TSTP Solution File: SET641+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET641+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 14:30:33 EDT 2023
% Result : Theorem 129.42s 129.59s
% Output : CNFRefutation 129.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET641+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
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 11:26:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 129.42/129.58 %-------------------------------------------
% 129.42/129.58 % File :CSE---1.6
% 129.42/129.58 % Problem :theBenchmark
% 129.42/129.58 % Transform :cnf
% 129.42/129.58 % Format :tptp:raw
% 129.42/129.58 % Command :java -jar mcs_scs.jar %d %s
% 129.42/129.58
% 129.42/129.58 % Result :Theorem 128.810000s
% 129.42/129.58 % Output :CNFRefutation 128.810000s
% 129.42/129.58 %-------------------------------------------
% 129.42/129.58 %--------------------------------------------------------------------------
% 129.42/129.58 % File : SET641+3 : TPTP v8.1.2. Released v2.2.0.
% 129.42/129.58 % Domain : Set Theory (Relations)
% 129.42/129.58 % Problem : If A is a subset of X x Y then A is a relation from X to Y
% 129.42/129.58 % Version : [Wor90] axioms : Reduced > Incomplete.
% 129.42/129.58 % English :
% 129.42/129.58
% 129.42/129.58 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 129.42/129.58 % : [Wor90] Woronowicz (1990), Relations Defined on Sets
% 129.42/129.58 % Source : [ILF]
% 129.42/129.58 % Names : RELSET_1 (3) [Wor90]
% 129.42/129.58
% 129.42/129.58 % Status : Theorem
% 129.42/129.58 % Rating : 0.17 v7.5.0, 0.19 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.09 v7.0.0, 0.13 v6.4.0, 0.15 v6.3.0, 0.21 v6.2.0, 0.20 v6.1.0, 0.27 v6.0.0, 0.22 v5.5.0, 0.26 v5.4.0, 0.25 v5.3.0, 0.33 v5.2.0, 0.20 v5.1.0, 0.24 v5.0.0, 0.25 v4.1.0, 0.26 v4.0.0, 0.25 v3.5.0, 0.26 v3.3.0, 0.21 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, 0.25 v2.3.0, 0.33 v2.2.1
% 129.42/129.58 % Syntax : Number of formulae : 19 ( 1 unt; 0 def)
% 129.42/129.58 % Number of atoms : 79 ( 2 equ)
% 129.42/129.58 % Maximal formula atoms : 9 ( 4 avg)
% 129.42/129.58 % Number of connectives : 64 ( 4 ~; 0 |; 11 &)
% 129.42/129.58 % ( 7 <=>; 42 =>; 0 <=; 0 <~>)
% 129.42/129.58 % Maximal formula depth : 14 ( 7 avg)
% 129.42/129.58 % Maximal term depth : 3 ( 1 avg)
% 129.42/129.59 % Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% 129.42/129.59 % Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% 129.42/129.59 % Number of variables : 46 ( 39 !; 7 ?)
% 129.42/129.59 % SPC : FOF_THM_RFO_SEQ
% 129.42/129.59
% 129.42/129.59 % Comments :
% 129.42/129.59 %--------------------------------------------------------------------------
% 129.42/129.59 %---- line(relset_1 - df(1),1916080)
% 129.42/129.59 fof(p1,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ( ! [D] :
% 129.42/129.59 ( ilf_type(D,subset_type(cross_product(B,C)))
% 129.42/129.59 => ilf_type(D,relation_type(B,C)) )
% 129.42/129.59 & ! [E] :
% 129.42/129.59 ( ilf_type(E,relation_type(B,C))
% 129.42/129.59 => ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- type_nonempty(line(relset_1 - df(1),1916080))
% 129.42/129.59 fof(p2,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ? [D] : ilf_type(D,relation_type(C,B)) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- line(zfmisc_1 - df(1),1903822)
% 129.42/129.59 fof(p3,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ! [D] :
% 129.42/129.59 ( ilf_type(D,set_type)
% 129.42/129.59 => ( member(D,cross_product(B,C))
% 129.42/129.59 <=> ? [E] :
% 129.42/129.59 ( ilf_type(E,set_type)
% 129.42/129.59 & ? [F] :
% 129.42/129.59 ( ilf_type(F,set_type)
% 129.42/129.59 & member(E,B)
% 129.42/129.59 & member(F,C)
% 129.42/129.59 & D = ordered_pair(E,F) ) ) ) ) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- declaration(line(zfmisc_1 - df(1),1903822))
% 129.42/129.59 fof(p4,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ilf_type(cross_product(B,C),set_type) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- line(tarski - df(3),1832749)
% 129.42/129.59 fof(p5,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ( subset(B,C)
% 129.42/129.59 <=> ! [D] :
% 129.42/129.59 ( ilf_type(D,set_type)
% 129.42/129.59 => ( member(D,B)
% 129.42/129.59 => member(D,C) ) ) ) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- declaration(op(ordered_pair,2,function))
% 129.42/129.59 fof(p6,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ilf_type(ordered_pair(B,C),set_type) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- line(hidden - axiom9,1832648)
% 129.42/129.59 fof(p7,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ( ilf_type(C,subset_type(B))
% 129.42/129.59 <=> ilf_type(C,member_type(power_set(B))) ) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- type_nonempty(line(hidden - axiom9,1832648))
% 129.42/129.59 fof(p8,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ? [C] : ilf_type(C,subset_type(B)) ) ).
% 129.42/129.59
% 129.42/129.59 %---- property(reflexivity,op(subset,2,predicate))
% 129.42/129.59 fof(p9,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => subset(B,B) ) ).
% 129.42/129.59
% 129.42/129.59 %---- line(hidden - axiom11,1832644)
% 129.42/129.59 fof(p10,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ( member(B,power_set(C))
% 129.42/129.59 <=> ! [D] :
% 129.42/129.59 ( ilf_type(D,set_type)
% 129.42/129.59 => ( member(D,B)
% 129.42/129.59 => member(D,C) ) ) ) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- declaration(line(hidden - axiom11,1832644))
% 129.42/129.59 fof(p11,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ( ~ empty(power_set(B))
% 129.42/129.59 & ilf_type(power_set(B),set_type) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- line(hidden - axiom12,1832640)
% 129.42/129.59 fof(p12,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ( ~ empty(C)
% 129.42/129.59 & ilf_type(C,set_type) )
% 129.42/129.59 => ( ilf_type(B,member_type(C))
% 129.42/129.59 <=> member(B,C) ) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- type_nonempty(line(hidden - axiom12,1832640))
% 129.42/129.59 fof(p13,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ( ~ empty(B)
% 129.42/129.59 & ilf_type(B,set_type) )
% 129.42/129.59 => ? [C] : ilf_type(C,member_type(B)) ) ).
% 129.42/129.59
% 129.42/129.59 %---- line(hidden - axiom13,1832628)
% 129.42/129.59 fof(p14,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ( empty(B)
% 129.42/129.59 <=> ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ~ member(C,B) ) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- line(relat_1 - df(1),1917627)
% 129.42/129.59 fof(p15,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ( relation_like(B)
% 129.42/129.59 <=> ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ( member(C,B)
% 129.42/129.59 => ? [D] :
% 129.42/129.59 ( ilf_type(D,set_type)
% 129.42/129.59 & ? [E] :
% 129.42/129.59 ( ilf_type(E,set_type)
% 129.42/129.59 & C = ordered_pair(D,E) ) ) ) ) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- conditional_cluster(axiom15,relation_like)
% 129.42/129.59 fof(p16,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ( empty(B)
% 129.42/129.59 & ilf_type(B,set_type) )
% 129.42/129.59 => relation_like(B) ) ).
% 129.42/129.59
% 129.42/129.59 %---- conditional_cluster(axiom16,relation_like)
% 129.42/129.59 fof(p17,axiom,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ! [D] :
% 129.42/129.59 ( ilf_type(D,subset_type(cross_product(B,C)))
% 129.42/129.59 => relation_like(D) ) ) ) ).
% 129.42/129.59
% 129.42/129.59 %---- declaration(set)
% 129.42/129.59 fof(p18,axiom,
% 129.42/129.59 ! [B] : ilf_type(B,set_type) ).
% 129.42/129.59
% 129.42/129.59 %---- line(relset_1 - th(3),1916094)
% 129.42/129.59 fof(prove_relset_1_3,conjecture,
% 129.42/129.59 ! [B] :
% 129.42/129.59 ( ilf_type(B,set_type)
% 129.42/129.59 => ! [C] :
% 129.42/129.59 ( ilf_type(C,set_type)
% 129.42/129.59 => ! [D] :
% 129.42/129.59 ( ilf_type(D,set_type)
% 129.42/129.59 => ( subset(B,cross_product(C,D))
% 129.42/129.59 => ilf_type(B,relation_type(C,D)) ) ) ) ) ).
% 129.42/129.59
% 129.42/129.59 %--------------------------------------------------------------------------
% 129.42/129.59 %-------------------------------------------
% 129.42/129.59 % Proof found
% 129.42/129.59 % SZS status Theorem for theBenchmark
% 129.42/129.59 % SZS output start Proof
% 129.42/129.59 %ClaNum:85(EqnAxiom:40)
% 129.42/129.59 %VarNum:194(SingletonVarNum:62)
% 129.42/129.59 %MaxLitNum:9
% 129.42/129.59 %MaxfuncDepth:2
% 129.42/129.59 %SharedTerms:11
% 129.42/129.59 %goalClause: 45 46
% 129.42/129.59 %singleGoalClaCount:2
% 129.42/129.59 [45]P3(a1,f2(a6,a7))
% 129.42/129.59 [46]~P1(a1,f8(a6,a7))
% 129.42/129.59 [44]P1(x441,a5)
% 129.42/129.59 [48]P3(x481,x481)+~P1(x481,a5)
% 129.42/129.59 [49]~P1(x491,a5)+~P2(f9(x491))
% 129.42/129.59 [55]~P1(x551,a5)+P1(f11(x551),f21(x551))
% 129.42/129.59 [47]~P2(x471)+P4(x471)+~P1(x471,a5)
% 129.42/129.59 [53]P2(x531)+P5(f10(x531),x531)+~P1(x531,a5)
% 129.42/129.59 [54]P4(x541)+P5(f3(x541),x541)+~P1(x541,a5)
% 129.42/129.59 [56]P2(x561)+P1(f16(x561),f18(x561))+~P1(x561,a5)
% 129.42/129.59 [68]~P1(x682,a5)+~P1(x681,a5)+P1(f13(x681,x682),f8(x682,x681))
% 129.42/129.59 [57]~P2(x571)+~P5(x572,x571)+~P1(x572,a5)+~P1(x571,a5)
% 129.42/129.59 [64]P3(x641,x642)+P5(f12(x641,x642),x641)+~P1(x642,a5)+~P1(x641,a5)
% 129.42/129.59 [66]P5(f17(x661,x662),x661)+~P1(x662,a5)+~P1(x661,a5)+P5(x661,f9(x662))
% 129.42/129.59 [72]P3(x721,x722)+~P1(x722,a5)+~P1(x721,a5)+~P5(f12(x721,x722),x722)
% 129.42/129.59 [74]~P1(x742,a5)+~P1(x741,a5)+~P5(f17(x741,x742),x742)+P5(x741,f9(x742))
% 129.42/129.59 [67]~P1(x672,a5)+~P1(x671,a5)+~P1(x671,f21(x672))+P1(x671,f18(f9(x672)))
% 129.42/129.59 [71]~P1(x712,a5)+~P1(x711,a5)+P1(x711,f21(x712))+~P1(x711,f18(f9(x712)))
% 129.42/129.59 [77]P4(x771)+~P1(x772,a5)+~P1(x773,a5)+~P1(x771,f21(f2(x773,x772)))
% 129.42/129.59 [78]~P1(x783,a5)+~P1(x782,a5)+~P1(x781,f8(x782,x783))+P1(x781,f21(f2(x782,x783)))
% 129.42/129.59 [79]~P1(x793,a5)+~P1(x792,a5)+P1(x791,f8(x792,x793))+~P1(x791,f21(f2(x792,x793)))
% 129.42/129.59 [60]~P5(x602,x601)+P2(x601)+~P1(x601,a5)+~P1(x602,a5)+P1(x602,f18(x601))
% 129.42/129.59 [61]P2(x611)+P5(x612,x611)+~P1(x611,a5)+~P1(x612,a5)+~P1(x612,f18(x611))
% 129.42/129.59 [76]~P4(x761)+~P5(x762,x761)+~P1(x761,a5)+~P1(x762,a5)+E(f20(f19(x761,x762),f4(x761,x762)),x762)
% 129.42/129.59 [63]P4(x631)+~P1(x631,a5)+~P1(x633,a5)+~P1(x632,a5)+~E(f3(x631),f20(x632,x633))
% 129.42/129.59 [83]~P1(x833,a5)+~P1(x832,a5)+~P1(x831,a5)+~P5(x833,f2(x831,x832))+P5(f14(x831,x832,x833),x831)
% 129.42/129.59 [84]~P1(x843,a5)+~P1(x842,a5)+~P1(x841,a5)+~P5(x843,f2(x841,x842))+P5(f15(x841,x842,x843),x842)
% 129.42/129.59 [85]~P1(x852,a5)+~P1(x851,a5)+~P1(x853,a5)+~P5(x853,f2(x851,x852))+E(f20(f14(x851,x852,x853),f15(x851,x852,x853)),x853)
% 129.42/129.59 [73]~P3(x733,x732)+P5(x731,x732)+~P5(x731,x733)+~P1(x731,a5)+~P1(x732,a5)+~P1(x733,a5)
% 129.42/129.59 [75]P5(x751,x752)+~P5(x751,x753)+~P1(x751,a5)+~P1(x752,a5)+~P1(x753,a5)+~P5(x753,f9(x752))
% 129.42/129.59 [80]~P5(x805,x803)+~P5(x804,x802)+~P1(x801,a5)+~P1(x803,a5)+~P1(x802,a5)+~P1(x805,a5)+~P1(x804,a5)+P5(x801,f2(x802,x803))+~E(x801,f20(x804,x805))
% 129.42/129.59 %EqnAxiom
% 129.42/129.59 [1]E(x11,x11)
% 129.42/129.59 [2]E(x22,x21)+~E(x21,x22)
% 129.42/129.59 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 129.42/129.59 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 129.42/129.59 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 129.42/129.59 [6]~E(x61,x62)+E(f8(x61,x63),f8(x62,x63))
% 129.42/129.60 [7]~E(x71,x72)+E(f8(x73,x71),f8(x73,x72))
% 129.42/129.60 [8]~E(x81,x82)+E(f9(x81),f9(x82))
% 129.42/129.60 [9]~E(x91,x92)+E(f14(x91,x93,x94),f14(x92,x93,x94))
% 129.42/129.60 [10]~E(x101,x102)+E(f14(x103,x101,x104),f14(x103,x102,x104))
% 129.42/129.60 [11]~E(x111,x112)+E(f14(x113,x114,x111),f14(x113,x114,x112))
% 129.42/129.60 [12]~E(x121,x122)+E(f10(x121),f10(x122))
% 129.42/129.60 [13]~E(x131,x132)+E(f3(x131),f3(x132))
% 129.42/129.60 [14]~E(x141,x142)+E(f20(x141,x143),f20(x142,x143))
% 129.42/129.60 [15]~E(x151,x152)+E(f20(x153,x151),f20(x153,x152))
% 129.42/129.60 [16]~E(x161,x162)+E(f4(x161,x163),f4(x162,x163))
% 129.42/129.60 [17]~E(x171,x172)+E(f4(x173,x171),f4(x173,x172))
% 129.42/129.60 [18]~E(x181,x182)+E(f11(x181),f11(x182))
% 129.42/129.60 [19]~E(x191,x192)+E(f21(x191),f21(x192))
% 129.42/129.60 [20]~E(x201,x202)+E(f16(x201),f16(x202))
% 129.42/129.60 [21]~E(x211,x212)+E(f18(x211),f18(x212))
% 129.42/129.60 [22]~E(x221,x222)+E(f15(x221,x223,x224),f15(x222,x223,x224))
% 129.42/129.60 [23]~E(x231,x232)+E(f15(x233,x231,x234),f15(x233,x232,x234))
% 129.42/129.60 [24]~E(x241,x242)+E(f15(x243,x244,x241),f15(x243,x244,x242))
% 129.42/129.60 [25]~E(x251,x252)+E(f17(x251,x253),f17(x252,x253))
% 129.42/129.60 [26]~E(x261,x262)+E(f17(x263,x261),f17(x263,x262))
% 129.42/129.60 [27]~E(x271,x272)+E(f13(x271,x273),f13(x272,x273))
% 129.42/129.60 [28]~E(x281,x282)+E(f13(x283,x281),f13(x283,x282))
% 129.42/129.60 [29]~E(x291,x292)+E(f19(x291,x293),f19(x292,x293))
% 129.42/129.60 [30]~E(x301,x302)+E(f19(x303,x301),f19(x303,x302))
% 129.42/129.60 [31]~E(x311,x312)+E(f12(x311,x313),f12(x312,x313))
% 129.42/129.60 [32]~E(x321,x322)+E(f12(x323,x321),f12(x323,x322))
% 129.42/129.60 [33]P1(x332,x333)+~E(x331,x332)+~P1(x331,x333)
% 129.42/129.60 [34]P1(x343,x342)+~E(x341,x342)+~P1(x343,x341)
% 129.42/129.60 [35]P5(x352,x353)+~E(x351,x352)+~P5(x351,x353)
% 129.42/129.60 [36]P5(x363,x362)+~E(x361,x362)+~P5(x363,x361)
% 129.42/129.60 [37]P3(x372,x373)+~E(x371,x372)+~P3(x371,x373)
% 129.42/129.60 [38]P3(x383,x382)+~E(x381,x382)+~P3(x383,x381)
% 129.42/129.60 [39]~P4(x391)+P4(x392)+~E(x391,x392)
% 129.42/129.60 [40]~P2(x401)+P2(x402)+~E(x401,x402)
% 129.42/129.60
% 129.42/129.60 %-------------------------------------------
% 129.42/129.60 cnf(88,plain,
% 129.42/129.60 (P1(x881,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(89,plain,
% 129.42/129.60 (~E(f8(a6,a7),a5)),
% 129.42/129.60 inference(scs_inference,[],[44,46,48,34,2])).
% 129.42/129.60 cnf(90,plain,
% 129.42/129.60 (~P2(f9(x901))),
% 129.42/129.60 inference(scs_inference,[],[44,88,46,48,34,2,49])).
% 129.42/129.60 cnf(92,plain,
% 129.42/129.60 (P1(f11(x921),f21(x921))),
% 129.42/129.60 inference(scs_inference,[],[44,88,46,48,34,2,49,55])).
% 129.42/129.60 cnf(94,plain,
% 129.42/129.60 (~P1(x941,f8(a6,a7))+~E(x941,a1)),
% 129.42/129.60 inference(scs_inference,[],[44,88,46,48,34,2,49,55,33])).
% 129.42/129.60 cnf(100,plain,
% 129.42/129.60 (~P1(f9(x1001),a5)+P5(f10(f9(x1001)),f9(x1001))),
% 129.42/129.60 inference(scs_inference,[],[44,88,46,48,34,2,49,55,33,68,78,40,53])).
% 129.42/129.60 cnf(102,plain,
% 129.42/129.60 (~P1(f9(x1021),a5)+P1(f16(f9(x1021)),f18(f9(x1021)))),
% 129.42/129.60 inference(scs_inference,[],[44,88,46,48,34,2,49,55,33,68,78,40,53,56])).
% 129.42/129.60 cnf(104,plain,
% 129.42/129.60 (P4(f13(x1041,x1041))),
% 129.42/129.60 inference(scs_inference,[],[44,88,46,48,34,2,49,55,33,68,78,40,53,56,77])).
% 129.42/129.60 cnf(126,plain,
% 129.42/129.60 (P1(f16(f9(x1261)),f18(f9(x1261)))),
% 129.42/129.60 inference(scs_inference,[],[44,102])).
% 129.42/129.60 cnf(127,plain,
% 129.42/129.60 (P1(x1271,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(128,plain,
% 129.42/129.60 (P5(f10(f9(x1281)),f9(x1281))),
% 129.42/129.60 inference(scs_inference,[],[44,127,102,100])).
% 129.42/129.60 cnf(129,plain,
% 129.42/129.60 (P1(x1291,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(131,plain,
% 129.42/129.60 (P4(f11(f2(x1311,x1311)))),
% 129.42/129.60 inference(scs_inference,[],[44,127,129,92,104,102,100,39,77])).
% 129.42/129.60 cnf(132,plain,
% 129.42/129.60 (P1(f11(x1321),f21(x1321))),
% 129.42/129.60 inference(rename_variables,[],[92])).
% 129.42/129.60 cnf(139,plain,
% 129.42/129.60 (P5(f16(f9(x1391)),f9(x1391))+~P1(f9(x1391),a5)),
% 129.42/129.60 inference(scs_inference,[],[44,127,129,92,132,104,90,102,100,39,77,79,66,61])).
% 129.42/129.60 cnf(157,plain,
% 129.42/129.60 (P5(f16(f9(x1571)),f9(x1571))),
% 129.42/129.60 inference(scs_inference,[],[44,139])).
% 129.42/129.60 cnf(196,plain,
% 129.42/129.60 (P1(f16(f9(x1961)),f21(x1961))+~P1(x1961,a5)),
% 129.42/129.60 inference(scs_inference,[],[44,126,71])).
% 129.42/129.60 cnf(197,plain,
% 129.42/129.60 (P1(x1971,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(200,plain,
% 129.42/129.60 (P1(x2001,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(201,plain,
% 129.42/129.60 (P1(x2011,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(203,plain,
% 129.42/129.60 (P1(f13(x2031,x2032),f8(x2032,x2031))),
% 129.42/129.60 inference(scs_inference,[],[44,197,201,200,126,90,71,61,68])).
% 129.42/129.60 cnf(222,plain,
% 129.42/129.60 (~E(f13(a7,a6),a1)),
% 129.42/129.60 inference(scs_inference,[],[44,203,196,94])).
% 129.42/129.60 cnf(227,plain,
% 129.42/129.60 (P1(x2271,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(228,plain,
% 129.42/129.60 (P1(x2281,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(230,plain,
% 129.42/129.60 (P5(x2301,f9(x2302))+P5(f17(x2301,x2302),x2301)),
% 129.42/129.60 inference(scs_inference,[],[44,228,227,203,157,196,94,54,75,66])).
% 129.42/129.60 cnf(234,plain,
% 129.42/129.60 (~P1(a1,f21(f2(a6,a7)))),
% 129.42/129.60 inference(scs_inference,[],[44,228,227,203,157,46,196,94,54,75,66,63,79])).
% 129.42/129.60 cnf(254,plain,
% 129.42/129.60 (~P1(f11(x2541),a5)+P1(f11(x2541),f18(f9(x2541)))),
% 129.42/129.60 inference(scs_inference,[],[222,92,44,2,67])).
% 129.42/129.60 cnf(259,plain,
% 129.42/129.60 (P1(f11(x2591),f18(f9(x2591)))),
% 129.42/129.60 inference(scs_inference,[],[44,254])).
% 129.42/129.60 cnf(267,plain,
% 129.42/129.60 (P1(f10(f9(x2671)),f18(f9(x2671)))+~P1(f9(x2671),a5)),
% 129.42/129.60 inference(scs_inference,[],[90,128,44,60])).
% 129.42/129.60 cnf(268,plain,
% 129.42/129.60 (P1(x2681,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(269,plain,
% 129.42/129.60 (~P2(f9(x2691))),
% 129.42/129.60 inference(rename_variables,[],[90])).
% 129.42/129.60 cnf(272,plain,
% 129.42/129.60 (P5(f11(x2721),f9(x2721))+~P1(f11(x2721),a5)),
% 129.42/129.60 inference(scs_inference,[],[90,269,131,259,128,44,268,60,39,61])).
% 129.42/129.60 cnf(280,plain,
% 129.42/129.60 (P1(x2801,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(282,plain,
% 129.42/129.60 (P1(x2821,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(293,plain,
% 129.42/129.60 (P1(f15(f9(x2931),f9(x2931),f9(x2931)),f18(f9(x2931)))+~P5(f9(x2931),f2(f9(x2931),f9(x2931)))+~P1(f15(f9(x2931),f9(x2931),f9(x2931)),a5)),
% 129.42/129.60 inference(scs_inference,[],[89,90,44,280,282,272,267,84,57,56,53,3,40,60])).
% 129.42/129.60 cnf(648,plain,
% 129.42/129.60 (~P5(f9(x6481),f9(x6481))+P5(f9(x6481),f2(f9(x6481),f9(x6481)))+~E(f9(x6481),f20(f16(f9(x6481)),f9(x6481)))+~P1(f16(f9(x6481)),a5)),
% 129.42/129.60 inference(scs_inference,[],[157,44,80])).
% 129.42/129.60 cnf(651,plain,
% 129.42/129.60 (P1(x6511,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(652,plain,
% 129.42/129.60 (P1(x6521,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(656,plain,
% 129.42/129.60 (P1(x6561,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(659,plain,
% 129.42/129.60 (~P5(f9(x6591),f9(x6591))+P5(f15(f9(x6591),f9(x6591),f9(x6591)),f9(x6591))+~E(f9(x6591),f20(f16(f9(x6591)),f9(x6591)))+~P1(f16(f9(x6591)),a5)),
% 129.42/129.60 inference(scs_inference,[],[157,44,652,656,651,80,75,84])).
% 129.42/129.60 cnf(683,plain,
% 129.42/129.60 (P1(x6831,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(684,plain,
% 129.42/129.60 (P5(f9(x6841),f2(f9(x6841),f9(x6841)))+~E(f9(x6841),f20(f16(f9(x6841)),f9(x6841)))+~P5(f9(x6841),f9(x6841))),
% 129.42/129.60 inference(scs_inference,[],[44,683,659,648])).
% 129.42/129.60 cnf(942,plain,
% 129.42/129.60 (P1(f15(f9(x9421),f9(x9421),f9(x9421)),f18(f9(x9421)))+~P5(f9(x9421),f2(f9(x9421),f9(x9421)))),
% 129.42/129.60 inference(scs_inference,[],[44,293])).
% 129.42/129.60 cnf(998,plain,
% 129.42/129.60 (~E(x9981,x9982)+~P2(x9981)+P4(x9982)),
% 129.42/129.60 inference(scs_inference,[],[44,47,39])).
% 129.42/129.60 cnf(999,plain,
% 129.42/129.60 (~P2(x9991)+P4(x9991)),
% 129.42/129.60 inference(equality_inference,[],[998])).
% 129.42/129.60 cnf(1000,plain,
% 129.42/129.60 (P4(x10001)+P5(f10(x10001),x10001)),
% 129.42/129.60 inference(scs_inference,[],[44,999,53])).
% 129.42/129.60 cnf(1149,plain,
% 129.42/129.60 (P1(f15(f9(x11491),f9(x11491),f9(x11491)),f18(f9(x11491)))+~E(f9(x11491),f20(f16(f9(x11491)),f9(x11491)))+~P5(f9(x11491),f9(x11491))),
% 129.42/129.60 inference(scs_inference,[],[684,942])).
% 129.42/129.60 cnf(1332,plain,
% 129.42/129.60 (~E(f9(x13321),f20(f16(f9(x13321)),f9(x13321)))+~P5(f9(x13321),f9(x13321))+P1(x13322,f18(f9(x13321)))+~E(f15(f9(x13321),f9(x13321),f9(x13321)),x13322)),
% 129.42/129.60 inference(scs_inference,[],[1149,33])).
% 129.42/129.60 cnf(1988,plain,
% 129.42/129.60 (P4(f10(f9(x19881)))+P5(f10(f10(f9(x19881))),x19881)+~P1(x19881,a5)+~P1(f10(f10(f9(x19881))),a5)),
% 129.42/129.60 inference(scs_inference,[],[128,44,1000,75])).
% 129.42/129.60 cnf(6618,plain,
% 129.42/129.60 (~P1(a1,a5)+~P1(a1,f18(f9(f2(a6,a7))))),
% 129.42/129.60 inference(scs_inference,[],[234,44,1988,71])).
% 129.42/129.60 cnf(6621,plain,
% 129.42/129.60 (~P1(a1,f18(f9(f2(a6,a7))))),
% 129.42/129.60 inference(scs_inference,[],[44,6618])).
% 129.42/129.60 cnf(6724,plain,
% 129.42/129.60 (~P5(a1,f9(f2(a6,a7)))+~P1(f9(f2(a6,a7)),a5)),
% 129.42/129.60 inference(scs_inference,[],[6621,90,44,1332,60])).
% 129.42/129.60 cnf(6729,plain,
% 129.42/129.60 (~P5(a1,f9(f2(a6,a7)))),
% 129.42/129.60 inference(scs_inference,[],[44,6724])).
% 129.42/129.60 cnf(6731,plain,
% 129.42/129.60 (P5(f17(a1,f2(a6,a7)),a1)),
% 129.42/129.60 inference(scs_inference,[],[6729,230])).
% 129.42/129.60 cnf(6744,plain,
% 129.42/129.60 (~P2(a1)+~P1(f17(a1,f2(a6,a7)),a5)),
% 129.42/129.60 inference(scs_inference,[],[6731,44,57])).
% 129.42/129.60 cnf(6751,plain,
% 129.42/129.60 (~P2(a1)),
% 129.42/129.60 inference(scs_inference,[],[44,6744])).
% 129.42/129.60 cnf(6776,plain,
% 129.42/129.60 (~P5(f17(a1,f2(a6,a7)),f2(a6,a7))+~P1(a1,a5)),
% 129.42/129.60 inference(scs_inference,[],[6729,44,74])).
% 129.42/129.60 cnf(6782,plain,
% 129.42/129.60 (~P5(f17(a1,f2(a6,a7)),f2(a6,a7))),
% 129.42/129.60 inference(scs_inference,[],[44,6776])).
% 129.42/129.60 cnf(6848,plain,
% 129.42/129.60 (P1(x68481,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(6849,plain,
% 129.42/129.60 (P1(x68491,a5)),
% 129.42/129.60 inference(rename_variables,[],[44])).
% 129.42/129.60 cnf(6851,plain,
% 129.42/129.60 (~P1(a1,a5)),
% 129.42/129.60 inference(scs_inference,[],[45,6751,6782,6731,44,6849,6848,61,73])).
% 129.42/129.60 cnf(6858,plain,
% 129.42/129.60 ($false),
% 129.42/129.60 inference(scs_inference,[],[6851,44]),
% 129.42/129.60 ['proof']).
% 129.42/129.60 % SZS output end Proof
% 129.42/129.60 % Total time :128.810000s
%------------------------------------------------------------------------------