TSTP Solution File: SET662+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET662+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 : n028.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 1.22s 1.31s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET662+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
% 0.15/0.34 % Computer : n028.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 10:47:07 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.18/0.57 start to proof:theBenchmark
% 1.22/1.30 %-------------------------------------------
% 1.22/1.30 % File :CSE---1.6
% 1.22/1.30 % Problem :theBenchmark
% 1.22/1.30 % Transform :cnf
% 1.22/1.30 % Format :tptp:raw
% 1.22/1.30 % Command :java -jar mcs_scs.jar %d %s
% 1.22/1.30
% 1.22/1.30 % Result :Theorem 0.670000s
% 1.22/1.30 % Output :CNFRefutation 0.670000s
% 1.22/1.30 %-------------------------------------------
% 1.22/1.30 %--------------------------------------------------------------------------
% 1.22/1.30 % File : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% 1.22/1.30 % Domain : Set Theory (Relations)
% 1.22/1.30 % Problem : The empty set is a relation from X to Y
% 1.22/1.30 % Version : [Wor90] axioms : Reduced > Incomplete.
% 1.22/1.30 % English :
% 1.22/1.30
% 1.22/1.30 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 1.22/1.30 % : [Wor90] Woronowicz (1990), Relations Defined on Sets
% 1.22/1.30 % Source : [ILF]
% 1.22/1.30 % Names : RELSET_1 (25) [Wor90]
% 1.22/1.30
% 1.22/1.30 % Status : Theorem
% 1.22/1.30 % Rating : 0.19 v8.1.0, 0.25 v7.5.0, 0.22 v7.4.0, 0.27 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.26 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.24 v6.1.0, 0.27 v6.0.0, 0.35 v5.5.0, 0.26 v5.4.0, 0.21 v5.3.0, 0.22 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.0, 0.12 v3.7.0, 0.15 v3.5.0, 0.16 v3.4.0, 0.11 v3.3.0, 0.14 v3.2.0, 0.18 v3.1.0, 0.11 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
% 1.22/1.30 % Syntax : Number of formulae : 22 ( 3 unt; 0 def)
% 1.22/1.30 % Number of atoms : 75 ( 1 equ)
% 1.22/1.30 % Maximal formula atoms : 7 ( 3 avg)
% 1.22/1.30 % Number of connectives : 58 ( 5 ~; 0 |; 7 &)
% 1.22/1.30 % ( 6 <=>; 40 =>; 0 <=; 0 <~>)
% 1.22/1.30 % Maximal formula depth : 11 ( 5 avg)
% 1.22/1.30 % Maximal term depth : 3 ( 1 avg)
% 1.22/1.30 % Number of predicates : 7 ( 6 usr; 0 prp; 1-2 aty)
% 1.22/1.30 % Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% 1.22/1.30 % Number of variables : 43 ( 38 !; 5 ?)
% 1.22/1.30 % SPC : FOF_THM_RFO_SEQ
% 1.22/1.30
% 1.22/1.30 % Comments :
% 1.22/1.30 %--------------------------------------------------------------------------
% 1.22/1.30 %---- line(relat_1 - th(58),1918738)
% 1.22/1.30 fof(p1,axiom,
% 1.22/1.30 ! [B] :
% 1.22/1.30 ( ilf_type(B,set_type)
% 1.22/1.30 => ! [C] :
% 1.22/1.30 ( ilf_type(C,set_type)
% 1.22/1.30 => subset(empty_set,cross_product(B,C)) ) ) ).
% 1.22/1.30
% 1.22/1.30 %---- line(relset_1 - df(1),1916080)
% 1.22/1.30 fof(p2,axiom,
% 1.22/1.30 ! [B] :
% 1.22/1.30 ( ilf_type(B,set_type)
% 1.22/1.30 => ! [C] :
% 1.22/1.30 ( ilf_type(C,set_type)
% 1.22/1.30 => ( ! [D] :
% 1.22/1.30 ( ilf_type(D,subset_type(cross_product(B,C)))
% 1.22/1.30 => ilf_type(D,relation_type(B,C)) )
% 1.22/1.30 & ! [E] :
% 1.22/1.30 ( ilf_type(E,relation_type(B,C))
% 1.22/1.30 => ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ) ).
% 1.22/1.30
% 1.22/1.30 %---- type_nonempty(line(relset_1 - df(1),1916080))
% 1.22/1.30 fof(p3,axiom,
% 1.22/1.30 ! [B] :
% 1.22/1.30 ( ilf_type(B,set_type)
% 1.22/1.30 => ! [C] :
% 1.22/1.30 ( ilf_type(C,set_type)
% 1.22/1.30 => ? [D] : ilf_type(D,relation_type(C,B)) ) ) ).
% 1.22/1.30
% 1.22/1.30 %---- line(hidden - axiom233,1832636)
% 1.22/1.30 fof(p4,axiom,
% 1.22/1.30 ! [B] :
% 1.22/1.30 ( ilf_type(B,set_type)
% 1.22/1.30 => ~ member(B,empty_set) ) ).
% 1.22/1.31
% 1.22/1.31 %---- declaration(line(hidden - axiom233,1832636)) Part 1
% 1.22/1.31 fof(p5a,axiom,
% 1.22/1.31 empty(empty_set) ).
% 1.22/1.31
% 1.22/1.31 %---- declaration(line(hidden - axiom233,1832636)) Part 2
% 1.22/1.31 fof(p5b,axiom,
% 1.22/1.31 type(empty_set,set_type) ).
% 1.22/1.31
% 1.22/1.31 %---- declaration(op(cross_product,2,function))
% 1.22/1.31 fof(p6,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ! [C] :
% 1.22/1.31 ( ilf_type(C,set_type)
% 1.22/1.31 => ilf_type(cross_product(B,C),set_type) ) ) ).
% 1.22/1.31
% 1.22/1.31 %---- line(hidden - axiom234,1832648)
% 1.22/1.31 fof(p7,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ! [C] :
% 1.22/1.31 ( ilf_type(C,set_type)
% 1.22/1.31 => ( ilf_type(C,subset_type(B))
% 1.22/1.31 <=> ilf_type(C,member_type(power_set(B))) ) ) ) ).
% 1.22/1.31
% 1.22/1.31 %---- type_nonempty(line(hidden - axiom234,1832648))
% 1.22/1.31 fof(p8,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ? [C] : ilf_type(C,subset_type(B)) ) ).
% 1.22/1.31
% 1.22/1.31 %---- line(tarski - df(3),1832749)
% 1.22/1.31 fof(p9,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ! [C] :
% 1.22/1.31 ( ilf_type(C,set_type)
% 1.22/1.31 => ( subset(B,C)
% 1.22/1.31 <=> ! [D] :
% 1.22/1.31 ( ilf_type(D,set_type)
% 1.22/1.31 => ( member(D,B)
% 1.22/1.31 => member(D,C) ) ) ) ) ) ).
% 1.22/1.31
% 1.22/1.31 %---- property(reflexivity,op(subset,2,predicate))
% 1.22/1.31 fof(p10,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => subset(B,B) ) ).
% 1.22/1.31
% 1.22/1.31 %---- line(hidden - axiom236,1832628)
% 1.22/1.31 fof(p11,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ( empty(B)
% 1.22/1.31 <=> ! [C] :
% 1.22/1.31 ( ilf_type(C,set_type)
% 1.22/1.31 => ~ member(C,B) ) ) ) ).
% 1.22/1.31
% 1.22/1.31 %---- line(hidden - axiom238,1832644)
% 1.22/1.31 fof(p12,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ! [C] :
% 1.22/1.31 ( ilf_type(C,set_type)
% 1.22/1.31 => ( member(B,power_set(C))
% 1.22/1.31 <=> ! [D] :
% 1.22/1.31 ( ilf_type(D,set_type)
% 1.22/1.31 => ( member(D,B)
% 1.22/1.31 => member(D,C) ) ) ) ) ) ).
% 1.22/1.31
% 1.22/1.31 %---- declaration(line(hidden - axiom238,1832644))
% 1.22/1.31 fof(p13,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ( ~ empty(power_set(B))
% 1.22/1.31 & ilf_type(power_set(B),set_type) ) ) ).
% 1.22/1.31
% 1.22/1.31 %---- line(hidden - axiom239,1832640)
% 1.22/1.31 fof(p14,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ! [C] :
% 1.22/1.31 ( ( ~ empty(C)
% 1.22/1.31 & ilf_type(C,set_type) )
% 1.22/1.31 => ( ilf_type(B,member_type(C))
% 1.22/1.31 <=> member(B,C) ) ) ) ).
% 1.22/1.31
% 1.22/1.31 %---- type_nonempty(line(hidden - axiom239,1832640))
% 1.22/1.31 fof(p15,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ( ~ empty(B)
% 1.22/1.31 & ilf_type(B,set_type) )
% 1.22/1.31 => ? [C] : ilf_type(C,member_type(B)) ) ).
% 1.22/1.31
% 1.22/1.31 %---- line(relat_1 - df(1),1917627)
% 1.22/1.31 fof(p16,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ( relation_like(B)
% 1.22/1.31 <=> ! [C] :
% 1.22/1.31 ( ilf_type(C,set_type)
% 1.22/1.31 => ( member(C,B)
% 1.22/1.31 => ? [D] :
% 1.22/1.31 ( ilf_type(D,set_type)
% 1.22/1.31 & ? [E] :
% 1.22/1.31 ( ilf_type(E,set_type)
% 1.22/1.31 & C = ordered_pair(D,E) ) ) ) ) ) ) ).
% 1.22/1.31
% 1.22/1.31 %---- conditional_cluster(axiom240,relation_like)
% 1.22/1.31 fof(p17,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ( empty(B)
% 1.22/1.31 & ilf_type(B,set_type) )
% 1.22/1.31 => relation_like(B) ) ).
% 1.22/1.31
% 1.22/1.31 %---- conditional_cluster(axiom241,relation_like)
% 1.22/1.31 fof(p18,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ! [C] :
% 1.22/1.31 ( ilf_type(C,set_type)
% 1.22/1.31 => ! [D] :
% 1.22/1.31 ( ilf_type(D,subset_type(cross_product(B,C)))
% 1.22/1.31 => relation_like(D) ) ) ) ).
% 1.22/1.31
% 1.22/1.31 %---- declaration(op(ordered_pair,2,function))
% 1.22/1.31 fof(p19,axiom,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ! [C] :
% 1.22/1.31 ( ilf_type(C,set_type)
% 1.22/1.31 => ilf_type(ordered_pair(B,C),set_type) ) ) ).
% 1.22/1.31
% 1.22/1.31 %---- declaration(set)
% 1.22/1.31 fof(p20,axiom,
% 1.22/1.31 ! [B] : ilf_type(B,set_type) ).
% 1.22/1.31
% 1.22/1.31 %---- line(relset_1 - th(25),1916495)
% 1.22/1.31 fof(prove_relset_1_25,conjecture,
% 1.22/1.31 ! [B] :
% 1.22/1.31 ( ilf_type(B,set_type)
% 1.22/1.31 => ! [C] :
% 1.22/1.31 ( ilf_type(C,set_type)
% 1.22/1.31 => ilf_type(empty_set,relation_type(B,C)) ) ) ).
% 1.22/1.31
% 1.22/1.31 %--------------------------------------------------------------------------
% 1.22/1.31 %-------------------------------------------
% 1.22/1.31 % Proof found
% 1.22/1.31 % SZS status Theorem for theBenchmark
% 1.22/1.31 % SZS output start Proof
% 1.22/1.31 %ClaNum:77(EqnAxiom:36)
% 1.22/1.31 %VarNum:152(SingletonVarNum:51)
% 1.22/1.31 %MaxLitNum:6
% 1.22/1.31 %MaxfuncDepth:2
% 1.22/1.31 %SharedTerms:10
% 1.22/1.31 %goalClause: 42
% 1.22/1.31 %singleGoalClaCount:1
% 1.22/1.31 [37]P1(a1)
% 1.22/1.31 [40]P3(a1,a4)
% 1.22/1.31 [42]~P2(a1,f6(a3,a5))
% 1.22/1.31 [41]P2(x411,a4)
% 1.22/1.31 [44]P6(x441,x441)+~P2(x441,a4)
% 1.22/1.31 [47]~P5(x471,a1)+~P2(x471,a4)
% 1.22/1.31 [45]~P2(x451,a4)+~P1(f7(x451))
% 1.22/1.31 [52]~P2(x521,a4)+P2(f9(x521),f19(x521))
% 1.22/1.31 [43]~P1(x431)+P4(x431)+~P2(x431,a4)
% 1.22/1.31 [50]P1(x501)+P5(f8(x501),x501)+~P2(x501,a4)
% 1.22/1.31 [51]P4(x511)+P5(f12(x511),x511)+~P2(x511,a4)
% 1.22/1.31 [53]P1(x531)+P2(f13(x531),f17(x531))+~P2(x531,a4)
% 1.22/1.31 [55]~P2(x552,a4)+~P2(x551,a4)+P6(a1,f2(x551,x552))
% 1.22/1.31 [66]~P2(x662,a4)+~P2(x661,a4)+P2(f10(x661,x662),f6(x662,x661))
% 1.22/1.31 [54]~P1(x541)+~P5(x542,x541)+~P2(x542,a4)+~P2(x541,a4)
% 1.22/1.31 [62]P6(x621,x622)+P5(f11(x621,x622),x621)+~P2(x622,a4)+~P2(x621,a4)
% 1.22/1.31 [64]P5(f14(x641,x642),x641)+~P2(x642,a4)+~P2(x641,a4)+P5(x641,f7(x642))
% 1.22/1.31 [70]P6(x701,x702)+~P2(x702,a4)+~P2(x701,a4)+~P5(f11(x701,x702),x702)
% 1.22/1.31 [72]~P2(x722,a4)+~P2(x721,a4)+~P5(f14(x721,x722),x722)+P5(x721,f7(x722))
% 1.22/1.31 [65]~P2(x652,a4)+~P2(x651,a4)+~P2(x651,f19(x652))+P2(x651,f17(f7(x652)))
% 1.22/1.31 [69]~P2(x692,a4)+~P2(x691,a4)+P2(x691,f19(x692))+~P2(x691,f17(f7(x692)))
% 1.22/1.31 [75]P4(x751)+~P2(x752,a4)+~P2(x753,a4)+~P2(x751,f19(f2(x753,x752)))
% 1.22/1.31 [76]~P2(x763,a4)+~P2(x762,a4)+~P2(x761,f6(x762,x763))+P2(x761,f19(f2(x762,x763)))
% 1.22/1.31 [77]~P2(x773,a4)+~P2(x772,a4)+P2(x771,f6(x772,x773))+~P2(x771,f19(f2(x772,x773)))
% 1.22/1.31 [58]~P5(x582,x581)+P1(x581)+~P2(x581,a4)+~P2(x582,a4)+P2(x582,f17(x581))
% 1.22/1.31 [59]P1(x591)+P5(x592,x591)+~P2(x591,a4)+~P2(x592,a4)+~P2(x592,f17(x591))
% 1.22/1.31 [74]~P4(x741)+~P5(x742,x741)+~P2(x741,a4)+~P2(x742,a4)+E(f18(f15(x741,x742),f16(x741,x742)),x742)
% 1.22/1.31 [61]P4(x611)+~P2(x611,a4)+~P2(x613,a4)+~P2(x612,a4)+~E(f12(x611),f18(x612,x613))
% 1.22/1.31 [71]~P5(x711,x713)+P5(x711,x712)+~P6(x713,x712)+~P2(x711,a4)+~P2(x712,a4)+~P2(x713,a4)
% 1.22/1.31 [73]P5(x731,x732)+~P5(x731,x733)+~P2(x731,a4)+~P2(x732,a4)+~P2(x733,a4)+~P5(x733,f7(x732))
% 1.22/1.31 %EqnAxiom
% 1.22/1.31 [1]E(x11,x11)
% 1.22/1.31 [2]E(x22,x21)+~E(x21,x22)
% 1.22/1.31 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.22/1.31 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 1.22/1.31 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 1.22/1.31 [6]~E(x61,x62)+E(f7(x61),f7(x62))
% 1.22/1.31 [7]~E(x71,x72)+E(f2(x71,x73),f2(x72,x73))
% 1.22/1.31 [8]~E(x81,x82)+E(f2(x83,x81),f2(x83,x82))
% 1.22/1.31 [9]~E(x91,x92)+E(f8(x91),f8(x92))
% 1.22/1.31 [10]~E(x101,x102)+E(f12(x101),f12(x102))
% 1.22/1.31 [11]~E(x111,x112)+E(f11(x111,x113),f11(x112,x113))
% 1.22/1.31 [12]~E(x121,x122)+E(f11(x123,x121),f11(x123,x122))
% 1.22/1.31 [13]~E(x131,x132)+E(f17(x131),f17(x132))
% 1.22/1.31 [14]~E(x141,x142)+E(f9(x141),f9(x142))
% 1.22/1.31 [15]~E(x151,x152)+E(f19(x151),f19(x152))
% 1.22/1.31 [16]~E(x161,x162)+E(f13(x161),f13(x162))
% 1.22/1.31 [17]~E(x171,x172)+E(f15(x171,x173),f15(x172,x173))
% 1.22/1.31 [18]~E(x181,x182)+E(f15(x183,x181),f15(x183,x182))
% 1.22/1.31 [19]~E(x191,x192)+E(f14(x191,x193),f14(x192,x193))
% 1.22/1.31 [20]~E(x201,x202)+E(f14(x203,x201),f14(x203,x202))
% 1.22/1.31 [21]~E(x211,x212)+E(f16(x211,x213),f16(x212,x213))
% 1.22/1.31 [22]~E(x221,x222)+E(f16(x223,x221),f16(x223,x222))
% 1.22/1.31 [23]~E(x231,x232)+E(f18(x231,x233),f18(x232,x233))
% 1.22/1.31 [24]~E(x241,x242)+E(f18(x243,x241),f18(x243,x242))
% 1.22/1.31 [25]~E(x251,x252)+E(f10(x251,x253),f10(x252,x253))
% 1.22/1.31 [26]~E(x261,x262)+E(f10(x263,x261),f10(x263,x262))
% 1.22/1.31 [27]~P1(x271)+P1(x272)+~E(x271,x272)
% 1.22/1.31 [28]P2(x282,x283)+~E(x281,x282)+~P2(x281,x283)
% 1.22/1.31 [29]P2(x293,x292)+~E(x291,x292)+~P2(x293,x291)
% 1.22/1.31 [30]~P4(x301)+P4(x302)+~E(x301,x302)
% 1.22/1.31 [31]P3(x312,x313)+~E(x311,x312)+~P3(x311,x313)
% 1.22/1.31 [32]P3(x323,x322)+~E(x321,x322)+~P3(x323,x321)
% 1.22/1.31 [33]P5(x332,x333)+~E(x331,x332)+~P5(x331,x333)
% 1.22/1.31 [34]P5(x343,x342)+~E(x341,x342)+~P5(x343,x341)
% 1.22/1.31 [35]P6(x352,x353)+~E(x351,x352)+~P6(x351,x353)
% 1.22/1.31 [36]P6(x363,x362)+~E(x361,x362)+~P6(x363,x361)
% 1.22/1.31
% 1.22/1.31 %-------------------------------------------
% 1.22/1.31 cnf(78,plain,
% 1.22/1.31 (~P5(x781,a1)),
% 1.22/1.31 inference(scs_inference,[],[41,47])).
% 1.22/1.31 cnf(81,plain,
% 1.22/1.31 (P2(x811,a4)),
% 1.22/1.31 inference(rename_variables,[],[41])).
% 1.22/1.31 cnf(82,plain,
% 1.22/1.31 (P4(a1)),
% 1.22/1.31 inference(scs_inference,[],[42,41,81,37,47,44,29,43])).
% 1.22/1.31 cnf(83,plain,
% 1.22/1.31 (P2(x831,a4)),
% 1.22/1.31 inference(rename_variables,[],[41])).
% 1.22/1.31 cnf(86,plain,
% 1.22/1.31 (~P1(f7(x861))),
% 1.22/1.31 inference(scs_inference,[],[42,41,81,83,37,47,44,29,43,2,45])).
% 1.22/1.31 cnf(88,plain,
% 1.22/1.31 (P2(f9(x881),f19(x881))),
% 1.22/1.31 inference(scs_inference,[],[42,41,81,83,37,47,44,29,43,2,45,52])).
% 1.22/1.31 cnf(94,plain,
% 1.22/1.31 (P2(f10(x941,x941),f6(x941,x941))),
% 1.22/1.31 inference(scs_inference,[],[42,41,81,83,37,47,44,29,43,2,45,52,34,27,55,66])).
% 1.22/1.31 cnf(96,plain,
% 1.22/1.31 (~E(f7(a1),a1)+P5(f14(a1,a1),a1)),
% 1.22/1.31 inference(scs_inference,[],[42,41,81,83,37,47,44,29,43,2,45,52,34,27,55,66,64])).
% 1.22/1.31 cnf(120,plain,
% 1.22/1.31 (~E(f7(a1),a1)),
% 1.22/1.31 inference(scs_inference,[],[78,96])).
% 1.22/1.31 cnf(121,plain,
% 1.22/1.31 (~P5(x1211,a1)),
% 1.22/1.31 inference(rename_variables,[],[78])).
% 1.22/1.31 cnf(122,plain,
% 1.22/1.31 (P2(f13(f7(x1221)),f17(f7(x1221)))),
% 1.22/1.31 inference(scs_inference,[],[41,86,78,96,53])).
% 1.22/1.31 cnf(123,plain,
% 1.22/1.31 (P2(x1231,a4)),
% 1.22/1.31 inference(rename_variables,[],[41])).
% 1.22/1.31 cnf(126,plain,
% 1.22/1.31 (P2(f9(x1261),f19(x1261))),
% 1.22/1.31 inference(rename_variables,[],[88])).
% 1.22/1.32 cnf(128,plain,
% 1.22/1.32 (P2(f10(x1281,x1281),f19(f2(x1281,x1281)))),
% 1.22/1.32 inference(scs_inference,[],[41,123,94,88,86,78,96,53,77,76])).
% 1.22/1.32 cnf(132,plain,
% 1.22/1.32 (P4(f9(f2(x1321,x1321)))),
% 1.22/1.32 inference(scs_inference,[],[41,123,94,88,126,86,78,82,96,53,77,76,30,75])).
% 1.22/1.32 cnf(133,plain,
% 1.22/1.32 (P2(f9(x1331),f19(x1331))),
% 1.22/1.32 inference(rename_variables,[],[88])).
% 1.22/1.32 cnf(135,plain,
% 1.22/1.32 (P5(a1,f7(a1))),
% 1.22/1.32 inference(scs_inference,[],[41,123,94,88,126,86,78,121,82,96,53,77,76,30,75,64])).
% 1.22/1.32 cnf(136,plain,
% 1.22/1.32 (~P5(x1361,a1)),
% 1.22/1.32 inference(rename_variables,[],[78])).
% 1.22/1.32 cnf(137,plain,
% 1.22/1.32 (P2(x1371,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(138,plain,
% 1.22/1.32 (P2(x1381,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(142,plain,
% 1.22/1.32 (P2(f9(x1421),f17(f7(x1421)))),
% 1.22/1.32 inference(scs_inference,[],[41,123,138,137,94,88,126,133,86,78,121,82,96,53,77,76,30,75,64,70,65])).
% 1.22/1.32 cnf(144,plain,
% 1.22/1.32 (P2(x1441,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(148,plain,
% 1.22/1.32 (P2(x1481,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(150,plain,
% 1.22/1.32 (P2(f10(x1501,x1502),f6(x1502,x1501))),
% 1.22/1.32 inference(scs_inference,[],[41,123,138,148,137,144,94,88,126,133,86,78,121,136,82,96,53,77,76,30,75,64,70,65,62,66])).
% 1.22/1.32 cnf(156,plain,
% 1.22/1.32 (P2(x1561,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(157,plain,
% 1.22/1.32 (P2(x1571,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(161,plain,
% 1.22/1.32 (P2(x1611,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(164,plain,
% 1.22/1.32 (P2(a1,f17(f7(a1)))),
% 1.22/1.32 inference(scs_inference,[],[41,157,161,156,128,122,150,120,135,86,42,28,75,3,69,58])).
% 1.22/1.32 cnf(165,plain,
% 1.22/1.32 (P2(x1651,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(166,plain,
% 1.22/1.32 (~P1(f7(x1661))),
% 1.22/1.32 inference(rename_variables,[],[86])).
% 1.22/1.32 cnf(167,plain,
% 1.22/1.32 (P2(x1671,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(169,plain,
% 1.22/1.32 (~P5(f7(a1),f7(a1))),
% 1.22/1.32 inference(scs_inference,[],[78,41,157,161,165,156,167,128,122,150,120,135,86,42,28,75,3,69,58,73])).
% 1.22/1.32 cnf(171,plain,
% 1.22/1.32 (P2(x1711,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(172,plain,
% 1.22/1.32 (P2(x1721,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(175,plain,
% 1.22/1.32 (~P2(f7(a1),f17(f7(a1)))),
% 1.22/1.32 inference(scs_inference,[],[78,41,157,161,165,172,156,167,128,122,150,120,135,86,166,42,28,75,3,69,58,73,59])).
% 1.22/1.32 cnf(177,plain,
% 1.22/1.32 (P2(x1771,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(179,plain,
% 1.22/1.32 (~E(a4,f17(f7(a1)))),
% 1.22/1.32 inference(scs_inference,[],[78,41,157,161,165,172,177,156,167,128,122,150,120,135,86,166,42,28,75,3,69,58,73,59,29])).
% 1.22/1.32 cnf(180,plain,
% 1.22/1.32 (P2(x1801,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(181,plain,
% 1.22/1.32 (P5(f14(f7(a1),a1),f7(a1))),
% 1.22/1.32 inference(scs_inference,[],[78,41,157,161,165,172,177,180,171,156,167,128,122,150,120,135,86,166,42,28,75,3,69,58,73,59,29,64])).
% 1.22/1.32 cnf(190,plain,
% 1.22/1.32 (~E(f14(f7(a1),a1),f7(a1))),
% 1.22/1.32 inference(scs_inference,[],[181,169,33])).
% 1.22/1.32 cnf(193,plain,
% 1.22/1.32 (P2(a1,f19(a1))),
% 1.22/1.32 inference(scs_inference,[],[41,142,175,181,169,164,33,28,69])).
% 1.22/1.32 cnf(194,plain,
% 1.22/1.32 (P2(x1941,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(196,plain,
% 1.22/1.32 (~P6(f7(a1),a1)+~P2(f7(a1),a4)),
% 1.22/1.32 inference(scs_inference,[],[78,41,194,142,175,181,169,164,135,33,28,69,71])).
% 1.22/1.32 cnf(203,plain,
% 1.22/1.32 (P2(x2031,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(204,plain,
% 1.22/1.32 (P5(f11(f7(a1),a1),f7(a1))+~P2(a1,a4)),
% 1.22/1.32 inference(scs_inference,[],[41,203,196,62])).
% 1.22/1.32 cnf(205,plain,
% 1.22/1.32 (P2(x2051,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(208,plain,
% 1.22/1.32 (P2(f14(f7(a1),a1),f17(f7(a1)))+~P2(f7(a1),a4)),
% 1.22/1.32 inference(scs_inference,[],[41,203,205,190,181,86,196,62,2,58])).
% 1.22/1.32 cnf(209,plain,
% 1.22/1.32 (P2(x2091,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(212,plain,
% 1.22/1.32 (~P5(a1,f14(f7(a1),a1))+~P2(f14(f7(a1),a1),a4)),
% 1.22/1.32 inference(scs_inference,[],[78,41,203,205,209,190,181,86,196,62,2,58,73])).
% 1.22/1.32 cnf(216,plain,
% 1.22/1.32 (~P5(a1,f14(f7(a1),a1))),
% 1.22/1.32 inference(scs_inference,[],[41,212])).
% 1.22/1.32 cnf(217,plain,
% 1.22/1.32 (P2(x2171,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(219,plain,
% 1.22/1.32 (P2(x2191,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(220,plain,
% 1.22/1.32 (P5(f11(f7(a1),a1),f7(a1))),
% 1.22/1.32 inference(scs_inference,[],[41,217,219,212,208,204])).
% 1.22/1.32 cnf(226,plain,
% 1.22/1.32 (P5(f8(f7(x2261)),f7(x2261))),
% 1.22/1.32 inference(scs_inference,[],[41,86,50])).
% 1.22/1.32 cnf(227,plain,
% 1.22/1.32 (P2(x2271,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(230,plain,
% 1.22/1.32 (~P5(x2301,a1)),
% 1.22/1.32 inference(rename_variables,[],[78])).
% 1.22/1.32 cnf(232,plain,
% 1.22/1.32 (P2(x2321,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(233,plain,
% 1.22/1.32 (~P5(x2331,a1)),
% 1.22/1.32 inference(rename_variables,[],[78])).
% 1.22/1.32 cnf(234,plain,
% 1.22/1.32 (P2(x2341,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(236,plain,
% 1.22/1.32 (P5(a1,f7(x2361))),
% 1.22/1.32 inference(scs_inference,[],[41,227,234,232,78,230,233,220,86,50,34,73,64])).
% 1.22/1.32 cnf(251,plain,
% 1.22/1.32 (P2(x2511,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(255,plain,
% 1.22/1.32 (P5(f8(f7(x2551)),f7(x2551))),
% 1.22/1.32 inference(rename_variables,[],[226])).
% 1.22/1.32 cnf(259,plain,
% 1.22/1.32 (P2(x2591,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(261,plain,
% 1.22/1.32 (~E(x2611,a3)+~P2(a1,f19(f2(a3,a5)))),
% 1.22/1.32 inference(scs_inference,[],[78,132,226,255,193,179,216,236,169,42,41,251,259,34,29,77,30,33,2,73,28])).
% 1.22/1.32 cnf(263,plain,
% 1.22/1.32 (~P2(a1,f19(f2(a3,a5)))),
% 1.22/1.32 inference(equality_inference,[],[261])).
% 1.22/1.32 cnf(534,plain,
% 1.22/1.32 (P2(x5341,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(537,plain,
% 1.22/1.32 (P2(x5371,a4)),
% 1.22/1.32 inference(rename_variables,[],[41])).
% 1.22/1.32 cnf(539,plain,
% 1.22/1.32 (~E(x5391,a1)+~P2(f7(f2(a3,a5)),a4)),
% 1.22/1.32 inference(scs_inference,[],[263,236,86,41,534,537,58,69,28])).
% 1.22/1.32 cnf(540,plain,
% 1.22/1.32 (~P2(f7(f2(a3,a5)),a4)),
% 1.22/1.32 inference(equality_inference,[],[539])).
% 1.22/1.32 cnf(541,plain,
% 1.22/1.32 ($false),
% 1.22/1.32 inference(scs_inference,[],[540,41]),
% 1.22/1.32 ['proof']).
% 1.22/1.32 % SZS output end Proof
% 1.22/1.32 % Total time :0.670000s
%------------------------------------------------------------------------------