TSTP Solution File: SET666+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET666+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 14:30:38 EDT 2023
% Result : Theorem 128.31s 128.51s
% Output : CNFRefutation 128.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n010.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 13:01:35 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.52 start to proof:theBenchmark
% 128.31/128.50 %-------------------------------------------
% 128.31/128.50 % File :CSE---1.6
% 128.31/128.50 % Problem :theBenchmark
% 128.31/128.50 % Transform :cnf
% 128.31/128.50 % Format :tptp:raw
% 128.31/128.50 % Command :java -jar mcs_scs.jar %d %s
% 128.31/128.50
% 128.31/128.50 % Result :Theorem 127.760000s
% 128.31/128.50 % Output :CNFRefutation 127.760000s
% 128.31/128.50 %-------------------------------------------
% 128.31/128.50 %--------------------------------------------------------------------------
% 128.31/128.50 % File : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% 128.31/128.50 % Domain : Set Theory (Relations)
% 128.31/128.50 % Problem : The identity relation on X is a relation from X to X
% 128.31/128.50 % Version : [Wor90] axioms : Reduced > Incomplete.
% 128.31/128.50 % English :
% 128.31/128.50
% 128.31/128.50 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 128.31/128.51 % : [Wor90] Woronowicz (1990), Relations Defined on Sets
% 128.31/128.51 % Source : [ILF]
% 128.31/128.51 % Names : RELSET_1 (29) [Wor90]
% 128.31/128.51
% 128.31/128.51 % Status : Theorem
% 128.31/128.51 % Rating : 0.25 v7.5.0, 0.28 v7.4.0, 0.30 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.22 v7.0.0, 0.20 v6.4.0, 0.27 v6.3.0, 0.29 v6.2.0, 0.28 v6.1.0, 0.30 v6.0.0, 0.26 v5.5.0, 0.30 v5.4.0, 0.29 v5.3.0, 0.37 v5.2.0, 0.25 v5.1.0, 0.29 v4.1.0, 0.35 v4.0.1, 0.39 v4.0.0, 0.38 v3.7.0, 0.35 v3.5.0, 0.37 v3.4.0, 0.26 v3.3.0, 0.29 v3.2.0, 0.36 v3.1.0, 0.33 v2.6.0, 0.29 v2.5.0, 0.25 v2.4.0, 0.50 v2.3.0, 0.33 v2.2.1
% 128.31/128.51 % Syntax : Number of formulae : 25 ( 2 unt; 0 def)
% 128.31/128.51 % Number of atoms : 88 ( 2 equ)
% 128.31/128.51 % Maximal formula atoms : 7 ( 3 avg)
% 128.31/128.51 % Number of connectives : 67 ( 4 ~; 0 |; 9 &)
% 128.31/128.51 % ( 9 <=>; 45 =>; 0 <=; 0 <~>)
% 128.31/128.51 % Maximal formula depth : 11 ( 6 avg)
% 128.31/128.51 % Maximal term depth : 3 ( 1 avg)
% 128.31/128.51 % Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% 128.31/128.51 % Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% 128.31/128.51 % Number of variables : 50 ( 43 !; 7 ?)
% 128.31/128.51 % SPC : FOF_THM_RFO_SEQ
% 128.31/128.51
% 128.31/128.51 % Comments :
% 128.31/128.51 %--------------------------------------------------------------------------
% 128.31/128.51 %---- line(relset_1 - df(1),1916080)
% 128.31/128.51 fof(p1,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ( ! [D] :
% 128.31/128.51 ( ilf_type(D,subset_type(cross_product(B,C)))
% 128.31/128.51 => ilf_type(D,relation_type(B,C)) )
% 128.31/128.51 & ! [E] :
% 128.31/128.51 ( ilf_type(E,relation_type(B,C))
% 128.31/128.51 => ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- type_nonempty(line(relset_1 - df(1),1916080))
% 128.31/128.51 fof(p2,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ? [D] : ilf_type(D,relation_type(C,B)) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- line(relset_1 - th(28),1916537)
% 128.31/128.51 fof(p3,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => subset(identity_relation_of(B),cross_product(B,B)) ) ).
% 128.31/128.51
% 128.31/128.51 %---- line(relat_1 - df(10),1918876)
% 128.31/128.51 fof(p4,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ! [D] :
% 128.31/128.51 ( ilf_type(D,set_type)
% 128.31/128.51 => ( member(ordered_pair(C,D),identity_relation_of(B))
% 128.31/128.51 <=> ( member(C,B)
% 128.31/128.51 & C = D ) ) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- declaration(line(relat_1 - df(10),1918876))
% 128.31/128.51 fof(p5,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ilf_type(identity_relation_of(B),binary_relation_type) ) ).
% 128.31/128.51
% 128.31/128.51 %---- line(relset_1 - axiom299,1916837)
% 128.31/128.51 fof(p6,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ( ilf_type(C,identity_relation_of_type(B))
% 128.31/128.51 <=> ilf_type(C,relation_type(B,B)) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- type_nonempty(line(relset_1 - axiom299,1916837))
% 128.31/128.51 fof(p7,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ? [C] : ilf_type(C,identity_relation_of_type(B)) ) ).
% 128.31/128.51
% 128.31/128.51 %---- declaration(op(cross_product,2,function))
% 128.31/128.51 fof(p8,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ilf_type(cross_product(B,C),set_type) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- declaration(op(ordered_pair,2,function))
% 128.31/128.51 fof(p9,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ilf_type(ordered_pair(B,C),set_type) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- line(relat_1 - axiom300,1917641)
% 128.31/128.51 fof(p10,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ( ilf_type(B,binary_relation_type)
% 128.31/128.51 <=> ( relation_like(B)
% 128.31/128.51 & ilf_type(B,set_type) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- type_nonempty(line(relat_1 - axiom300,1917641))
% 128.31/128.51 fof(p11,axiom,
% 128.31/128.51 ? [B] : ilf_type(B,binary_relation_type) ).
% 128.31/128.51
% 128.31/128.51 %---- line(hidden - axiom301,1832648)
% 128.31/128.51 fof(p12,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ( ilf_type(C,subset_type(B))
% 128.31/128.51 <=> ilf_type(C,member_type(power_set(B))) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- type_nonempty(line(hidden - axiom301,1832648))
% 128.31/128.51 fof(p13,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ? [C] : ilf_type(C,subset_type(B)) ) ).
% 128.31/128.51
% 128.31/128.51 %---- line(tarski - df(3),1832749)
% 128.31/128.51 fof(p14,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ( subset(B,C)
% 128.31/128.51 <=> ! [D] :
% 128.31/128.51 ( ilf_type(D,set_type)
% 128.31/128.51 => ( member(D,B)
% 128.31/128.51 => member(D,C) ) ) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- property(reflexivity,op(subset,2,predicate))
% 128.31/128.51 fof(p15,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => subset(B,B) ) ).
% 128.31/128.51
% 128.31/128.51 %---- line(hidden - axiom303,1832644)
% 128.31/128.51 fof(p16,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ( member(B,power_set(C))
% 128.31/128.51 <=> ! [D] :
% 128.31/128.51 ( ilf_type(D,set_type)
% 128.31/128.51 => ( member(D,B)
% 128.31/128.51 => member(D,C) ) ) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- declaration(line(hidden - axiom303,1832644))
% 128.31/128.51 fof(p17,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ( ~ empty(power_set(B))
% 128.31/128.51 & ilf_type(power_set(B),set_type) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- line(hidden - axiom304,1832640)
% 128.31/128.51 fof(p18,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ( ~ empty(C)
% 128.31/128.51 & ilf_type(C,set_type) )
% 128.31/128.51 => ( ilf_type(B,member_type(C))
% 128.31/128.51 <=> member(B,C) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- type_nonempty(line(hidden - axiom304,1832640))
% 128.31/128.51 fof(p19,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ( ~ empty(B)
% 128.31/128.51 & ilf_type(B,set_type) )
% 128.31/128.51 => ? [C] : ilf_type(C,member_type(B)) ) ).
% 128.31/128.51
% 128.31/128.51 %---- line(relat_1 - df(1),1917627)
% 128.31/128.51 fof(p20,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ( relation_like(B)
% 128.31/128.51 <=> ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ( member(C,B)
% 128.31/128.51 => ? [D] :
% 128.31/128.51 ( ilf_type(D,set_type)
% 128.31/128.51 & ? [E] :
% 128.31/128.51 ( ilf_type(E,set_type)
% 128.31/128.51 & C = ordered_pair(D,E) ) ) ) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- conditional_cluster(axiom306,relation_like)
% 128.31/128.51 fof(p21,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ! [D] :
% 128.31/128.51 ( ilf_type(D,subset_type(cross_product(B,C)))
% 128.31/128.51 => relation_like(D) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- line(hidden - axiom307,1832628)
% 128.31/128.51 fof(p22,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ( empty(B)
% 128.31/128.51 <=> ! [C] :
% 128.31/128.51 ( ilf_type(C,set_type)
% 128.31/128.51 => ~ member(C,B) ) ) ) ).
% 128.31/128.51
% 128.31/128.51 %---- conditional_cluster(axiom308,empty)
% 128.31/128.51 fof(p23,axiom,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ( empty(B)
% 128.31/128.51 & ilf_type(B,set_type) )
% 128.31/128.51 => relation_like(B) ) ).
% 128.31/128.51
% 128.31/128.51 %---- declaration(set)
% 128.31/128.51 fof(p24,axiom,
% 128.31/128.51 ! [B] : ilf_type(B,set_type) ).
% 128.31/128.51
% 128.31/128.51 %---- line(relset_1 - th(29),1916543)
% 128.31/128.51 fof(prove_relset_1_29,conjecture,
% 128.31/128.51 ! [B] :
% 128.31/128.51 ( ilf_type(B,set_type)
% 128.31/128.51 => ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ) ).
% 128.31/128.51
% 128.31/128.51 %--------------------------------------------------------------------------
% 128.31/128.51 %-------------------------------------------
% 128.31/128.51 % Proof found
% 128.31/128.51 % SZS status Theorem for theBenchmark
% 128.31/128.51 % SZS output start Proof
% 128.31/128.51 %ClaNum:84(EqnAxiom:37)
% 128.31/128.51 %VarNum:201(SingletonVarNum:66)
% 128.31/128.51 %MaxLitNum:6
% 128.31/128.52 %MaxfuncDepth:2
% 128.31/128.52 %SharedTerms:9
% 128.31/128.52 %goalClause: 41
% 128.31/128.52 %singleGoalClaCount:1
% 128.31/128.52 [38]P1(a1,a2)
% 128.31/128.52 [41]~P1(f10(a3),f17(a3))
% 128.31/128.52 [40]P1(x401,a9)
% 128.31/128.52 [43]P5(x431,x431)+~P1(x431,a9)
% 128.31/128.52 [44]~P1(x441,a9)+~P2(f18(x441))
% 128.31/128.52 [45]~P1(x451,a9)+P1(f10(x451),a2)
% 128.31/128.52 [53]~P1(x531,a9)+P1(f7(x531),f17(x531))
% 128.31/128.52 [54]~P1(x541,a9)+P1(f11(x541),f22(x541))
% 128.31/128.52 [56]~P1(x561,a9)+P5(f10(x561),f5(x561,x561))
% 128.31/128.52 [42]~P2(x421)+P3(x421)+~P1(x421,a9)
% 128.31/128.52 [47]~P3(x471)+~P1(x471,a9)+P1(x471,a2)
% 128.31/128.52 [50]P3(x501)+~P1(x501,a9)+~P1(x501,a2)
% 128.31/128.52 [51]P3(x511)+P4(f4(x511),x511)+~P1(x511,a9)
% 128.31/128.52 [52]P2(x521)+P4(f6(x521),x521)+~P1(x521,a9)
% 128.31/128.52 [55]P2(x551)+P1(f12(x551),f19(x551))+~P1(x551,a9)
% 128.31/128.52 [68]~P1(x682,a9)+~P1(x681,a9)+P1(f8(x681,x682),f21(x682,x681))
% 128.31/128.52 [57]~P2(x571)+~P4(x572,x571)+~P1(x572,a9)+~P1(x571,a9)
% 128.31/128.52 [64]P5(x641,x642)+P4(f13(x641,x642),x641)+~P1(x642,a9)+~P1(x641,a9)
% 128.31/128.52 [66]P4(f14(x661,x662),x661)+~P1(x662,a9)+~P1(x661,a9)+P4(x661,f18(x662))
% 128.31/128.52 [72]~P1(x722,a9)+~P1(x721,a9)+~P1(x721,f17(x722))+P1(x721,f21(x722,x722))
% 128.31/128.52 [73]P5(x731,x732)+~P1(x732,a9)+~P1(x731,a9)+~P4(f13(x731,x732),x732)
% 128.31/128.52 [75]~P1(x752,a9)+~P1(x751,a9)+~P1(x751,f21(x752,x752))+P1(x751,f17(x752))
% 128.31/128.52 [76]~P1(x762,a9)+~P1(x761,a9)+~P4(f14(x761,x762),x762)+P4(x761,f18(x762))
% 128.31/128.52 [67]~P1(x672,a9)+~P1(x671,a9)+~P1(x671,f22(x672))+P1(x671,f19(f18(x672)))
% 128.31/128.52 [71]~P1(x712,a9)+~P1(x711,a9)+P1(x711,f22(x712))+~P1(x711,f19(f18(x712)))
% 128.31/128.52 [82]P3(x821)+~P1(x822,a9)+~P1(x823,a9)+~P1(x821,f22(f5(x823,x822)))
% 128.31/128.52 [83]~P1(x833,a9)+~P1(x832,a9)+~P1(x831,f21(x832,x833))+P1(x831,f22(f5(x832,x833)))
% 128.31/128.52 [84]~P1(x843,a9)+~P1(x842,a9)+P1(x841,f21(x842,x843))+~P1(x841,f22(f5(x842,x843)))
% 128.31/128.52 [60]~P4(x602,x601)+P2(x601)+~P1(x601,a9)+~P1(x602,a9)+P1(x602,f19(x601))
% 128.31/128.52 [61]P2(x611)+P4(x612,x611)+~P1(x611,a9)+~P1(x612,a9)+~P1(x612,f19(x611))
% 128.31/128.52 [80]~P3(x801)+~P4(x802,x801)+~P1(x801,a9)+~P1(x802,a9)+E(f20(f15(x801,x802),f16(x801,x802)),x802)
% 128.31/128.52 [63]P3(x631)+~P1(x631,a9)+~P1(x633,a9)+~P1(x632,a9)+~E(f4(x631),f20(x632,x633))
% 128.31/128.52 [79]E(x791,x792)+~P1(x792,a9)+~P1(x791,a9)+~P4(f20(x791,x792),f10(x793))+~P1(x793,a9)
% 128.31/128.52 [81]P4(x811,x812)+~P1(x812,a9)+~P1(x811,a9)+~P4(f20(x811,x813),f10(x812))+~P1(x813,a9)
% 128.31/128.52 [74]~P4(x741,x743)+P4(x741,x742)+~P5(x743,x742)+~P1(x741,a9)+~P1(x742,a9)+~P1(x743,a9)
% 128.31/128.52 [77]P4(x771,x772)+~P4(x771,x773)+~P1(x771,a9)+~P1(x772,a9)+~P1(x773,a9)+~P4(x773,f18(x772))
% 128.31/128.52 [78]~E(x781,x782)+~P4(x781,x783)+~P1(x782,a9)+~P1(x783,a9)+~P1(x781,a9)+P4(f20(x781,x782),f10(x783))
% 128.31/128.52 %EqnAxiom
% 128.31/128.52 [1]E(x11,x11)
% 128.31/128.52 [2]E(x22,x21)+~E(x21,x22)
% 128.31/128.52 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 128.31/128.52 [4]~E(x41,x42)+E(f10(x41),f10(x42))
% 128.31/128.52 [5]~E(x51,x52)+E(f17(x51),f17(x52))
% 128.31/128.52 [6]~E(x61,x62)+E(f18(x61),f18(x62))
% 128.31/128.52 [7]~E(x71,x72)+E(f22(x71),f22(x72))
% 128.31/128.52 [8]~E(x81,x82)+E(f21(x81,x83),f21(x82,x83))
% 128.31/128.52 [9]~E(x91,x92)+E(f21(x93,x91),f21(x93,x92))
% 128.31/128.52 [10]~E(x101,x102)+E(f4(x101),f4(x102))
% 128.31/128.52 [11]~E(x111,x112)+E(f6(x111),f6(x112))
% 128.31/128.52 [12]~E(x121,x122)+E(f13(x121,x123),f13(x122,x123))
% 128.31/128.52 [13]~E(x131,x132)+E(f13(x133,x131),f13(x133,x132))
% 128.31/128.52 [14]~E(x141,x142)+E(f15(x141,x143),f15(x142,x143))
% 128.31/128.52 [15]~E(x151,x152)+E(f15(x153,x151),f15(x153,x152))
% 128.31/128.52 [16]~E(x161,x162)+E(f7(x161),f7(x162))
% 128.31/128.52 [17]~E(x171,x172)+E(f5(x171,x173),f5(x172,x173))
% 128.31/128.52 [18]~E(x181,x182)+E(f5(x183,x181),f5(x183,x182))
% 128.31/128.52 [19]~E(x191,x192)+E(f11(x191),f11(x192))
% 128.31/128.52 [20]~E(x201,x202)+E(f20(x201,x203),f20(x202,x203))
% 128.31/128.52 [21]~E(x211,x212)+E(f20(x213,x211),f20(x213,x212))
% 128.31/128.52 [22]~E(x221,x222)+E(f12(x221),f12(x222))
% 128.31/128.52 [23]~E(x231,x232)+E(f19(x231),f19(x232))
% 128.31/128.52 [24]~E(x241,x242)+E(f8(x241,x243),f8(x242,x243))
% 128.31/128.52 [25]~E(x251,x252)+E(f8(x253,x251),f8(x253,x252))
% 128.31/128.52 [26]~E(x261,x262)+E(f16(x261,x263),f16(x262,x263))
% 128.31/128.52 [27]~E(x271,x272)+E(f16(x273,x271),f16(x273,x272))
% 128.31/128.52 [28]~E(x281,x282)+E(f14(x281,x283),f14(x282,x283))
% 128.31/128.52 [29]~E(x291,x292)+E(f14(x293,x291),f14(x293,x292))
% 128.31/128.52 [30]P1(x302,x303)+~E(x301,x302)+~P1(x301,x303)
% 128.31/128.52 [31]P1(x313,x312)+~E(x311,x312)+~P1(x313,x311)
% 128.31/128.52 [32]~P3(x321)+P3(x322)+~E(x321,x322)
% 128.31/128.52 [33]P4(x332,x333)+~E(x331,x332)+~P4(x331,x333)
% 128.31/128.52 [34]P4(x343,x342)+~E(x341,x342)+~P4(x343,x341)
% 128.31/128.52 [35]P5(x352,x353)+~E(x351,x352)+~P5(x351,x353)
% 128.31/128.52 [36]P5(x363,x362)+~E(x361,x362)+~P5(x363,x361)
% 128.31/128.52 [37]~P2(x371)+P2(x372)+~E(x371,x372)
% 128.31/128.52
% 128.31/128.52 %-------------------------------------------
% 128.31/128.52 cnf(86,plain,
% 128.31/128.52 (~E(a9,f17(a3))),
% 128.31/128.52 inference(scs_inference,[],[41,40,43,31])).
% 128.31/128.52 cnf(87,plain,
% 128.31/128.52 (P1(x871,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(89,plain,
% 128.31/128.52 (P1(x891,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(91,plain,
% 128.31/128.52 (~E(f17(a3),a9)),
% 128.31/128.52 inference(scs_inference,[],[41,40,87,38,43,31,50,2])).
% 128.31/128.52 cnf(92,plain,
% 128.31/128.52 (P1(f10(x921),a2)),
% 128.31/128.52 inference(scs_inference,[],[41,40,87,89,38,43,31,50,2,45])).
% 128.31/128.52 cnf(94,plain,
% 128.31/128.52 (~P2(f18(x941))),
% 128.31/128.52 inference(scs_inference,[],[41,40,87,89,38,43,31,50,2,45,44])).
% 128.31/128.52 cnf(96,plain,
% 128.31/128.52 (P1(f11(x961),f22(x961))),
% 128.31/128.52 inference(scs_inference,[],[41,40,87,89,38,43,31,50,2,45,44,54])).
% 128.31/128.52 cnf(98,plain,
% 128.31/128.52 (P1(f7(x981),f17(x981))),
% 128.31/128.52 inference(scs_inference,[],[41,40,87,89,38,43,31,50,2,45,44,54,53])).
% 128.31/128.52 cnf(100,plain,
% 128.31/128.52 (P5(f10(x1001),f5(x1001,x1001))),
% 128.31/128.52 inference(scs_inference,[],[41,40,87,89,38,43,31,50,2,45,44,54,53,56])).
% 128.31/128.52 cnf(103,plain,
% 128.31/128.52 (~E(f7(a3),f10(a3))),
% 128.31/128.52 inference(scs_inference,[],[41,40,87,89,38,43,31,50,2,45,44,54,53,56,32,30])).
% 128.31/128.52 cnf(105,plain,
% 128.31/128.52 (P1(x1051,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(108,plain,
% 128.31/128.52 (P1(x1081,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(110,plain,
% 128.31/128.52 (P1(f8(a3,a3),f22(f5(a3,a3)))),
% 128.31/128.52 inference(scs_inference,[],[41,40,87,89,105,108,38,43,31,50,2,45,44,54,53,56,32,30,68,55,83])).
% 128.31/128.52 cnf(147,plain,
% 128.31/128.52 (P1(f11(f5(x1471,x1471)),f21(x1471,x1471))),
% 128.31/128.52 inference(scs_inference,[],[40,96,84])).
% 128.31/128.52 cnf(148,plain,
% 128.31/128.52 (P1(f11(x1481),f22(x1481))),
% 128.31/128.52 inference(rename_variables,[],[96])).
% 128.31/128.52 cnf(150,plain,
% 128.31/128.52 (P4(f6(f18(x1501)),f18(x1501))),
% 128.31/128.52 inference(scs_inference,[],[40,96,94,84,52])).
% 128.31/128.52 cnf(151,plain,
% 128.31/128.52 (P1(x1511,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(153,plain,
% 128.31/128.52 (P1(f12(f18(x1531)),f19(f18(x1531)))),
% 128.31/128.52 inference(scs_inference,[],[40,151,96,94,84,52,55])).
% 128.31/128.52 cnf(154,plain,
% 128.31/128.52 (P1(x1541,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(156,plain,
% 128.31/128.52 (P3(f10(x1561))),
% 128.31/128.52 inference(scs_inference,[],[40,151,154,96,94,92,84,52,55,50])).
% 128.31/128.52 cnf(157,plain,
% 128.31/128.52 (P1(x1571,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(159,plain,
% 128.31/128.52 (P1(f8(x1591,x1591),f21(x1591,x1591))),
% 128.31/128.52 inference(scs_inference,[],[40,151,154,157,96,94,92,84,52,55,50,68])).
% 128.31/128.52 cnf(163,plain,
% 128.31/128.52 (P1(f11(x1631),f22(x1631))),
% 128.31/128.52 inference(rename_variables,[],[96])).
% 128.31/128.52 cnf(165,plain,
% 128.31/128.52 (~P1(f11(x1651),a9)+P1(f11(x1651),f19(f18(x1651)))),
% 128.31/128.52 inference(scs_inference,[],[40,151,154,157,96,148,163,94,92,103,84,52,55,50,68,3,82,67])).
% 128.31/128.52 cnf(182,plain,
% 128.31/128.52 (P1(f11(x1821),f19(f18(x1821)))),
% 128.31/128.52 inference(scs_inference,[],[40,165])).
% 128.31/128.52 cnf(183,plain,
% 128.31/128.52 (P1(x1831,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(184,plain,
% 128.31/128.52 (P1(f8(x1841,x1841),f22(f5(x1841,x1841)))),
% 128.31/128.52 inference(scs_inference,[],[40,183,159,165,83])).
% 128.31/128.52 cnf(188,plain,
% 128.31/128.52 (P1(x1881,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(189,plain,
% 128.31/128.52 (P1(x1891,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(192,plain,
% 128.31/128.52 (P1(x1921,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(196,plain,
% 128.31/128.52 (P1(x1961,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(197,plain,
% 128.31/128.52 (P1(x1971,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(201,plain,
% 128.31/128.52 (P1(x2011,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(202,plain,
% 128.31/128.52 (P1(x2021,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(204,plain,
% 128.31/128.52 (P1(f7(x2041),f21(x2041,x2041))),
% 128.31/128.52 inference(scs_inference,[],[40,183,189,192,197,201,188,196,202,147,159,153,110,86,98,94,165,83,82,75,61,79,72])).
% 128.31/128.52 cnf(236,plain,
% 128.31/128.52 (P1(f7(x2361),f22(f5(x2361,x2361)))),
% 128.31/128.52 inference(scs_inference,[],[40,204,83])).
% 128.31/128.52 cnf(238,plain,
% 128.31/128.52 (P1(x2381,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(240,plain,
% 128.31/128.52 (P3(f8(x2401,x2401))),
% 128.31/128.52 inference(scs_inference,[],[40,238,184,204,83,82])).
% 128.31/128.52 cnf(241,plain,
% 128.31/128.52 (P1(x2411,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(242,plain,
% 128.31/128.52 (P1(x2421,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(244,plain,
% 128.31/128.52 (P1(f8(x2441,x2441),f17(x2441))),
% 128.31/128.52 inference(scs_inference,[],[40,238,242,241,184,204,159,83,82,75])).
% 128.31/128.52 cnf(246,plain,
% 128.31/128.52 (P1(x2461,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(250,plain,
% 128.31/128.52 (P1(f6(f18(x2501)),f19(f18(x2501)))),
% 128.31/128.52 inference(scs_inference,[],[40,238,242,241,246,184,204,159,150,94,83,82,75,64,60])).
% 128.31/128.52 cnf(252,plain,
% 128.31/128.52 (P1(x2521,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(253,plain,
% 128.31/128.52 (P1(x2531,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(255,plain,
% 128.31/128.52 (~P4(f20(f17(a3),a9),f10(f17(a3)))),
% 128.31/128.52 inference(scs_inference,[],[40,238,242,252,241,246,253,184,204,91,159,150,94,83,82,75,64,60,79])).
% 128.31/128.52 cnf(297,plain,
% 128.31/128.52 (~E(a2,f17(a3))),
% 128.31/128.52 inference(scs_inference,[],[40,240,92,41,67,47,31])).
% 128.31/128.52 cnf(315,plain,
% 128.31/128.52 (P3(f7(x3151))),
% 128.31/128.52 inference(scs_inference,[],[244,255,236,41,40,30,34,82])).
% 128.31/128.52 cnf(342,plain,
% 128.31/128.52 (P4(f11(x3421),f18(x3421))+~P1(f18(x3421),a9)),
% 128.31/128.52 inference(scs_inference,[],[182,94,40,61])).
% 128.31/128.52 cnf(352,plain,
% 128.31/128.52 (P1(x3521,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(353,plain,
% 128.31/128.52 (~P1(f10(a3),f21(a3,a3))+~P1(f10(a3),a9)),
% 128.31/128.52 inference(scs_inference,[],[41,40,352,342,75])).
% 128.31/128.52 cnf(354,plain,
% 128.31/128.52 (P1(x3541,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(357,plain,
% 128.31/128.52 (P1(x3571,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(358,plain,
% 128.31/128.52 (P1(x3581,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(364,plain,
% 128.31/128.52 (P1(x3641,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(365,plain,
% 128.31/128.52 (P1(x3651,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(367,plain,
% 128.31/128.52 (P4(x3671,f18(x3672))+P4(f14(x3671,x3672),x3671)),
% 128.31/128.52 inference(scs_inference,[],[250,96,41,40,352,354,358,364,357,365,342,75,78,84,71,66])).
% 128.31/128.52 cnf(392,plain,
% 128.31/128.52 (~P1(f10(a3),f21(a3,a3))),
% 128.31/128.52 inference(scs_inference,[],[40,353])).
% 128.31/128.52 cnf(393,plain,
% 128.31/128.52 (P1(x3931,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(398,plain,
% 128.31/128.52 (~P1(f10(a3),f22(f5(a3,a3)))),
% 128.31/128.52 inference(scs_inference,[],[92,40,393,353,31,76,84])).
% 128.31/128.52 cnf(399,plain,
% 128.31/128.52 (P1(x3991,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(401,plain,
% 128.31/128.52 (P1(f12(f18(x4011)),f22(x4011))+~P1(x4011,a9)),
% 128.31/128.52 inference(scs_inference,[],[92,153,40,393,399,353,31,76,84,71])).
% 128.31/128.52 cnf(419,plain,
% 128.31/128.52 (P1(f12(f18(x4191)),f22(x4191))),
% 128.31/128.52 inference(scs_inference,[],[40,401])).
% 128.31/128.52 cnf(459,plain,
% 128.31/128.52 (~E(f17(a3),a2)),
% 128.31/128.52 inference(scs_inference,[],[297,2])).
% 128.31/128.52 cnf(460,plain,
% 128.31/128.52 (~E(a2,f22(f5(a3,a3)))),
% 128.31/128.52 inference(scs_inference,[],[92,297,398,2,31])).
% 128.31/128.52 cnf(645,plain,
% 128.31/128.52 (P1(x6451,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(646,plain,
% 128.31/128.52 (P1(x6461,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(649,plain,
% 128.31/128.52 (P1(x6491,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(650,plain,
% 128.31/128.52 (P4(x6501,f18(x6502))+~P4(f14(x6501,x6502),x6502)),
% 128.31/128.52 inference(scs_inference,[],[459,398,40,646,649,645,79,31,76])).
% 128.31/128.52 cnf(6262,plain,
% 128.31/128.52 (P1(f12(f18(f5(x62621,x62621))),f21(x62621,x62621))),
% 128.31/128.52 inference(scs_inference,[],[40,419,84])).
% 128.31/128.52 cnf(6268,plain,
% 128.31/128.52 (~E(f12(f18(f5(a3,a3))),f10(a3))),
% 128.31/128.52 inference(scs_inference,[],[392,6262,30])).
% 128.31/128.52 cnf(6456,plain,
% 128.31/128.52 (~P1(f12(f18(f5(a3,a3))),a9)+~P4(f20(f12(f18(f5(a3,a3))),f10(a3)),f10(f10(a3)))),
% 128.31/128.52 inference(scs_inference,[],[6268,40,79])).
% 128.31/128.52 cnf(6468,plain,
% 128.31/128.52 (P1(x64681,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(6470,plain,
% 128.31/128.52 (P1(x64701,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(6472,plain,
% 128.31/128.52 (~P1(f10(a3),f19(f18(f5(a3,a3))))),
% 128.31/128.52 inference(scs_inference,[],[40,6468,6470,398,6456,71,31])).
% 128.31/128.52 cnf(6484,plain,
% 128.31/128.52 (~P4(f10(a3),f18(f5(a3,a3)))+~P1(f10(a3),a9)),
% 128.31/128.52 inference(scs_inference,[],[40,94,6472,60])).
% 128.31/128.52 cnf(6490,plain,
% 128.31/128.52 (~P4(f10(a3),f18(f5(a3,a3)))),
% 128.31/128.52 inference(scs_inference,[],[40,6484])).
% 128.31/128.52 cnf(6496,plain,
% 128.31/128.52 (P1(f12(f18(f5(x64961,x64961))),f17(x64961))+~P1(f12(f18(f5(x64961,x64961))),a9)),
% 128.31/128.52 inference(scs_inference,[],[40,6262,75])).
% 128.31/128.52 cnf(6499,plain,
% 128.31/128.52 (~E(a9,f19(f18(f5(a3,a3))))),
% 128.31/128.52 inference(scs_inference,[],[40,6262,6472,75,31])).
% 128.31/128.52 cnf(6506,plain,
% 128.31/128.52 (P4(f14(f10(a3),f5(a3,a3)),f10(a3))),
% 128.31/128.52 inference(scs_inference,[],[6499,40,6490,6496,2,367])).
% 128.31/128.52 cnf(6508,plain,
% 128.31/128.52 (~P4(f14(f10(a3),f5(a3,a3)),f5(a3,a3))),
% 128.31/128.52 inference(scs_inference,[],[6499,40,6490,6496,2,367,650])).
% 128.31/128.52 cnf(6517,plain,
% 128.31/128.52 (~P2(f10(a3))+~P1(f14(f10(a3),f5(a3,a3)),a9)),
% 128.31/128.52 inference(scs_inference,[],[40,6508,6506,34,57])).
% 128.31/128.52 cnf(6518,plain,
% 128.31/128.52 (P1(x65181,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(6521,plain,
% 128.31/128.52 (~P1(a2,a9)+~P4(f20(a2,f22(f5(a3,a3))),f10(f22(f5(a3,a3))))),
% 128.31/128.52 inference(scs_inference,[],[460,40,6518,6508,6506,34,57,33,79])).
% 128.31/128.52 cnf(6527,plain,
% 128.31/128.52 (P1(x65271,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(6528,plain,
% 128.31/128.52 (~P2(f10(a3))),
% 128.31/128.52 inference(scs_inference,[],[40,6527,6521,6517])).
% 128.31/128.52 cnf(6569,plain,
% 128.31/128.52 (P1(x65691,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(6570,plain,
% 128.31/128.52 (P1(x65701,a9)),
% 128.31/128.52 inference(rename_variables,[],[40])).
% 128.31/128.52 cnf(6572,plain,
% 128.31/128.53 (P1(f7(x65721),f19(f18(f5(x65721,x65721))))),
% 128.31/128.53 inference(scs_inference,[],[40,6570,6569,236,315,80,67])).
% 128.31/128.53 cnf(6588,plain,
% 128.31/128.53 (P1(x65881,a9)),
% 128.31/128.53 inference(rename_variables,[],[40])).
% 128.31/128.53 cnf(6589,plain,
% 128.31/128.53 (P1(x65891,a9)),
% 128.31/128.53 inference(rename_variables,[],[40])).
% 128.31/128.53 cnf(6592,plain,
% 128.31/128.53 (P1(x65921,a9)),
% 128.31/128.53 inference(rename_variables,[],[40])).
% 128.31/128.53 cnf(6593,plain,
% 128.31/128.53 (P1(x65931,a9)),
% 128.31/128.53 inference(rename_variables,[],[40])).
% 128.31/128.53 cnf(6597,plain,
% 128.31/128.53 (P1(x65971,a9)),
% 128.31/128.53 inference(rename_variables,[],[40])).
% 128.31/128.53 cnf(6598,plain,
% 128.31/128.53 (P1(x65981,a9)),
% 128.31/128.53 inference(rename_variables,[],[40])).
% 128.31/128.53 cnf(6601,plain,
% 128.31/128.53 (~P1(f5(a3,a3),a9)),
% 128.31/128.53 inference(scs_inference,[],[40,6589,6592,6597,6588,6593,6598,156,94,100,6572,6528,6508,6506,60,61,80,74])).
% 128.31/128.53 cnf(6609,plain,
% 128.31/128.53 ($false),
% 128.31/128.53 inference(scs_inference,[],[6601,40]),
% 128.31/128.53 ['proof']).
% 128.31/128.53 % SZS output end Proof
% 128.31/128.53 % Total time :127.760000s
%------------------------------------------------------------------------------