% 101.56/101.60 %SharedTerms:14
% 101.56/101.60 %goalClause: 19 20 26 27 28 29
% 101.56/101.60 [14]P1(x141,x141)
% 101.56/101.60 [15]E(f1(x151,x152),f1(x152,x151))
% 101.56/101.60 [16]P1(x161,f1(x161,x162))
% 101.56/101.60 [19]P1(a2,a3)+E(f1(a2,a6),a3)
% 101.56/101.60 [20]P1(a6,a3)+E(f1(a2,a6),a3)
% 101.56/101.60 [18]~E(x181,x182)+P1(x181,x182)
% 101.56/101.60 [22]P1(x221,x222)+P2(f4(x221,x222),x221)
% 101.56/101.60 [30]P1(x301,x302)+~P2(f4(x301,x302),x302)
% 101.56/101.60 [24]~P2(x241,x243)+P2(x241,f1(x242,x243))
% 101.56/101.60 [25]~P2(x251,x252)+P2(x251,f1(x252,x253))
% 101.56/101.60 [21]~P1(x212,x211)+~P1(x211,x212)+E(x211,x212)
% 101.56/101.60 [31]E(x311,x312)+P2(f5(x311,x312),x312)+P2(f5(x311,x312),x311)
% 101.56/101.60 [34]E(x341,x342)+~P2(f5(x341,x342),x342)+~P2(f5(x341,x342),x341)
% 101.56/101.60 [23]~P2(x231,x233)+P2(x231,x232)+~P1(x233,x232)
% 101.56/101.60 [32]~P1(x322,x323)+~P1(x321,x323)+P1(f1(x321,x322),x323)
% 101.56/101.60 [33]P2(x331,x332)+P2(x331,x333)+~P2(x331,f1(x333,x332))
% 101.56/101.60 [27]P1(a2,a7)+~P1(a2,a3)+~P1(a6,a3)+~E(f1(a2,a6),a3)
% 101.56/101.60 [28]~P1(a2,a3)+~P1(a6,a3)+P1(a6,a7)+~E(f1(a2,a6),a3)
% 101.56/101.60 [29]~P1(a2,a3)+~P1(a6,a3)+~P1(a3,a7)+~E(f1(a2,a6),a3)
% 101.56/101.60 [26]~P1(a2,x261)+~P1(a6,x261)+P1(a3,x261)+E(f1(a2,a6),a3)
% 101.56/101.60 %EqnAxiom
% 101.56/101.60 [1]E(x11,x11)
% 101.56/101.60 [2]E(x22,x21)+~E(x21,x22)
% 101.56/101.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 101.56/101.60 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 101.56/101.60 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 101.56/101.60 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 101.56/101.60 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 101.56/101.60 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83))
% 101.56/101.60 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92))
% 101.56/101.60 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 101.56/101.60 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 101.56/101.60 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 101.56/101.60 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 101.56/101.60
% 101.56/101.60 %-------------------------------------------
% 101.56/101.61 cnf(35,plain,
% 101.56/101.61 (P1(f1(x351,x352),f1(x352,x351))),
% 101.56/101.61 inference(scs_inference,[],[14,15,11])).
% 101.56/101.61 cnf(36,plain,
% 101.56/101.61 (P1(x361,x361)),
% 101.56/101.61 inference(rename_variables,[],[14])).
% 101.56/101.61 cnf(39,plain,
% 101.56/101.61 (P1(f1(x391,x391),x391)),
% 101.56/101.61 inference(scs_inference,[],[14,36,16,15,11,10,32])).
% 101.56/101.61 cnf(41,plain,
% 101.56/101.61 (~P2(x411,f1(x412,x413))+P2(x411,f1(x413,x412))),
% 101.56/101.61 inference(scs_inference,[],[14,36,16,15,11,10,32,13])).
% 101.56/101.61 cnf(51,plain,
% 101.56/101.61 (E(x511,f1(x511,x511))),
% 101.56/101.61 inference(scs_inference,[],[14,16,39,32,21])).
% 101.56/101.61 cnf(54,plain,
% 101.56/101.61 (E(f4(x541,x542),f4(x541,f1(x542,x542)))),
% 101.56/101.61 inference(scs_inference,[],[14,16,39,32,21,9])).
% 101.56/101.61 cnf(55,plain,
% 101.56/101.61 (E(f4(x551,x552),f4(f1(x551,x551),x552))),
% 101.56/101.61 inference(scs_inference,[],[14,16,39,32,21,9,8])).
% 101.56/101.61 cnf(56,plain,
% 101.56/101.61 (E(f5(x561,x562),f5(x561,f1(x562,x562)))),
% 101.56/101.61 inference(scs_inference,[],[14,16,39,32,21,9,8,7])).
% 101.56/101.61 cnf(57,plain,
% 101.56/101.61 (E(f5(x571,x572),f5(f1(x571,x571),x572))),
% 101.56/101.61 inference(scs_inference,[],[14,16,39,32,21,9,8,7,6])).
% 101.56/101.61 cnf(58,plain,
% 101.56/101.61 (E(f1(x581,x582),f1(x581,f1(x582,x582)))),
% 101.56/101.61 inference(scs_inference,[],[14,16,39,32,21,9,8,7,6,5])).
% 101.56/101.61 cnf(59,plain,
% 101.56/101.61 (E(f1(x591,x592),f1(f1(x591,x591),x592))),
% 101.56/101.61 inference(scs_inference,[],[14,16,39,32,21,9,8,7,6,5,4])).
% 101.56/101.61 cnf(60,plain,
% 101.56/101.61 (E(f4(x601,x601),f4(f1(x601,x601),f1(x601,x601)))),
% 101.56/101.61 inference(scs_inference,[],[14,16,39,32,21,9,8,7,6,5,4,3])).
% 101.56/101.61 cnf(61,plain,
% 101.56/101.61 (P1(f4(x611,x611),f4(x611,f1(x611,x611)))),
% 101.56/101.61 inference(scs_inference,[],[14,16,39,32,21,9,8,7,6,5,4,3,18])).
% 101.56/101.61 cnf(63,plain,
% 101.56/101.61 (E(f4(f1(x631,x631),f1(x631,x631)),f4(x631,x631))),
% 101.56/101.61 inference(scs_inference,[],[60,2])).
% 101.56/101.61 cnf(64,plain,
% 101.56/101.61 (E(f1(x641,x642),f1(f1(x642,x641),f1(x642,x641)))),
% 101.56/101.61 inference(scs_inference,[],[15,60,51,2,3])).
% 101.56/101.61 cnf(65,plain,
% 101.56/101.61 (E(x651,f1(x651,x651))),
% 101.56/101.61 inference(rename_variables,[],[51])).
% 101.56/101.61 cnf(66,plain,
% 101.56/101.61 (P1(f4(x661,x661),f4(f1(x661,x661),f1(x661,x661)))),
% 101.56/101.61 inference(scs_inference,[],[15,60,61,51,55,2,3,11])).
% 101.56/101.61 cnf(68,plain,
% 101.56/101.61 (P1(f1(f1(x681,x682),f1(x681,x682)),f1(x682,x681))),
% 101.56/101.61 inference(scs_inference,[],[15,35,60,61,51,65,55,2,3,11,10])).
% 101.56/101.61 cnf(73,plain,
% 101.56/101.61 (P1(a3,f1(a6,x731))+~P1(a2,f1(a6,x731))+E(f1(a2,a6),a3)),
% 101.56/101.61 inference(scs_inference,[],[16,26])).
% 101.56/101.61 cnf(77,plain,
% 101.56/101.61 (P1(x771,f1(x771,x772))),
% 101.56/101.61 inference(rename_variables,[],[16])).
% 101.56/101.61 cnf(80,plain,
% 101.56/101.61 (P1(f4(f1(x801,x801),f1(x801,x801)),f4(x801,x801))),
% 101.56/101.61 inference(scs_inference,[],[16,63,68,21,18])).
% 101.56/101.61 cnf(82,plain,
% 101.56/101.61 (P1(f1(x821,x821),f1(x821,x822))),
% 101.56/101.61 inference(scs_inference,[],[16,77,63,68,21,18,32])).
% 101.56/101.61 cnf(84,plain,
% 101.56/101.61 (P1(x841,f1(f1(x842,x841),f1(x842,x841)))),
% 101.56/101.61 inference(scs_inference,[],[16,77,63,64,68,21,18,32,11])).
% 101.56/101.61 cnf(86,plain,
% 101.56/101.61 (P1(f1(f1(x861,x861),f1(x861,x861)),x861)),
% 101.56/101.61 inference(scs_inference,[],[16,77,63,64,68,39,21,18,32,11,10])).
% 101.56/101.61 cnf(89,plain,
% 101.56/101.61 (P1(f1(f1(x891,x891),f1(x891,x891)),f1(x891,x892))),
% 101.56/101.61 inference(scs_inference,[],[82,32])).
% 101.56/101.61 cnf(91,plain,
% 101.56/101.61 (E(f4(x911,f1(x912,x912)),f4(x911,x912))),
% 101.56/101.61 inference(scs_inference,[],[54,82,32,2])).
% 101.56/101.61 cnf(92,plain,
% 101.56/101.61 (E(f1(f1(x921,x921),f1(x921,x921)),x921)),
% 101.56/101.61 inference(scs_inference,[],[86,54,84,82,32,2,21])).
% 101.56/101.61 cnf(99,plain,
% 101.56/101.61 (P1(f1(x991,x992),f1(x992,f1(x991,x991)))),
% 101.56/101.61 inference(scs_inference,[],[35,86,54,56,57,58,84,82,32,2,21,3,11])).
% 101.56/101.61 cnf(100,plain,
% 101.56/101.61 (E(f1(x1001,x1002),f1(x1001,f1(x1002,x1002)))),
% 101.56/101.61 inference(rename_variables,[],[58])).
% 101.56/101.61 cnf(101,plain,
% 101.56/101.61 (P1(f1(x1011,f1(x1012,x1012)),f1(x1012,x1011))),
% 101.56/101.61 inference(scs_inference,[],[35,86,54,56,57,58,100,84,82,32,2,21,3,11,10])).
% 101.56/101.61 cnf(105,plain,
% 101.56/101.61 (E(f1(x1051,f1(x1051,x1051)),x1051)),
% 101.56/101.61 inference(scs_inference,[],[92,59,3])).
% 101.56/101.61 cnf(110,plain,
% 101.56/101.61 (P1(f4(x1101,x1101),f4(f1(x1101,x1101),x1101))),
% 101.56/101.61 inference(scs_inference,[],[66,105,91,18,11])).
% 101.56/101.61 cnf(112,plain,
% 101.56/101.61 (E(f4(x1121,f1(x1122,x1122)),f4(x1121,x1122))),
% 101.56/101.61 inference(rename_variables,[],[91])).
% 101.56/101.61 cnf(113,plain,
% 101.56/101.61 (P1(f4(f1(x1131,x1131),x1131),f4(x1131,x1131))),
% 101.56/101.61 inference(scs_inference,[],[66,80,105,91,112,18,11,10])).
% 101.56/101.61 cnf(119,plain,
% 101.56/101.61 (E(f1(x1191,x1191),x1191)),
% 101.56/101.61 inference(scs_inference,[],[51,110,113,21,2])).
% 101.56/101.61 cnf(127,plain,
% 101.56/101.61 (E(f1(x1271,f1(x1272,x1272)),f1(x1271,x1272))),
% 101.56/101.61 inference(scs_inference,[],[39,51,110,113,14,21,2,32,6,4,8,7,5])).
% 101.56/101.61 cnf(163,plain,
% 101.56/101.61 (E(f1(x1631,f1(x1632,x1632)),f1(x1632,x1631))),
% 101.56/101.61 inference(scs_inference,[],[99,101,21])).
% 101.56/101.61 cnf(246,plain,
% 101.56/101.61 (P1(f1(f1(x2461,x2462),f1(x2461,x2461)),f1(x2461,x2462))),
% 101.56/101.61 inference(scs_inference,[],[82,14,32])).
% 101.56/101.61 cnf(253,plain,
% 101.56/101.61 (E(f1(x2531,x2532),f1(f1(x2531,x2532),f1(x2531,x2531)))),
% 101.56/101.61 inference(scs_inference,[],[246,16,21])).
% 101.56/101.61 cnf(277,plain,
% 101.56/101.61 (P1(f1(f1(x2771,x2771),f1(x2771,x2771)),f1(x2772,x2771))),
% 101.56/101.61 inference(scs_inference,[],[89,163,11])).
% 101.56/101.61 cnf(283,plain,
% 101.56/101.62 (P1(x2831,f1(x2832,x2831))),
% 101.56/101.62 inference(scs_inference,[],[92,277,10])).
% 101.56/101.62 cnf(405,plain,
% 101.56/101.62 (E(f1(x4051,f1(x4052,x4052)),f1(x4051,x4052))),
% 101.56/101.62 inference(rename_variables,[],[127])).
% 101.56/101.62 cnf(406,plain,
% 101.56/101.62 (P1(f1(x4061,x4061),f1(x4062,x4061))),
% 101.56/101.62 inference(scs_inference,[],[127,405,253,283,3,11])).
% 101.56/101.62 cnf(1347,plain,
% 101.56/101.62 (~P2(x13471,f1(x13472,x13472))+P2(x13471,x13472)),
% 101.56/101.62 inference(scs_inference,[],[119,13])).
% 101.56/101.62 cnf(1519,plain,
% 101.56/101.62 (P1(f1(a2,a2),a3)+P1(a2,a3)),
% 101.56/101.62 inference(scs_inference,[],[82,19,11])).
% 101.56/101.62 cnf(1520,plain,
% 101.56/101.62 (P1(a2,a3)),
% 101.56/101.62 inference(scs_inference,[],[119,1519,10])).
% 101.56/101.62 cnf(1521,plain,
% 101.56/101.62 (~P1(a6,a3)+P1(a2,a7)+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[1520,27])).
% 101.56/101.62 cnf(1522,plain,
% 101.56/101.62 (~P1(a6,a3)+P1(a6,a7)+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[1520,28])).
% 101.56/101.62 cnf(1523,plain,
% 101.56/101.62 (~P1(a6,a3)+~P1(a3,a7)+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[1520,29])).
% 101.56/101.62 cnf(1613,plain,
% 101.56/101.62 (~P2(x16131,a2)+P2(x16131,a3)),
% 101.56/101.62 inference(scs_inference,[],[1520,23])).
% 101.56/101.62 cnf(1619,plain,
% 101.56/101.62 (P1(f1(a2,a3),a3)),
% 101.56/101.62 inference(scs_inference,[],[1520,14,32])).
% 101.56/101.62 cnf(1625,plain,
% 101.56/101.62 (E(a3,f1(a2,a3))),
% 101.56/101.62 inference(scs_inference,[],[283,1619,21])).
% 101.56/101.62 cnf(1626,plain,
% 101.56/101.62 (P1(x16261,f1(x16262,x16261))),
% 101.56/101.62 inference(rename_variables,[],[283])).
% 101.56/101.62 cnf(1628,plain,
% 101.56/101.62 (P1(f1(a3,a2),a3)),
% 101.56/101.62 inference(scs_inference,[],[1520,283,1619,14,21,32])).
% 101.56/101.62 cnf(1633,plain,
% 101.56/101.62 (E(f1(a2,a3),a3)),
% 101.56/101.62 inference(scs_inference,[],[1520,283,1626,1619,14,21,32,10,2])).
% 101.56/101.62 cnf(1640,plain,
% 101.56/101.62 (E(f1(a3,a2),a3)),
% 101.56/101.62 inference(scs_inference,[],[1628,16,21])).
% 101.56/101.62 cnf(1643,plain,
% 101.56/101.62 (E(f1(a2,a3),f1(a3,a3))),
% 101.56/101.62 inference(scs_inference,[],[51,1628,16,1633,21,3])).
% 101.56/101.62 cnf(1646,plain,
% 101.56/101.62 (E(a3,f1(a3,a2))),
% 101.56/101.62 inference(scs_inference,[],[1640,2])).
% 101.56/101.62 cnf(1679,plain,
% 101.56/101.62 (P1(f1(a2,a3),f1(a3,x16791))),
% 101.56/101.62 inference(scs_inference,[],[1625,16,10])).
% 101.56/101.62 cnf(1691,plain,
% 101.56/101.62 (~P2(x16911,f1(a2,a3))+P2(x16911,f1(a3,x16912))),
% 101.56/101.62 inference(scs_inference,[],[1679,1643,13,23])).
% 101.56/101.62 cnf(2042,plain,
% 101.56/101.62 (E(x20421,a3)+~P2(f5(x20421,a3),x20421)+~P2(f5(x20421,a3),a2)),
% 101.56/101.62 inference(scs_inference,[],[1613,34])).
% 101.56/101.62 cnf(2049,plain,
% 101.56/101.62 (E(a3,x20491)+~P2(f5(a3,x20491),x20491)+~P2(f5(a3,x20491),a2)),
% 101.56/101.62 inference(scs_inference,[],[1613,34])).
% 101.56/101.62 cnf(2156,plain,
% 101.56/101.62 (P1(a6,a3)),
% 101.56/101.62 inference(scs_inference,[],[283,20,11])).
% 101.56/101.62 cnf(2157,plain,
% 101.56/101.62 (P1(a2,a7)+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[2156,1521])).
% 101.56/101.62 cnf(2158,plain,
% 101.56/101.62 (P1(a6,a7)+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[2156,1522])).
% 101.56/101.62 cnf(2159,plain,
% 101.56/101.62 (~P1(a3,a7)+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[2156,1523])).
% 101.56/101.62 cnf(2261,plain,
% 101.56/101.62 (P1(f1(a2,a2),a7)+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[51,2157,10])).
% 101.56/101.62 cnf(2262,plain,
% 101.56/101.62 (P1(f1(a6,a6),a7)+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[2158,32])).
% 101.56/101.62 cnf(2265,plain,
% 101.56/101.62 (~E(a3,a7)+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[2159,18])).
% 101.56/101.62 cnf(2269,plain,
% 101.56/101.62 (P1(a6,f1(a2,a3))),
% 101.56/101.62 inference(scs_inference,[],[1625,2156,11])).
% 101.56/101.62 cnf(2309,plain,
% 101.56/101.62 (~E(a7,a3)+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[2265,2])).
% 101.56/101.62 cnf(2311,plain,
% 101.56/101.62 (P1(a6,f1(a3,a2))),
% 101.56/101.62 inference(scs_inference,[],[1646,2156,11])).
% 101.56/101.62 cnf(2331,plain,
% 101.56/101.62 (~E(a7,f1(a3,a2))+~E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[1640,2309,3])).
% 101.56/101.62 cnf(2350,plain,
% 101.56/101.62 (E(f1(a6,a3),a3)),
% 101.56/101.62 inference(scs_inference,[],[2156,283,14,32,21])).
% 101.56/101.62 cnf(2354,plain,
% 101.56/101.62 (P1(f1(a6,a3),f1(a3,a3))),
% 101.56/101.62 inference(scs_inference,[],[2156,51,283,14,32,21,13,11])).
% 101.56/101.62 cnf(2359,plain,
% 101.56/101.62 (E(a3,f1(a6,a3))),
% 101.56/101.62 inference(scs_inference,[],[2350,2])).
% 101.56/101.62 cnf(2363,plain,
% 101.56/101.62 (P1(f1(a3,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[2156,2350,14,406,2354,2,21,32])).
% 101.56/101.62 cnf(2368,plain,
% 101.56/101.62 (P1(f1(a6,a3),f1(x23681,a3))),
% 101.56/101.62 inference(scs_inference,[],[2156,51,283,2350,14,406,2354,2,21,32,3,10])).
% 101.56/101.62 cnf(2378,plain,
% 101.56/101.62 (P1(a2,f1(a6,a3))),
% 101.56/101.62 inference(scs_inference,[],[283,1640,2359,3,11])).
% 101.56/101.62 cnf(2398,plain,
% 101.56/101.62 (E(a3,f1(a3,a6))),
% 101.56/101.62 inference(scs_inference,[],[2363,16,21])).
% 101.56/101.62 cnf(2403,plain,
% 101.56/101.62 (E(f1(a3,a2),f1(a3,a6))),
% 101.56/101.62 inference(scs_inference,[],[283,1640,2363,16,21,10,3])).
% 101.56/101.62 cnf(2420,plain,
% 101.56/101.62 (E(f1(a3,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[2398,2])).
% 101.56/101.62 cnf(2514,plain,
% 101.56/101.62 (P1(f1(a2,a6),f1(a2,a3))),
% 101.56/101.62 inference(scs_inference,[],[2269,16,32])).
% 101.56/101.62 cnf(2543,plain,
% 101.56/101.62 (P1(f1(a2,a6),f1(a3,a2))),
% 101.56/101.62 inference(scs_inference,[],[2311,283,32])).
% 101.56/101.62 cnf(2587,plain,
% 101.56/101.62 (E(f1(a2,a3),f1(a2,a6))+~P1(a3,f1(a2,a6))),
% 101.56/101.62 inference(scs_inference,[],[2514,16,21,32])).
% 101.56/101.62 cnf(2646,plain,
% 101.56/101.62 (P1(f1(a2,a6),f1(a6,a3))),
% 101.56/101.62 inference(scs_inference,[],[2378,16,32])).
% 101.56/101.62 cnf(2656,plain,
% 101.56/101.62 (P1(x26561,f1(x26562,x26561))),
% 101.56/101.62 inference(rename_variables,[],[283])).
% 101.56/101.62 cnf(2657,plain,
% 101.56/101.62 (E(f1(a2,a6),f1(a6,a3))+~P1(a3,f1(a2,a6))),
% 101.56/101.62 inference(scs_inference,[],[283,2656,2646,21,10,32])).
% 101.56/101.62 cnf(2720,plain,
% 101.56/101.62 (P1(f1(a2,a6),f1(a3,a6))),
% 101.56/101.62 inference(scs_inference,[],[2403,2543,11])).
% 101.56/101.62 cnf(2744,plain,
% 101.56/101.62 (P1(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[2420,2720,11])).
% 101.56/101.62 cnf(2753,plain,
% 101.56/101.62 (E(f1(a2,a6),a3)),
% 101.56/101.62 inference(scs_inference,[],[283,15,2744,21,11,73])).
% 101.56/101.62 cnf(2763,plain,
% 101.56/101.62 (P1(a2,a7)),
% 101.56/101.62 inference(scs_inference,[],[2753,2157])).
% 101.56/101.62 cnf(2764,plain,
% 101.56/101.62 (P1(a6,a7)),
% 101.56/101.62 inference(scs_inference,[],[2753,2158])).
% 101.56/101.62 cnf(2765,plain,
% 101.56/101.62 (~P1(a3,a7)),
% 101.56/101.62 inference(scs_inference,[],[2753,2159])).
% 101.56/101.62 cnf(2766,plain,
% 101.56/101.62 (P1(f1(a2,a2),a7)),
% 101.56/101.62 inference(scs_inference,[],[2753,2261])).
% 101.56/101.62 cnf(2767,plain,
% 101.56/101.62 (P1(f1(a6,a6),a7)),
% 101.56/101.62 inference(scs_inference,[],[2753,2262])).
% 101.56/101.62 cnf(2768,plain,
% 101.56/101.62 (~E(a3,a7)),
% 101.56/101.62 inference(scs_inference,[],[2753,2265])).
% 101.56/101.62 cnf(2769,plain,
% 101.56/101.62 (~E(a7,a3)),
% 101.56/101.62 inference(scs_inference,[],[2753,2309])).
% 101.56/101.62 cnf(2770,plain,
% 101.56/101.62 (~E(a7,f1(a3,a2))),
% 101.56/101.62 inference(scs_inference,[],[2753,2331])).
% 101.56/101.62 cnf(2774,plain,
% 101.56/101.62 (E(a3,f1(a2,a6))),
% 101.56/101.62 inference(scs_inference,[],[2753,2])).
% 101.56/101.62 cnf(2779,plain,
% 101.56/101.62 (E(f1(a2,a3),f1(a2,a6))),
% 101.56/101.62 inference(scs_inference,[],[283,2753,2,18,10,2587])).
% 101.56/101.62 cnf(2780,plain,
% 101.56/101.62 (E(f1(a2,a6),f1(a6,a3))),
% 101.56/101.62 inference(scs_inference,[],[283,2753,2,18,10,2587,2657])).
% 101.56/101.62 cnf(2781,plain,
% 101.56/101.62 (E(f1(x27811,a3),f1(a2,a6))+~P1(f1(x27811,a3),f1(a2,a6))),
% 101.56/101.62 inference(scs_inference,[],[283,2753,2,18,10,2587,2657,21])).
% 101.56/101.62 cnf(2786,plain,
% 101.56/101.62 (P1(f1(a3,a3),f1(a2,a6))),
% 101.56/101.62 inference(scs_inference,[],[2420,283,2368,2753,2,18,10,2587,2657,21,3,23,32])).
% 101.56/101.62 cnf(2789,plain,
% 101.56/101.62 (~P2(f4(a3,a7),a7)),
% 101.56/101.62 inference(scs_inference,[],[2765,30])).
% 101.56/101.62 cnf(2791,plain,
% 101.56/101.62 (~P2(f4(a3,a7),f1(a7,a7))),
% 101.56/101.62 inference(scs_inference,[],[2765,119,30,13])).
% 101.56/101.62 cnf(2798,plain,
% 101.56/101.62 (~E(f1(a7,a7),a3)),
% 101.56/101.62 inference(scs_inference,[],[283,39,2765,16,119,30,13,11,21,10])).
% 101.56/101.62 cnf(2800,plain,
% 101.56/101.62 (~E(f1(a7,a7),f1(a3,a2))),
% 101.56/101.62 inference(scs_inference,[],[51,283,39,2765,16,119,2770,30,13,11,21,10,3])).
% 101.56/101.62 cnf(2809,plain,
% 101.56/101.62 (P2(f4(a3,a7),f1(x28091,a3))),
% 101.56/101.62 inference(scs_inference,[],[51,283,39,2765,2786,16,119,2768,2770,30,13,11,21,10,3,2,22,2781,2049,24])).
% 101.56/101.62 cnf(2811,plain,
% 101.56/101.62 (P2(f4(a3,a7),f1(a3,x28111))),
% 101.56/101.62 inference(scs_inference,[],[51,283,39,2765,2786,16,119,2768,2770,30,13,11,21,10,3,2,22,2781,2049,24,25])).
% 101.56/101.62 cnf(2844,plain,
% 101.56/101.62 (E(f1(a6,a3),f1(a2,a6))),
% 101.56/101.62 inference(scs_inference,[],[2780,2])).
% 101.56/101.62 cnf(2855,plain,
% 101.56/101.62 (~E(f1(a3,x28551),f1(a7,a7))),
% 101.56/101.62 inference(scs_inference,[],[2791,2800,2811,2,13])).
% 101.56/101.62 cnf(2909,plain,
% 101.56/101.62 (~E(f1(a7,a7),f1(a3,x29091))),
% 101.56/101.62 inference(scs_inference,[],[2767,2855,2844,18,21,2])).
% 101.56/101.62 cnf(2917,plain,
% 101.56/101.62 (P2(f4(a3,a7),f1(a6,a2))),
% 101.56/101.62 inference(scs_inference,[],[2798,2779,2753,2809,3,13,41])).
% 101.56/101.62 cnf(2932,plain,
% 101.56/101.62 (~P2(f4(a3,a7),a2)),
% 101.56/101.62 inference(scs_inference,[],[1640,2765,2763,2766,2791,2917,2789,13,10,21,23])).
% 101.56/101.62 cnf(2942,plain,
% 101.56/101.62 (~P1(f1(x29421,a3),a2)),
% 101.56/101.62 inference(scs_inference,[],[51,2932,2764,406,2809,2909,21,11,23])).
% 101.56/101.62 cnf(2944,plain,
% 101.56/101.62 (~E(a7,f1(a3,a7))),
% 101.56/101.62 inference(scs_inference,[],[51,283,2932,2764,406,2809,2909,21,11,23,10])).
% 101.56/101.62 cnf(2957,plain,
% 101.56/101.62 (P1(x29571,f1(x29572,x29571))),
% 101.56/101.62 inference(rename_variables,[],[283])).
% 101.56/101.62 cnf(2964,plain,
% 101.56/101.62 (P2(f4(a3,a7),f1(x29641,a6))),
% 101.56/101.62 inference(scs_inference,[],[283,2957,2932,2944,2917,21,33,2,25,23])).
% 101.56/101.62 cnf(2973,plain,
% 101.56/101.62 (P2(f4(a3,a2),a3)),
% 101.56/101.62 inference(scs_inference,[],[283,2957,39,2932,2944,2942,2917,2769,21,33,2,25,23,32,2042,22])).
% 101.56/101.62 cnf(2975,plain,
% 101.56/101.62 (~P2(f4(a3,a2),a2)),
% 101.56/101.62 inference(scs_inference,[],[283,2957,39,2932,2944,2942,2917,2769,21,33,2,25,23,32,2042,22,30])).
% 101.56/101.62 cnf(2977,plain,
% 101.56/101.62 (P2(f4(a3,a2),f1(x29771,a3))),
% 101.56/101.62 inference(scs_inference,[],[283,2957,39,2932,2944,2942,2917,2769,21,33,2,25,23,32,2042,22,30,24])).
% 101.56/101.62 cnf(2995,plain,
% 101.56/101.62 ($false),
% 101.56/101.62 inference(scs_inference,[],[51,2767,2964,2855,2789,2973,2975,2977,2774,1347,1691,13,3,23]),
% 101.56/101.62 ['proof']).
% 101.56/101.62 % SZS output end Proof
% 101.56/101.62 % Total time :100.880000s
%------------------------------------------------------------------------------