TSTP Solution File: SET679+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET679+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 14:30:42 EDT 2023
% Result : Theorem 0.63s 0.75s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET679+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
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:01:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.63/0.74 %-------------------------------------------
% 0.63/0.74 % File :CSE---1.6
% 0.63/0.74 % Problem :theBenchmark
% 0.63/0.74 % Transform :cnf
% 0.63/0.74 % Format :tptp:raw
% 0.63/0.74 % Command :java -jar mcs_scs.jar %d %s
% 0.63/0.74
% 0.63/0.74 % Result :Theorem 0.120000s
% 0.63/0.74 % Output :CNFRefutation 0.120000s
% 0.63/0.74 %-------------------------------------------
% 0.63/0.74 %--------------------------------------------------------------------------
% 0.63/0.74 % File : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% 0.63/0.74 % Domain : Set Theory (Relations)
% 0.63/0.74 % Problem : The identity relation on D is not the empty set
% 0.63/0.74 % Version : [Wor90] axioms : Reduced > Incomplete.
% 0.63/0.74 % English :
% 0.63/0.74
% 0.63/0.74 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.63/0.74 % : [Wor90] Woronowicz (1990), Relations Defined on Sets
% 0.63/0.74 % Source : [ILF]
% 0.63/0.74 % Names : RELSET_1 (46) [Wor90]
% 0.63/0.74
% 0.63/0.74 % Status : Theorem
% 0.63/0.74 % Rating : 0.31 v7.4.0, 0.23 v7.3.0, 0.28 v7.2.0, 0.24 v7.1.0, 0.17 v6.4.0, 0.15 v6.3.0, 0.29 v6.2.0, 0.32 v6.1.0, 0.33 v6.0.0, 0.35 v5.5.0, 0.33 v5.4.0, 0.29 v5.3.0, 0.33 v5.2.0, 0.30 v5.1.0, 0.29 v5.0.0, 0.33 v4.1.0, 0.26 v4.0.0, 0.25 v3.5.0, 0.26 v3.4.0, 0.16 v3.3.0, 0.21 v3.2.0, 0.27 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
% 0.63/0.74 % Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% 0.63/0.74 % Number of atoms : 82 ( 4 equ)
% 0.63/0.74 % Maximal formula atoms : 7 ( 3 avg)
% 0.63/0.74 % Number of connectives : 65 ( 7 ~; 0 |; 9 &)
% 0.63/0.74 % ( 11 <=>; 38 =>; 0 <=; 0 <~>)
% 0.63/0.74 % Maximal formula depth : 11 ( 5 avg)
% 0.63/0.74 % Maximal term depth : 3 ( 1 avg)
% 0.63/0.74 % Number of predicates : 7 ( 6 usr; 0 prp; 1-2 aty)
% 0.63/0.74 % Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% 0.63/0.74 % Number of variables : 42 ( 37 !; 5 ?)
% 0.63/0.74 % SPC : FOF_THM_RFO_SEQ
% 0.63/0.74
% 0.63/0.74 % Comments :
% 0.63/0.74 %--------------------------------------------------------------------------
% 0.63/0.74 %---- line(relat_1 - th(70),1918880)
% 0.63/0.74 fof(p1,axiom,
% 0.63/0.74 ! [B] :
% 0.63/0.74 ( ilf_type(B,set_type)
% 0.63/0.74 => ! [C] :
% 0.63/0.74 ( ilf_type(C,set_type)
% 0.63/0.74 => ( member(C,B)
% 0.63/0.74 <=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) ) ).
% 0.63/0.74
% 0.63/0.74 %---- line(hidden - axiom559,1832636)
% 0.63/0.74 fof(p2,axiom,
% 0.63/0.74 ! [B] :
% 0.63/0.74 ( ilf_type(B,set_type)
% 0.63/0.74 => ~ member(B,empty_set) ) ).
% 0.63/0.74
% 0.63/0.74 %---- declaration(line(hidden - axiom559,1832636)) Part 1
% 0.63/0.74 fof(p3a,axiom,
% 0.63/0.74 empty(empty_set) ).
% 0.63/0.74
% 0.63/0.74 %---- declaration(line(hidden - axiom559,1832636)) Part 2
% 0.63/0.74 fof(p3b,axiom,
% 0.63/0.74 type(empty_set,set_type) ).
% 0.63/0.74
% 0.63/0.75 %---- line(relat_1 - df(10),1918876)
% 0.63/0.75 fof(p4,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ! [C] :
% 0.63/0.75 ( ilf_type(C,set_type)
% 0.63/0.75 => ! [D] :
% 0.63/0.75 ( ilf_type(D,set_type)
% 0.63/0.75 => ( member(ordered_pair(C,D),identity_relation_of(B))
% 0.63/0.75 <=> ( member(C,B)
% 0.63/0.75 & C = D ) ) ) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- declaration(line(relat_1 - df(10),1918876))
% 0.63/0.75 fof(p5,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ilf_type(identity_relation_of(B),binary_relation_type) ) ).
% 0.63/0.75
% 0.63/0.75 %---- line(hidden - axiom560,1832615)
% 0.63/0.75 fof(p6,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ! [C] :
% 0.63/0.75 ( ilf_type(C,set_type)
% 0.63/0.75 => ( B = C
% 0.63/0.75 <=> ! [D] :
% 0.63/0.75 ( ilf_type(D,set_type)
% 0.63/0.75 => ( member(D,B)
% 0.63/0.75 <=> member(D,C) ) ) ) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- line(hidden - axiom561,1832619)
% 0.63/0.75 fof(p7,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ! [C] :
% 0.63/0.75 ( ilf_type(C,set_type)
% 0.63/0.75 => ( not_equal(B,C)
% 0.63/0.75 <=> B != C ) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- line(hidden - axiom562,1832628)
% 0.63/0.75 fof(p8,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ( empty(B)
% 0.63/0.75 <=> ! [C] :
% 0.63/0.75 ( ilf_type(C,set_type)
% 0.63/0.75 => ~ member(C,B) ) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- declaration(op(ordered_pair,2,function))
% 0.63/0.75 fof(p9,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ! [C] :
% 0.63/0.75 ( ilf_type(C,set_type)
% 0.63/0.75 => ilf_type(ordered_pair(B,C),set_type) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- line(relat_1 - axiom563,1917641)
% 0.63/0.75 fof(p10,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ( ilf_type(B,binary_relation_type)
% 0.63/0.75 <=> ( relation_like(B)
% 0.63/0.75 & ilf_type(B,set_type) ) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- type_nonempty(line(relat_1 - axiom563,1917641))
% 0.63/0.75 fof(p11,axiom,
% 0.63/0.75 ? [B] : ilf_type(B,binary_relation_type) ).
% 0.63/0.75
% 0.63/0.75 %---- line(relat_1 - df(1),1917627)
% 0.63/0.75 fof(p12,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ( relation_like(B)
% 0.63/0.75 <=> ! [C] :
% 0.63/0.75 ( ilf_type(C,set_type)
% 0.63/0.75 => ( member(C,B)
% 0.63/0.75 => ? [D] :
% 0.63/0.75 ( ilf_type(D,set_type)
% 0.63/0.75 & ? [E] :
% 0.63/0.75 ( ilf_type(E,set_type)
% 0.63/0.75 & C = ordered_pair(D,E) ) ) ) ) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- conditional_cluster(axiom566,relation_like)
% 0.63/0.75 fof(p13,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ( empty(B)
% 0.63/0.75 & ilf_type(B,set_type) )
% 0.63/0.75 => relation_like(B) ) ).
% 0.63/0.75
% 0.63/0.75 %---- conditional_cluster(axiom567,relation_like)
% 0.63/0.75 fof(p14,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ! [C] :
% 0.63/0.75 ( ilf_type(C,set_type)
% 0.63/0.75 => ! [D] :
% 0.63/0.75 ( ilf_type(D,subset_type(cross_product(B,C)))
% 0.63/0.75 => relation_like(D) ) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- declaration(op(cross_product,2,function))
% 0.63/0.75 fof(p15,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ! [C] :
% 0.63/0.75 ( ilf_type(C,set_type)
% 0.63/0.75 => ilf_type(cross_product(B,C),set_type) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- line(hidden - axiom568,1832648)
% 0.63/0.75 fof(p16,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ! [C] :
% 0.63/0.75 ( ilf_type(C,set_type)
% 0.63/0.75 => ( ilf_type(C,subset_type(B))
% 0.63/0.75 <=> ilf_type(C,member_type(power_set(B))) ) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- type_nonempty(line(hidden - axiom568,1832648))
% 0.63/0.75 fof(p17,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ? [C] : ilf_type(C,subset_type(B)) ) ).
% 0.63/0.75
% 0.63/0.75 %---- line(hidden - axiom569,1832644)
% 0.63/0.75 fof(p18,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ! [C] :
% 0.63/0.75 ( ilf_type(C,set_type)
% 0.63/0.75 => ( member(B,power_set(C))
% 0.63/0.75 <=> ! [D] :
% 0.63/0.75 ( ilf_type(D,set_type)
% 0.63/0.75 => ( member(D,B)
% 0.63/0.75 => member(D,C) ) ) ) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- declaration(line(hidden - axiom569,1832644))
% 0.63/0.75 fof(p19,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ( ~ empty(power_set(B))
% 0.63/0.75 & ilf_type(power_set(B),set_type) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- line(hidden - axiom570,1832640)
% 0.63/0.75 fof(p20,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ilf_type(B,set_type)
% 0.63/0.75 => ! [C] :
% 0.63/0.75 ( ( ~ empty(C)
% 0.63/0.75 & ilf_type(C,set_type) )
% 0.63/0.75 => ( ilf_type(B,member_type(C))
% 0.63/0.75 <=> member(B,C) ) ) ) ).
% 0.63/0.75
% 0.63/0.75 %---- type_nonempty(line(hidden - axiom570,1832640))
% 0.63/0.75 fof(p21,axiom,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ( ~ empty(B)
% 0.63/0.75 & ilf_type(B,set_type) )
% 0.63/0.75 => ? [C] : ilf_type(C,member_type(B)) ) ).
% 0.63/0.75
% 0.63/0.75 %---- declaration(set)
% 0.63/0.75 fof(p22,axiom,
% 0.63/0.75 ! [B] : ilf_type(B,set_type) ).
% 0.63/0.75
% 0.63/0.75 %---- line(relset_1 - th(46),1916859)
% 0.63/0.75 fof(prove_relset_1_46,conjecture,
% 0.63/0.75 ! [B] :
% 0.63/0.75 ( ( ~ empty(B)
% 0.63/0.75 & ilf_type(B,set_type) )
% 0.63/0.75 => not_equal(identity_relation_of(B),empty_set) ) ).
% 0.63/0.75
% 0.63/0.75 %--------------------------------------------------------------------------
% 0.63/0.75 %-------------------------------------------
% 0.63/0.75 % Proof found
% 0.63/0.75 % SZS status Theorem for theBenchmark
% 0.63/0.75 % SZS output start Proof
% 0.63/0.75 %ClaNum:79(EqnAxiom:33)
% 0.63/0.75 %VarNum:180(SingletonVarNum:57)
% 0.63/0.75 %MaxLitNum:6
% 0.63/0.75 %MaxfuncDepth:2
% 0.63/0.75 %SharedTerms:12
% 0.63/0.75 %goalClause: 39 40
% 0.63/0.75 %singleGoalClaCount:2
% 0.63/0.75 [34]P1(a1)
% 0.63/0.75 [35]P2(a4,a2)
% 0.63/0.75 [37]P3(a1,a8)
% 0.63/0.75 [39]~P1(a5)
% 0.63/0.75 [40]~P4(f9(a5),a1)
% 0.63/0.75 [38]P2(x381,a8)
% 0.63/0.75 [46]~P5(x461,a1)+~P2(x461,a8)
% 0.63/0.75 [42]~P2(x421,a8)+~P1(f16(x421))
% 0.63/0.75 [43]~P2(x431,a8)+P2(f9(x431),a2)
% 0.63/0.75 [52]~P2(x521,a8)+P2(f13(x521),f19(x521))
% 0.63/0.75 [41]~P1(x411)+P6(x411)+~P2(x411,a8)
% 0.63/0.75 [45]~P6(x451)+~P2(x451,a8)+P2(x451,a2)
% 0.63/0.75 [49]P6(x491)+~P2(x491,a8)+~P2(x491,a2)
% 0.63/0.75 [50]P1(x501)+P5(f6(x501),x501)+~P2(x501,a8)
% 0.63/0.75 [51]P6(x511)+P5(f10(x511),x511)+~P2(x511,a8)
% 0.63/0.75 [53]P1(x531)+P2(f14(x531),f17(x531))+~P2(x531,a8)
% 0.63/0.75 [54]P4(x541,x542)+E(x541,x542)+~P2(x542,a8)+~P2(x541,a8)
% 0.63/0.75 [55]~P4(x551,x552)+~E(x551,x552)+~P2(x552,a8)+~P2(x551,a8)
% 0.63/0.75 [56]~P1(x561)+~P5(x562,x561)+~P2(x562,a8)+~P2(x561,a8)
% 0.63/0.75 [64]P5(f15(x641,x642),x641)+~P2(x642,a8)+~P2(x641,a8)+P5(x641,f16(x642))
% 0.63/0.75 [68]~P5(x681,x682)+~P2(x682,a8)+~P2(x681,a8)+P5(f18(x681,x681),f9(x682))
% 0.63/0.75 [71]~P2(x712,a8)+~P2(x711,a8)+~P5(f15(x711,x712),x712)+P5(x711,f16(x712))
% 0.63/0.75 [72]P5(x721,x722)+~P2(x722,a8)+~P2(x721,a8)+~P5(f18(x721,x721),f9(x722))
% 0.63/0.75 [65]~P2(x652,a8)+~P2(x651,a8)+~P2(x651,f19(x652))+P2(x651,f17(f16(x652)))
% 0.63/0.75 [69]~P2(x692,a8)+~P2(x691,a8)+P2(x691,f19(x692))+~P2(x691,f17(f16(x692)))
% 0.63/0.75 [78]P6(x781)+~P2(x782,a8)+~P2(x783,a8)+~P2(x781,f19(f3(x783,x782)))
% 0.63/0.75 [60]~P5(x602,x601)+P1(x601)+~P2(x601,a8)+~P2(x602,a8)+P2(x602,f17(x601))
% 0.63/0.75 [61]P1(x611)+P5(x612,x611)+~P2(x611,a8)+~P2(x612,a8)+~P2(x612,f17(x611))
% 0.63/0.75 [70]E(x701,x702)+P5(f7(x701,x702),x702)+P5(f7(x701,x702),x701)+~P2(x702,a8)+~P2(x701,a8)
% 0.63/0.75 [79]E(x791,x792)+~P2(x792,a8)+~P2(x791,a8)+~P5(f7(x791,x792),x792)+~P5(f7(x791,x792),x791)
% 0.63/0.75 [76]~P6(x761)+~P5(x762,x761)+~P2(x761,a8)+~P2(x762,a8)+E(f18(f11(x761,x762),f12(x761,x762)),x762)
% 0.63/0.75 [62]P6(x621)+~P2(x621,a8)+~P2(x623,a8)+~P2(x622,a8)+~E(f10(x621),f18(x622,x623))
% 0.63/0.75 [75]E(x751,x752)+~P2(x752,a8)+~P2(x751,a8)+~P5(f18(x751,x752),f9(x753))+~P2(x753,a8)
% 0.63/0.75 [77]P5(x771,x772)+~P2(x772,a8)+~P2(x771,a8)+~P5(f18(x771,x773),f9(x772))+~P2(x773,a8)
% 0.63/0.75 [73]P5(x731,x732)+~P5(x731,x733)+~P2(x731,a8)+~P2(x732,a8)+~P2(x733,a8)+~P5(x733,f16(x732))
% 0.63/0.75 [74]~E(x741,x742)+~P5(x741,x743)+~P2(x742,a8)+~P2(x743,a8)+~P2(x741,a8)+P5(f18(x741,x742),f9(x743))
% 0.63/0.75 %EqnAxiom
% 0.63/0.75 [1]E(x11,x11)
% 0.63/0.75 [2]E(x22,x21)+~E(x21,x22)
% 0.63/0.75 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.63/0.75 [4]~E(x41,x42)+E(f9(x41),f9(x42))
% 0.63/0.75 [5]~E(x51,x52)+E(f16(x51),f16(x52))
% 0.63/0.75 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 0.63/0.75 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 0.63/0.75 [8]~E(x81,x82)+E(f18(x81,x83),f18(x82,x83))
% 0.63/0.75 [9]~E(x91,x92)+E(f18(x93,x91),f18(x93,x92))
% 0.63/0.75 [10]~E(x101,x102)+E(f6(x101),f6(x102))
% 0.63/0.75 [11]~E(x111,x112)+E(f10(x111),f10(x112))
% 0.63/0.75 [12]~E(x121,x122)+E(f19(x121),f19(x122))
% 0.63/0.75 [13]~E(x131,x132)+E(f12(x131,x133),f12(x132,x133))
% 0.63/0.75 [14]~E(x141,x142)+E(f12(x143,x141),f12(x143,x142))
% 0.63/0.75 [15]~E(x151,x152)+E(f13(x151),f13(x152))
% 0.63/0.75 [16]~E(x161,x162)+E(f17(x161),f17(x162))
% 0.63/0.75 [17]~E(x171,x172)+E(f14(x171),f14(x172))
% 0.63/0.75 [18]~E(x181,x182)+E(f11(x181,x183),f11(x182,x183))
% 0.63/0.75 [19]~E(x191,x192)+E(f11(x193,x191),f11(x193,x192))
% 0.63/0.75 [20]~E(x201,x202)+E(f3(x201,x203),f3(x202,x203))
% 0.63/0.75 [21]~E(x211,x212)+E(f3(x213,x211),f3(x213,x212))
% 0.63/0.75 [22]~E(x221,x222)+E(f15(x221,x223),f15(x222,x223))
% 0.63/0.75 [23]~E(x231,x232)+E(f15(x233,x231),f15(x233,x232))
% 0.63/0.75 [24]~P1(x241)+P1(x242)+~E(x241,x242)
% 0.63/0.75 [25]P2(x252,x253)+~E(x251,x252)+~P2(x251,x253)
% 0.63/0.75 [26]P2(x263,x262)+~E(x261,x262)+~P2(x263,x261)
% 0.63/0.75 [27]P5(x272,x273)+~E(x271,x272)+~P5(x271,x273)
% 0.63/0.75 [28]P5(x283,x282)+~E(x281,x282)+~P5(x283,x281)
% 0.63/0.75 [29]P3(x292,x293)+~E(x291,x292)+~P3(x291,x293)
% 0.63/0.75 [30]P3(x303,x302)+~E(x301,x302)+~P3(x303,x301)
% 0.63/0.75 [31]P4(x312,x313)+~E(x311,x312)+~P4(x311,x313)
% 0.63/0.75 [32]P4(x323,x322)+~E(x321,x322)+~P4(x323,x321)
% 0.63/0.75 [33]~P6(x331)+P6(x332)+~E(x331,x332)
% 0.63/0.75
% 0.63/0.75 %-------------------------------------------
% 0.63/0.75 cnf(80,plain,
% 0.63/0.75 (~P5(x801,a1)),
% 0.63/0.75 inference(scs_inference,[],[38,46])).
% 0.63/0.75 cnf(82,plain,
% 0.63/0.75 (P2(x821,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(85,plain,
% 0.63/0.75 (P2(x851,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(87,plain,
% 0.63/0.75 (P2(f9(x871),a2)),
% 0.63/0.75 inference(scs_inference,[],[38,82,85,34,35,46,49,41,43])).
% 0.63/0.75 cnf(89,plain,
% 0.63/0.75 (~P1(f16(x891))),
% 0.63/0.75 inference(scs_inference,[],[38,82,85,34,35,46,49,41,43,42])).
% 0.63/0.75 cnf(91,plain,
% 0.63/0.75 (P2(f13(x911),f19(x911))),
% 0.63/0.75 inference(scs_inference,[],[38,82,85,34,35,46,49,41,43,42,52])).
% 0.63/0.75 cnf(94,plain,
% 0.63/0.75 (~E(a1,a5)),
% 0.63/0.75 inference(scs_inference,[],[39,38,82,85,34,35,46,49,41,43,42,52,33,24])).
% 0.63/0.75 cnf(95,plain,
% 0.63/0.75 (P5(f6(a5),a5)),
% 0.63/0.75 inference(scs_inference,[],[39,38,82,85,34,35,46,49,41,43,42,52,33,24,50])).
% 0.63/0.75 cnf(96,plain,
% 0.63/0.75 (P2(x961,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(99,plain,
% 0.63/0.75 (P2(x991,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(103,plain,
% 0.63/0.75 (P4(a1,a5)+~P2(a5,a8)),
% 0.63/0.75 inference(scs_inference,[],[39,38,82,85,96,99,34,35,46,49,41,43,42,52,33,24,50,53,45,54])).
% 0.63/0.75 cnf(104,plain,
% 0.63/0.75 (P2(x1041,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(106,plain,
% 0.63/0.75 (P6(x1061)+~P2(x1061,f19(f3(x1062,x1062)))),
% 0.63/0.75 inference(scs_inference,[],[39,38,82,85,96,99,104,34,35,46,49,41,43,42,52,33,24,50,53,45,54,78])).
% 0.63/0.75 cnf(137,plain,
% 0.63/0.75 (P6(f13(f3(x1371,x1371)))),
% 0.63/0.75 inference(scs_inference,[],[91,94,2,106])).
% 0.63/0.75 cnf(141,plain,
% 0.63/0.75 (~P5(x1411,a1)),
% 0.63/0.75 inference(rename_variables,[],[80])).
% 0.63/0.75 cnf(142,plain,
% 0.63/0.75 (P2(x1421,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(143,plain,
% 0.63/0.75 (P2(x1431,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(145,plain,
% 0.63/0.75 (P5(f18(f6(a5),f6(a5)),f9(a5))),
% 0.63/0.75 inference(scs_inference,[],[38,143,142,91,80,95,94,2,106,72,68])).
% 0.63/0.75 cnf(146,plain,
% 0.63/0.75 (P2(x1461,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(147,plain,
% 0.63/0.75 (P2(x1471,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(150,plain,
% 0.63/0.75 (~P5(x1501,a1)),
% 0.63/0.75 inference(rename_variables,[],[80])).
% 0.63/0.75 cnf(151,plain,
% 0.63/0.75 (P2(x1511,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(152,plain,
% 0.63/0.75 (P2(x1521,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(155,plain,
% 0.63/0.75 (P2(x1551,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(156,plain,
% 0.63/0.75 (P2(x1561,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(157,plain,
% 0.63/0.75 (~P5(x1571,a1)),
% 0.63/0.75 inference(rename_variables,[],[80])).
% 0.63/0.75 cnf(159,plain,
% 0.63/0.75 (P5(f6(f16(x1591)),f16(x1591))),
% 0.63/0.75 inference(scs_inference,[],[38,143,146,152,156,151,142,91,89,80,141,150,95,94,2,106,72,68,64,70,50])).
% 0.63/0.75 cnf(161,plain,
% 0.63/0.75 (E(f9(a5),a1)),
% 0.63/0.75 inference(scs_inference,[],[40,38,143,146,152,156,151,155,142,147,91,89,80,141,150,95,94,2,106,72,68,64,70,50,54])).
% 0.63/0.75 cnf(164,plain,
% 0.63/0.75 (P1(x1641)+~P5(x1642,x1641)+~P2(x1642,a8)+~P2(x1641,a8)+P2(x1642,f17(x1641))),
% 0.63/0.75 inference(rename_variables,[],[60])).
% 0.63/0.75 cnf(165,plain,
% 0.63/0.75 (~E(a1,f16(a1))),
% 0.63/0.75 inference(scs_inference,[],[40,38,143,146,152,156,151,155,142,147,34,91,89,80,141,150,95,94,2,106,72,68,64,70,50,54,60,24])).
% 0.63/0.75 cnf(169,plain,
% 0.63/0.75 (P2(x1691,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(173,plain,
% 0.63/0.75 (P2(x1731,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(176,plain,
% 0.63/0.75 (P2(x1761,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(179,plain,
% 0.63/0.75 (~P5(x1791,a1)),
% 0.63/0.75 inference(rename_variables,[],[80])).
% 0.63/0.75 cnf(182,plain,
% 0.63/0.75 (~P5(x1821,a1)),
% 0.63/0.75 inference(rename_variables,[],[80])).
% 0.63/0.75 cnf(183,plain,
% 0.63/0.75 (P2(x1831,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(184,plain,
% 0.63/0.75 (P2(x1841,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(185,plain,
% 0.63/0.75 (P2(x1851,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(191,plain,
% 0.63/0.75 (P2(x1911,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(193,plain,
% 0.63/0.75 (P2(x1931,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(200,plain,
% 0.63/0.75 (E(f15(x2001,f9(a5)),f15(x2001,a1))),
% 0.63/0.75 inference(scs_inference,[],[39,40,38,143,146,152,156,185,193,191,151,155,173,176,183,142,147,169,184,34,91,89,80,141,150,157,179,182,87,95,94,2,106,72,68,64,70,50,54,60,24,53,69,49,103,32,31,28,3,73,164,77,75,23])).
% 0.63/0.75 cnf(201,plain,
% 0.63/0.75 (E(f15(f9(a5),x2011),f15(a1,x2011))),
% 0.63/0.75 inference(scs_inference,[],[39,40,38,143,146,152,156,185,193,191,151,155,173,176,183,142,147,169,184,34,91,89,80,141,150,157,179,182,87,95,94,2,106,72,68,64,70,50,54,60,24,53,69,49,103,32,31,28,3,73,164,77,75,23,22])).
% 0.63/0.75 cnf(202,plain,
% 0.63/0.75 (E(f3(x2021,f9(a5)),f3(x2021,a1))),
% 0.63/0.75 inference(scs_inference,[],[39,40,38,143,146,152,156,185,193,191,151,155,173,176,183,142,147,169,184,34,91,89,80,141,150,157,179,182,87,95,94,2,106,72,68,64,70,50,54,60,24,53,69,49,103,32,31,28,3,73,164,77,75,23,22,21])).
% 0.63/0.75 cnf(208,plain,
% 0.63/0.75 (E(f13(f9(a5)),f13(a1))),
% 0.63/0.75 inference(scs_inference,[],[39,40,38,143,146,152,156,185,193,191,151,155,173,176,183,142,147,169,184,34,91,89,80,141,150,157,179,182,87,95,94,2,106,72,68,64,70,50,54,60,24,53,69,49,103,32,31,28,3,73,164,77,75,23,22,21,20,19,18,17,16,15])).
% 0.63/0.75 cnf(211,plain,
% 0.63/0.75 (E(f19(f9(a5)),f19(a1))),
% 0.63/0.75 inference(scs_inference,[],[39,40,38,143,146,152,156,185,193,191,151,155,173,176,183,142,147,169,184,34,91,89,80,141,150,157,179,182,87,95,94,2,106,72,68,64,70,50,54,60,24,53,69,49,103,32,31,28,3,73,164,77,75,23,22,21,20,19,18,17,16,15,14,13,12])).
% 0.63/0.75 cnf(218,plain,
% 0.63/0.75 (E(f16(f9(a5)),f16(a1))),
% 0.63/0.75 inference(scs_inference,[],[39,40,38,143,146,152,156,185,193,191,151,155,173,176,183,142,147,169,184,34,91,89,80,141,150,157,179,182,87,95,94,2,106,72,68,64,70,50,54,60,24,53,69,49,103,32,31,28,3,73,164,77,75,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5])).
% 0.63/0.75 cnf(247,plain,
% 0.63/0.75 (P2(f13(x2471),f19(x2471))),
% 0.63/0.75 inference(rename_variables,[],[91])).
% 0.63/0.75 cnf(251,plain,
% 0.63/0.75 (E(f15(x2511,f9(a5)),f15(x2511,a1))),
% 0.63/0.75 inference(rename_variables,[],[200])).
% 0.63/0.75 cnf(253,plain,
% 0.63/0.75 (E(f15(x2531,a1),f15(x2531,f9(a5)))),
% 0.63/0.75 inference(scs_inference,[],[200,251,201,208,211,91,247,25,26,3,2])).
% 0.63/0.75 cnf(266,plain,
% 0.63/0.75 (P2(x2661,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(272,plain,
% 0.63/0.75 (~P4(f15(x2721,a1),f15(x2721,f9(a5)))+~P2(f15(x2721,f9(a5)),a8)),
% 0.63/0.75 inference(scs_inference,[],[80,38,266,137,159,253,165,218,45,3,2,28,55])).
% 0.63/0.75 cnf(275,plain,
% 0.63/0.75 (~P4(f15(x2751,a1),f15(x2751,a1))+~P2(f15(x2751,f9(a5)),a8)),
% 0.63/0.75 inference(scs_inference,[],[80,38,266,137,159,253,165,218,45,3,2,28,55,32])).
% 0.63/0.75 cnf(311,plain,
% 0.63/0.75 (P2(x3111,a8)),
% 0.63/0.75 inference(rename_variables,[],[38])).
% 0.63/0.75 cnf(316,plain,
% 0.63/0.75 ($false),
% 0.63/0.75 inference(scs_inference,[],[80,38,311,202,161,200,145,275,272,2,31,28]),
% 0.63/0.75 ['proof']).
% 0.63/0.75 % SZS output end Proof
% 0.63/0.75 % Total time :0.120000s
%------------------------------------------------------------------------------