TSTP Solution File: SET654+3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET654+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n003.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 14:30:36 EDT 2023
% Result : Theorem 0.76s 0.88s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET654+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n003.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 08:18:24 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.76/0.87 %-------------------------------------------
% 0.76/0.87 % File :CSE---1.6
% 0.76/0.87 % Problem :theBenchmark
% 0.76/0.87 % Transform :cnf
% 0.76/0.87 % Format :tptp:raw
% 0.76/0.87 % Command :java -jar mcs_scs.jar %d %s
% 0.76/0.87
% 0.76/0.87 % Result :Theorem 0.250000s
% 0.76/0.87 % Output :CNFRefutation 0.250000s
% 0.76/0.87 %-------------------------------------------
% 0.76/0.87 %--------------------------------------------------------------------------
% 0.76/0.87 % File : SET654+3 : TPTP v8.1.2. Released v2.2.0.
% 0.76/0.87 % Domain : Set Theory (Relations)
% 0.76/0.87 % Problem : Y a subset of Y1 => R (X to Y) is (X to Y1)
% 0.76/0.87 % Version : [Wor90] axioms : Reduced > Incomplete.
% 0.76/0.87 % English : If Y is a subset of Y1 then a relation R from X to Y is a
% 0.76/0.87 % relation from X to Y1.
% 0.76/0.87
% 0.76/0.87 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.76/0.87 % : [Wor90] Woronowicz (1990), Relations Defined on Sets
% 0.76/0.87 % Source : [ILF]
% 0.76/0.87 % Names : RELSET_1 (16) [Wor90]
% 0.76/0.87
% 0.76/0.87 % Status : Theorem
% 0.76/0.87 % Rating : 0.22 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.20 v7.3.0, 0.21 v7.1.0, 0.22 v7.0.0, 0.17 v6.4.0, 0.19 v6.3.0, 0.25 v6.2.0, 0.24 v6.1.0, 0.20 v6.0.0, 0.22 v5.5.0, 0.19 v5.4.0, 0.18 v5.3.0, 0.26 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 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
% 0.76/0.87 % Syntax : Number of formulae : 23 ( 1 unt; 0 def)
% 0.76/0.87 % Number of atoms : 92 ( 1 equ)
% 0.76/0.87 % Maximal formula atoms : 7 ( 4 avg)
% 0.76/0.87 % Number of connectives : 73 ( 4 ~; 0 |; 9 &)
% 0.76/0.87 % ( 6 <=>; 54 =>; 0 <=; 0 <~>)
% 0.76/0.87 % Maximal formula depth : 11 ( 6 avg)
% 0.76/0.87 % Maximal term depth : 3 ( 1 avg)
% 0.76/0.87 % Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% 0.76/0.87 % Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% 0.76/0.87 % Number of variables : 54 ( 49 !; 5 ?)
% 0.76/0.87 % SPC : FOF_THM_RFO_SEQ
% 0.76/0.87
% 0.76/0.87 % Comments :
% 0.76/0.87 %--------------------------------------------------------------------------
% 0.76/0.87 %---- line(boole - th(29),1909428)
% 0.76/0.87 fof(p1,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.87 ( ilf_type(B,set_type)
% 0.76/0.87 => ! [C] :
% 0.76/0.87 ( ilf_type(C,set_type)
% 0.76/0.87 => ! [D] :
% 0.76/0.87 ( ilf_type(D,set_type)
% 0.76/0.87 => ( ( subset(B,C)
% 0.76/0.87 & subset(C,D) )
% 0.76/0.87 => subset(B,D) ) ) ) ) ).
% 0.76/0.87
% 0.76/0.87 %---- line(relset_1 - th(12),1916203)
% 0.76/0.87 fof(p2,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.87 ( ilf_type(B,set_type)
% 0.76/0.87 => ! [C] :
% 0.76/0.87 ( ilf_type(C,set_type)
% 0.76/0.87 => ! [D] :
% 0.76/0.87 ( ilf_type(D,relation_type(B,C))
% 0.76/0.87 => ( subset(domain_of(D),B)
% 0.76/0.87 & subset(range_of(D),C) ) ) ) ) ).
% 0.76/0.87
% 0.76/0.87 %---- line(relset_1 - th(14),1916237)
% 0.76/0.87 fof(p3,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.87 ( ilf_type(B,set_type)
% 0.76/0.87 => ! [C] :
% 0.76/0.87 ( ilf_type(C,set_type)
% 0.76/0.87 => ! [D] :
% 0.76/0.87 ( ilf_type(D,set_type)
% 0.76/0.87 => ! [E] :
% 0.76/0.87 ( ilf_type(E,relation_type(D,B))
% 0.76/0.87 => ( subset(range_of(E),C)
% 0.76/0.87 => ilf_type(E,relation_type(D,C)) ) ) ) ) ) ).
% 0.76/0.87
% 0.76/0.87 %---- line(relset_1 - df(1),1916080)
% 0.76/0.87 fof(p4,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.87 ( ilf_type(B,set_type)
% 0.76/0.87 => ! [C] :
% 0.76/0.87 ( ilf_type(C,set_type)
% 0.76/0.87 => ( ! [D] :
% 0.76/0.87 ( ilf_type(D,subset_type(cross_product(B,C)))
% 0.76/0.87 => ilf_type(D,relation_type(B,C)) )
% 0.76/0.87 & ! [E] :
% 0.76/0.87 ( ilf_type(E,relation_type(B,C))
% 0.76/0.87 => ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ) ).
% 0.76/0.87
% 0.76/0.87 %---- type_nonempty(line(relset_1 - df(1),1916080))
% 0.76/0.87 fof(p5,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.87 ( ilf_type(B,set_type)
% 0.76/0.87 => ! [C] :
% 0.76/0.87 ( ilf_type(C,set_type)
% 0.76/0.87 => ? [D] : ilf_type(D,relation_type(C,B)) ) ) ).
% 0.76/0.87
% 0.76/0.87 %---- line(tarski - df(3),1832749)
% 0.76/0.87 fof(p6,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.87 ( ilf_type(B,set_type)
% 0.76/0.87 => ! [C] :
% 0.76/0.87 ( ilf_type(C,set_type)
% 0.76/0.87 => ( subset(B,C)
% 0.76/0.87 <=> ! [D] :
% 0.76/0.87 ( ilf_type(D,set_type)
% 0.76/0.87 => ( member(D,B)
% 0.76/0.87 => member(D,C) ) ) ) ) ) ).
% 0.76/0.87
% 0.76/0.87 %---- declaration(op(domain_of,1,function))
% 0.76/0.87 fof(p7,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.87 ( ilf_type(B,binary_relation_type)
% 0.76/0.87 => ilf_type(domain_of(B),set_type) ) ).
% 0.76/0.87
% 0.76/0.87 %---- declaration(op(cross_product,2,function))
% 0.76/0.87 fof(p8,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.87 ( ilf_type(B,set_type)
% 0.76/0.87 => ! [C] :
% 0.76/0.87 ( ilf_type(C,set_type)
% 0.76/0.87 => ilf_type(cross_product(B,C),set_type) ) ) ).
% 0.76/0.87
% 0.76/0.87 %---- declaration(op(range_of,1,function))
% 0.76/0.87 fof(p9,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.87 ( ilf_type(B,binary_relation_type)
% 0.76/0.87 => ilf_type(range_of(B),set_type) ) ).
% 0.76/0.87
% 0.76/0.87 %---- line(hidden - axiom123,1832648)
% 0.76/0.87 fof(p10,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.87 ( ilf_type(B,set_type)
% 0.76/0.87 => ! [C] :
% 0.76/0.87 ( ilf_type(C,set_type)
% 0.76/0.87 => ( ilf_type(C,subset_type(B))
% 0.76/0.87 <=> ilf_type(C,member_type(power_set(B))) ) ) ) ).
% 0.76/0.87
% 0.76/0.87 %---- type_nonempty(line(hidden - axiom123,1832648))
% 0.76/0.87 fof(p11,axiom,
% 0.76/0.87 ! [B] :
% 0.76/0.88 ( ilf_type(B,set_type)
% 0.76/0.88 => ? [C] : ilf_type(C,subset_type(B)) ) ).
% 0.76/0.88
% 0.76/0.88 %---- property(reflexivity,op(subset,2,predicate))
% 0.76/0.88 fof(p12,axiom,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ilf_type(B,set_type)
% 0.76/0.88 => subset(B,B) ) ).
% 0.76/0.88
% 0.76/0.88 %---- line(hidden - axiom125,1832644)
% 0.76/0.88 fof(p13,axiom,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ilf_type(B,set_type)
% 0.76/0.88 => ! [C] :
% 0.76/0.88 ( ilf_type(C,set_type)
% 0.76/0.88 => ( member(B,power_set(C))
% 0.76/0.88 <=> ! [D] :
% 0.76/0.88 ( ilf_type(D,set_type)
% 0.76/0.88 => ( member(D,B)
% 0.76/0.88 => member(D,C) ) ) ) ) ) ).
% 0.76/0.88
% 0.76/0.88 %---- declaration(line(hidden - axiom125,1832644))
% 0.76/0.88 fof(p14,axiom,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ilf_type(B,set_type)
% 0.76/0.88 => ( ~ empty(power_set(B))
% 0.76/0.88 & ilf_type(power_set(B),set_type) ) ) ).
% 0.76/0.88
% 0.76/0.88 %---- line(hidden - axiom126,1832640)
% 0.76/0.88 fof(p15,axiom,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ilf_type(B,set_type)
% 0.76/0.88 => ! [C] :
% 0.76/0.88 ( ( ~ empty(C)
% 0.76/0.88 & ilf_type(C,set_type) )
% 0.76/0.88 => ( ilf_type(B,member_type(C))
% 0.76/0.88 <=> member(B,C) ) ) ) ).
% 0.76/0.88
% 0.76/0.88 %---- type_nonempty(line(hidden - axiom126,1832640))
% 0.76/0.88 fof(p16,axiom,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ( ~ empty(B)
% 0.76/0.88 & ilf_type(B,set_type) )
% 0.76/0.88 => ? [C] : ilf_type(C,member_type(B)) ) ).
% 0.76/0.88
% 0.76/0.88 %---- line(hidden - axiom127,1832628)
% 0.76/0.88 fof(p17,axiom,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ilf_type(B,set_type)
% 0.76/0.88 => ( empty(B)
% 0.76/0.88 <=> ! [C] :
% 0.76/0.88 ( ilf_type(C,set_type)
% 0.76/0.88 => ~ member(C,B) ) ) ) ).
% 0.76/0.88
% 0.76/0.88 %---- line(relat_1 - df(1),1917627)
% 0.76/0.88 fof(p18,axiom,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ilf_type(B,set_type)
% 0.76/0.88 => ( relation_like(B)
% 0.76/0.88 <=> ! [C] :
% 0.76/0.88 ( ilf_type(C,set_type)
% 0.76/0.88 => ( member(C,B)
% 0.76/0.88 => ? [D] :
% 0.76/0.88 ( ilf_type(D,set_type)
% 0.76/0.88 & ? [E] :
% 0.76/0.88 ( ilf_type(E,set_type)
% 0.76/0.88 & C = ordered_pair(D,E) ) ) ) ) ) ) ).
% 0.76/0.88
% 0.76/0.88 %---- conditional_cluster(axiom129,relation_like)
% 0.76/0.88 fof(p19,axiom,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ( empty(B)
% 0.76/0.88 & ilf_type(B,set_type) )
% 0.76/0.88 => relation_like(B) ) ).
% 0.76/0.88
% 0.76/0.88 %---- conditional_cluster(axiom130,relation_like)
% 0.76/0.88 fof(p20,axiom,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ilf_type(B,set_type)
% 0.76/0.88 => ! [C] :
% 0.76/0.88 ( ilf_type(C,set_type)
% 0.76/0.88 => ! [D] :
% 0.76/0.88 ( ilf_type(D,subset_type(cross_product(B,C)))
% 0.76/0.88 => relation_like(D) ) ) ) ).
% 0.76/0.88
% 0.76/0.88 %---- declaration(op(ordered_pair,2,function))
% 0.76/0.88 fof(p21,axiom,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ilf_type(B,set_type)
% 0.76/0.88 => ! [C] :
% 0.76/0.88 ( ilf_type(C,set_type)
% 0.76/0.88 => ilf_type(ordered_pair(B,C),set_type) ) ) ).
% 0.76/0.88
% 0.76/0.88 %---- declaration(set)
% 0.76/0.88 fof(p22,axiom,
% 0.76/0.88 ! [B] : ilf_type(B,set_type) ).
% 0.76/0.88
% 0.76/0.88 %---- line(relset_1 - th(16),1916267)
% 0.76/0.88 fof(prove_relset_1_16,conjecture,
% 0.76/0.88 ! [B] :
% 0.76/0.88 ( ilf_type(B,set_type)
% 0.76/0.88 => ! [C] :
% 0.76/0.88 ( ilf_type(C,set_type)
% 0.76/0.88 => ! [D] :
% 0.76/0.88 ( ilf_type(D,set_type)
% 0.76/0.88 => ! [E] :
% 0.76/0.88 ( ilf_type(E,relation_type(D,B))
% 0.76/0.88 => ( subset(B,C)
% 0.76/0.88 => ilf_type(E,relation_type(D,C)) ) ) ) ) ) ).
% 0.76/0.88
% 0.76/0.88 %--------------------------------------------------------------------------
% 0.76/0.88 %-------------------------------------------
% 0.76/0.88 % Proof found
% 0.76/0.88 % SZS status Theorem for theBenchmark
% 0.76/0.88 % SZS output start Proof
% 0.76/0.88 %ClaNum:82(EqnAxiom:36)
% 0.76/0.88 %VarNum:180(SingletonVarNum:61)
% 0.76/0.88 %MaxLitNum:6
% 0.76/0.88 %MaxfuncDepth:2
% 0.76/0.88 %SharedTerms:14
% 0.76/0.88 %goalClause: 40 42 43
% 0.76/0.88 %singleGoalClaCount:3
% 0.76/0.88 [40]P3(a1,a6)
% 0.76/0.88 [42]P1(a8,f9(a7,a1))
% 0.76/0.88 [43]~P1(a8,f9(a7,a6))
% 0.76/0.88 [41]P1(x411,a5)
% 0.76/0.88 [45]P3(x451,x451)+~P1(x451,a5)
% 0.76/0.88 [46]~P1(x461,a5)+~P2(f10(x461))
% 0.76/0.88 [54]~P1(x541,a5)+P1(f12(x541),f23(x541))
% 0.76/0.88 [44]~P2(x441)+P4(x441)+~P1(x441,a5)
% 0.76/0.88 [52]P2(x521)+P5(f11(x521),x521)+~P1(x521,a5)
% 0.76/0.88 [53]P4(x531)+P5(f17(x531),x531)+~P1(x531,a5)
% 0.76/0.88 [55]P2(x551)+P1(f15(x551),f20(x551))+~P1(x551,a5)
% 0.76/0.88 [67]~P1(x672,a5)+~P1(x671,a5)+P1(f14(x671,x672),f9(x672,x671))
% 0.76/0.88 [56]~P2(x561)+~P5(x562,x561)+~P1(x562,a5)+~P1(x561,a5)
% 0.76/0.88 [63]P3(x631,x632)+P5(f13(x631,x632),x631)+~P1(x632,a5)+~P1(x631,a5)
% 0.76/0.88 [65]P5(f16(x651,x652),x651)+~P1(x652,a5)+~P1(x651,a5)+P5(x651,f10(x652))
% 0.76/0.88 [71]P3(x711,x712)+~P1(x712,a5)+~P1(x711,a5)+~P5(f13(x711,x712),x712)
% 0.76/0.88 [74]~P1(x742,a5)+~P1(x741,a5)+~P5(f16(x741,x742),x742)+P5(x741,f10(x742))
% 0.76/0.88 [66]~P1(x662,a5)+~P1(x661,a5)+~P1(x661,f23(x662))+P1(x661,f20(f10(x662)))
% 0.76/0.88 [70]~P1(x702,a5)+~P1(x701,a5)+P1(x701,f23(x702))+~P1(x701,f20(f10(x702)))
% 0.76/0.88 [75]~P1(x752,a5)+~P1(x751,f9(x752,x753))+P3(f2(x751),x752)+~P1(x753,a5)
% 0.76/0.88 [76]~P1(x762,a5)+~P1(x761,f9(x763,x762))+P3(f22(x761),x762)+~P1(x763,a5)
% 0.76/0.88 [79]P4(x791)+~P1(x792,a5)+~P1(x793,a5)+~P1(x791,f23(f4(x793,x792)))
% 0.76/0.88 [80]~P1(x803,a5)+~P1(x802,a5)+~P1(x801,f9(x802,x803))+P1(x801,f23(f4(x802,x803)))
% 0.76/0.88 [81]~P1(x813,a5)+~P1(x812,a5)+P1(x811,f9(x812,x813))+~P1(x811,f23(f4(x812,x813)))
% 0.76/0.88 [59]~P5(x592,x591)+P2(x591)+~P1(x591,a5)+~P1(x592,a5)+P1(x592,f20(x591))
% 0.76/0.88 [60]P2(x601)+P5(x602,x601)+~P1(x601,a5)+~P1(x602,a5)+~P1(x602,f20(x601))
% 0.76/0.88 [78]~P4(x781)+~P5(x782,x781)+~P1(x781,a5)+~P1(x782,a5)+E(f21(f18(x781,x782),f19(x781,x782)),x782)
% 0.76/0.88 [62]P4(x621)+~P1(x621,a5)+~P1(x623,a5)+~P1(x622,a5)+~E(f17(x621),f21(x622,x623))
% 0.76/0.88 [72]~P3(x721,x723)+P3(x721,x722)+~P3(x723,x722)+~P1(x722,a5)+~P1(x723,a5)+~P1(x721,a5)
% 0.76/0.88 [73]~P5(x731,x733)+P5(x731,x732)+~P3(x733,x732)+~P1(x731,a5)+~P1(x732,a5)+~P1(x733,a5)
% 0.76/0.88 [77]P5(x771,x772)+~P5(x771,x773)+~P1(x771,a5)+~P1(x772,a5)+~P1(x773,a5)+~P5(x773,f10(x772))
% 0.76/0.88 [82]~P1(x822,a5)+~P1(x823,a5)+~P3(f22(x821),x823)+~P1(x821,f9(x822,x824))+P1(x821,f9(x822,x823))+~P1(x824,a5)
% 0.76/0.88 %EqnAxiom
% 0.76/0.88 [1]E(x11,x11)
% 0.76/0.88 [2]E(x22,x21)+~E(x21,x22)
% 0.76/0.88 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.76/0.88 [4]~E(x41,x42)+E(f9(x41,x43),f9(x42,x43))
% 0.76/0.88 [5]~E(x51,x52)+E(f9(x53,x51),f9(x53,x52))
% 0.76/0.88 [6]~E(x61,x62)+E(f22(x61),f22(x62))
% 0.76/0.88 [7]~E(x71,x72)+E(f10(x71),f10(x72))
% 0.76/0.88 [8]~E(x81,x82)+E(f2(x81),f2(x82))
% 0.76/0.88 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 0.76/0.88 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 0.76/0.88 [11]~E(x111,x112)+E(f16(x111,x113),f16(x112,x113))
% 0.76/0.88 [12]~E(x121,x122)+E(f16(x123,x121),f16(x123,x122))
% 0.76/0.88 [13]~E(x131,x132)+E(f11(x131),f11(x132))
% 0.76/0.88 [14]~E(x141,x142)+E(f17(x141),f17(x142))
% 0.76/0.88 [15]~E(x151,x152)+E(f23(x151),f23(x152))
% 0.76/0.88 [16]~E(x161,x162)+E(f18(x161,x163),f18(x162,x163))
% 0.76/0.88 [17]~E(x171,x172)+E(f18(x173,x171),f18(x173,x172))
% 0.76/0.88 [18]~E(x181,x182)+E(f12(x181),f12(x182))
% 0.76/0.88 [19]~E(x191,x192)+E(f14(x191,x193),f14(x192,x193))
% 0.76/0.88 [20]~E(x201,x202)+E(f14(x203,x201),f14(x203,x202))
% 0.76/0.88 [21]~E(x211,x212)+E(f15(x211),f15(x212))
% 0.76/0.88 [22]~E(x221,x222)+E(f20(x221),f20(x222))
% 0.76/0.88 [23]~E(x231,x232)+E(f19(x231,x233),f19(x232,x233))
% 0.76/0.88 [24]~E(x241,x242)+E(f19(x243,x241),f19(x243,x242))
% 0.76/0.88 [25]~E(x251,x252)+E(f21(x251,x253),f21(x252,x253))
% 0.76/0.88 [26]~E(x261,x262)+E(f21(x263,x261),f21(x263,x262))
% 0.76/0.88 [27]~E(x271,x272)+E(f13(x271,x273),f13(x272,x273))
% 0.76/0.88 [28]~E(x281,x282)+E(f13(x283,x281),f13(x283,x282))
% 0.76/0.88 [29]P1(x292,x293)+~E(x291,x292)+~P1(x291,x293)
% 0.76/0.88 [30]P1(x303,x302)+~E(x301,x302)+~P1(x303,x301)
% 0.76/0.88 [31]P3(x312,x313)+~E(x311,x312)+~P3(x311,x313)
% 0.76/0.88 [32]P3(x323,x322)+~E(x321,x322)+~P3(x323,x321)
% 0.76/0.88 [33]~P4(x331)+P4(x332)+~E(x331,x332)
% 0.76/0.88 [34]P5(x342,x343)+~E(x341,x342)+~P5(x341,x343)
% 0.76/0.88 [35]P5(x353,x352)+~E(x351,x352)+~P5(x353,x351)
% 0.76/0.88 [36]~P2(x361)+P2(x362)+~E(x361,x362)
% 0.76/0.88
% 0.76/0.88 %-------------------------------------------
% 0.76/0.88 cnf(85,plain,
% 0.76/0.88 (P1(x851,a5)),
% 0.76/0.88 inference(rename_variables,[],[41])).
% 0.76/0.88 cnf(86,plain,
% 0.76/0.88 (~E(f9(a7,a6),a5)),
% 0.76/0.88 inference(scs_inference,[],[41,43,45,30,2])).
% 0.76/0.88 cnf(87,plain,
% 0.76/0.88 (~P2(f10(x871))),
% 0.76/0.88 inference(scs_inference,[],[41,85,43,45,30,2,46])).
% 0.76/0.88 cnf(89,plain,
% 0.76/0.88 (P1(f12(x891),f23(x891))),
% 0.76/0.88 inference(scs_inference,[],[41,85,43,45,30,2,46,54])).
% 0.76/0.88 cnf(91,plain,
% 0.76/0.88 (~P1(x911,f9(a7,a6))+~E(x911,a8)),
% 0.76/0.88 inference(scs_inference,[],[41,85,43,45,30,2,46,54,29])).
% 0.76/0.88 cnf(92,plain,
% 0.76/0.88 (P1(f14(x921,x921),f9(x921,x921))),
% 0.76/0.88 inference(scs_inference,[],[41,85,43,45,30,2,46,54,29,67])).
% 0.76/0.88 cnf(94,plain,
% 0.76/0.88 (P3(f22(f14(x941,x941)),x941)),
% 0.76/0.88 inference(scs_inference,[],[41,85,43,45,30,2,46,54,29,67,76])).
% 0.76/0.88 cnf(96,plain,
% 0.76/0.88 (P3(f2(f14(x961,x961)),x961)),
% 0.76/0.88 inference(scs_inference,[],[41,85,43,45,30,2,46,54,29,67,76,75])).
% 0.76/0.88 cnf(99,plain,
% 0.76/0.88 (~P1(f10(x991),a5)+P5(f11(f10(x991)),f10(x991))),
% 0.76/0.88 inference(scs_inference,[],[41,85,43,45,30,2,46,54,29,67,76,75,36,52])).
% 0.76/0.88 cnf(101,plain,
% 0.76/0.88 (~P1(f10(x1011),a5)+P1(f15(f10(x1011)),f20(f10(x1011)))),
% 0.76/0.88 inference(scs_inference,[],[41,85,43,45,30,2,46,54,29,67,76,75,36,52,55])).
% 0.76/0.88 cnf(103,plain,
% 0.76/0.88 (P4(x1031)+~P1(x1031,f23(f4(x1032,x1032)))),
% 0.76/0.88 inference(scs_inference,[],[41,85,43,45,30,2,46,54,29,67,76,75,36,52,55,79])).
% 0.76/0.88 cnf(122,plain,
% 0.76/0.88 (P1(f12(x1221),f23(x1221))),
% 0.76/0.88 inference(rename_variables,[],[89])).
% 0.76/0.88 cnf(124,plain,
% 0.76/0.88 (P1(f15(f10(x1241)),f20(f10(x1241)))),
% 0.76/0.88 inference(scs_inference,[],[41,89,103,101])).
% 0.76/0.88 cnf(125,plain,
% 0.76/0.88 (P1(x1251,a5)),
% 0.76/0.88 inference(rename_variables,[],[41])).
% 0.76/0.88 cnf(127,plain,
% 0.76/0.88 (P1(x1271,a5)),
% 0.76/0.88 inference(rename_variables,[],[41])).
% 0.76/0.88 cnf(131,plain,
% 0.76/0.88 (P1(f14(x1311,x1311),f23(f4(x1311,x1311)))),
% 0.76/0.88 inference(scs_inference,[],[41,125,127,92,89,122,103,101,99,81,80])).
% 0.76/0.88 cnf(132,plain,
% 0.76/0.88 (P1(x1321,a5)),
% 0.76/0.88 inference(rename_variables,[],[41])).
% 0.76/0.88 cnf(133,plain,
% 0.76/0.88 (P1(x1331,a5)),
% 0.76/0.88 inference(rename_variables,[],[41])).
% 0.76/0.88 cnf(135,plain,
% 0.76/0.88 (P1(f14(x1351,x1352),f9(x1352,x1351))),
% 0.76/0.88 inference(scs_inference,[],[41,125,127,133,132,92,89,122,103,101,99,81,80,67])).
% 0.76/0.88 cnf(138,plain,
% 0.76/0.88 (P1(x1381,a5)),
% 0.76/0.88 inference(rename_variables,[],[41])).
% 0.76/0.88 cnf(139,plain,
% 0.76/0.88 (P1(x1391,a5)),
% 0.76/0.88 inference(rename_variables,[],[41])).
% 0.76/0.88 cnf(141,plain,
% 0.76/0.88 (~E(f9(a7,a1),f9(a7,a6))),
% 0.76/0.88 inference(scs_inference,[],[42,41,125,127,133,132,43,92,89,122,103,101,99,81,80,67,75,30])).
% 0.76/0.88 cnf(142,plain,
% 0.76/0.88 (~E(a1,a6)),
% 0.76/0.88 inference(scs_inference,[],[42,41,125,127,133,132,43,92,89,122,103,101,99,81,80,67,75,30,5])).
% 0.76/0.88 cnf(144,plain,
% 0.76/0.88 (P5(f15(f10(x1441)),f10(x1441))),
% 0.76/0.88 inference(scs_inference,[],[42,41,125,127,133,138,132,139,43,92,89,122,87,103,101,99,81,80,67,75,30,5,33,60])).
% 0.76/0.88 cnf(147,plain,
% 0.76/0.88 (P1(x1471,a5)),
% 0.76/0.88 inference(rename_variables,[],[41])).
% 0.76/0.88 cnf(149,plain,
% 0.76/0.88 (P1(f11(f10(x1491)),f20(f10(x1491)))+~P1(f10(x1491),a5)),
% 0.76/0.88 inference(scs_inference,[],[42,41,125,127,133,138,132,139,147,43,92,89,122,87,103,101,99,81,80,67,75,30,5,33,60,65,59])).
% 0.76/0.88 cnf(155,plain,
% 0.76/0.88 (P5(f10(x1551),f10(f10(x1551)))+~P1(f10(x1551),a5)),
% 0.76/0.88 inference(scs_inference,[],[40,42,41,125,127,133,138,132,139,147,43,92,89,122,87,103,101,99,81,80,67,75,30,5,33,60,65,59,73,72,74])).
% 0.76/0.88 cnf(161,plain,
% 0.76/0.88 (P1(x1611,a5)),
% 0.76/0.88 inference(rename_variables,[],[41])).
% 0.76/0.88 cnf(162,plain,
% 0.76/0.88 (P1(f11(f10(x1621)),f20(f10(x1621)))),
% 0.76/0.88 inference(scs_inference,[],[41,161,155,149])).
% 0.76/0.88 cnf(163,plain,
% 0.76/0.88 (P1(x1631,a5)),
% 0.76/0.88 inference(rename_variables,[],[41])).
% 0.76/0.88 cnf(167,plain,
% 0.76/0.88 (P4(f14(x1671,x1671))),
% 0.76/0.88 inference(scs_inference,[],[41,161,163,131,135,141,155,149,91,3,79])).
% 0.76/0.88 cnf(206,plain,
% 0.76/0.88 (P1(f15(f10(x2061)),f23(x2061))+~P1(x2061,a5)),
% 0.76/0.88 inference(scs_inference,[],[41,124,70])).
% 0.76/0.88 cnf(245,plain,
% 0.76/0.88 (P1(f15(f10(x2451)),f23(x2451))),
% 0.76/0.88 inference(scs_inference,[],[41,206])).
% 0.76/0.88 cnf(292,plain,
% 0.76/0.88 (~P1(a1,a5)+P1(a8,f23(f4(a7,a1)))),
% 0.76/0.88 inference(scs_inference,[],[41,42,80])).
% 0.76/0.88 cnf(302,plain,
% 0.76/0.88 (P1(a8,f23(f4(a7,a1)))),
% 0.76/0.88 inference(scs_inference,[],[41,292])).
% 0.76/0.88 cnf(303,plain,
% 0.76/0.88 (P1(x3031,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(305,plain,
% 0.76/0.89 (~P1(f12(x3051),a5)+P1(f12(x3051),f20(f10(x3051)))),
% 0.76/0.89 inference(scs_inference,[],[41,303,245,89,292,29,66])).
% 0.76/0.89 cnf(314,plain,
% 0.76/0.89 (P1(x3141,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(317,plain,
% 0.76/0.89 (P1(x3171,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(323,plain,
% 0.76/0.89 (P5(f12(x3231),f10(x3231))+~P1(f12(x3231),a5)),
% 0.76/0.89 inference(scs_inference,[],[87,167,142,302,43,41,314,317,305,30,81,2,33,66,60])).
% 0.76/0.89 cnf(324,plain,
% 0.76/0.89 (P1(x3241,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(326,plain,
% 0.76/0.89 (~E(x3261,a7)+~P1(a8,f23(f4(a7,a6)))),
% 0.76/0.89 inference(scs_inference,[],[87,167,142,302,43,41,314,317,324,305,30,81,2,33,66,60,29])).
% 0.76/0.89 cnf(328,plain,
% 0.76/0.89 (~P1(a8,f23(f4(a7,a6)))),
% 0.76/0.89 inference(equality_inference,[],[326])).
% 0.76/0.89 cnf(330,plain,
% 0.76/0.89 (P1(x3301,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(331,plain,
% 0.76/0.89 (P1(f11(f10(x3311)),f23(x3311))+~P1(f11(f10(x3311)),a5)),
% 0.76/0.89 inference(scs_inference,[],[162,41,330,323,70])).
% 0.76/0.89 cnf(335,plain,
% 0.76/0.89 (P4(a8)+~P1(a1,a5)),
% 0.76/0.89 inference(scs_inference,[],[86,302,162,41,330,323,70,3,79])).
% 0.76/0.89 cnf(336,plain,
% 0.76/0.89 (P1(x3361,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(338,plain,
% 0.76/0.89 (P3(f22(a8),a1)+~P1(a1,a5)),
% 0.76/0.89 inference(scs_inference,[],[86,302,162,42,41,330,336,323,70,3,79,76])).
% 0.76/0.89 cnf(345,plain,
% 0.76/0.89 (P1(f11(f10(x3451)),f23(x3451))),
% 0.76/0.89 inference(scs_inference,[],[41,331])).
% 0.76/0.89 cnf(346,plain,
% 0.76/0.89 (P1(x3461,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(347,plain,
% 0.76/0.89 (P3(f22(a8),a1)),
% 0.76/0.89 inference(scs_inference,[],[41,346,331,338])).
% 0.76/0.89 cnf(348,plain,
% 0.76/0.89 (P1(x3481,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(349,plain,
% 0.76/0.89 (P4(a8)),
% 0.76/0.89 inference(scs_inference,[],[41,346,348,331,338,335])).
% 0.76/0.89 cnf(363,plain,
% 0.76/0.89 (~E(f12(f4(a7,a6)),a8)),
% 0.76/0.89 inference(scs_inference,[],[89,328,29])).
% 0.76/0.89 cnf(364,plain,
% 0.76/0.89 (P1(f12(x3641),f23(x3641))),
% 0.76/0.89 inference(rename_variables,[],[89])).
% 0.76/0.89 cnf(366,plain,
% 0.76/0.89 (P1(x3661,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(367,plain,
% 0.76/0.89 (P1(x3671,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(369,plain,
% 0.76/0.89 (P1(f12(f4(x3691,x3692)),f9(x3691,x3692))),
% 0.76/0.89 inference(scs_inference,[],[89,364,349,328,41,367,366,29,78,81])).
% 0.76/0.89 cnf(390,plain,
% 0.76/0.89 (~E(f23(f4(a7,a1)),f23(f4(a7,a6)))),
% 0.76/0.89 inference(scs_inference,[],[328,302,30])).
% 0.76/0.89 cnf(393,plain,
% 0.76/0.89 (P1(x3931,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(394,plain,
% 0.76/0.89 (P1(x3941,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(396,plain,
% 0.76/0.89 (P3(x3961,x3962)+P5(f13(x3961,x3962),x3961)),
% 0.76/0.89 inference(scs_inference,[],[87,328,302,41,394,393,30,15,59,63])).
% 0.76/0.89 cnf(409,plain,
% 0.76/0.89 (P1(x4091,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(411,plain,
% 0.76/0.89 (~P5(f2(f14(x4111,x4111)),f2(f14(x4111,x4111)))+~P5(f9(x4112,x4113),f9(x4112,x4113))+~P2(f9(x4112,x4114))+P5(f2(f14(x4111,x4111)),x4111)+~P1(x4111,a5)),
% 0.76/0.89 inference(scs_inference,[],[96,41,409,56,55,36,5,52,73])).
% 0.76/0.89 cnf(427,plain,
% 0.76/0.89 (~P1(a1,a5)+~P3(f22(a8),a6)+~P1(a6,a5)),
% 0.76/0.89 inference(scs_inference,[],[345,363,43,42,41,2,30,411,82])).
% 0.76/0.89 cnf(428,plain,
% 0.76/0.89 (P1(x4281,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(432,plain,
% 0.76/0.89 (~P1(a1,a5)+~P1(a8,f9(a6,a6))+~P1(a6,a5)),
% 0.76/0.89 inference(scs_inference,[],[345,363,144,43,42,41,428,2,30,411,82,3,34,76])).
% 0.76/0.89 cnf(442,plain,
% 0.76/0.89 (~P1(a1,a5)+~P1(a8,f9(a6,a6))),
% 0.76/0.89 inference(scs_inference,[],[41,432])).
% 0.76/0.89 cnf(465,plain,
% 0.76/0.89 (~P1(a6,a5)+~P3(f22(a8),a6)),
% 0.76/0.89 inference(scs_inference,[],[41,427])).
% 0.76/0.89 cnf(468,plain,
% 0.76/0.89 (P1(x4681,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(470,plain,
% 0.76/0.89 (P1(x4701,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(480,plain,
% 0.76/0.89 (P1(x4801,a5)),
% 0.76/0.89 inference(rename_variables,[],[41])).
% 0.76/0.89 cnf(482,plain,
% 0.76/0.89 (~P1(a1,a5)+~P1(a6,a5)),
% 0.76/0.89 inference(scs_inference,[],[94,390,369,347,40,302,41,468,470,480,2,465,442,396,31,29,30,6,71,72])).
% 0.76/0.89 cnf(498,plain,
% 0.76/0.89 (~P1(a6,a5)),
% 0.76/0.89 inference(scs_inference,[],[41,482])).
% 0.76/0.89 cnf(521,plain,
% 0.76/0.89 ($false),
% 0.76/0.89 inference(scs_inference,[],[498,41]),
% 0.76/0.89 ['proof']).
% 0.76/0.89 % SZS output end Proof
% 0.76/0.89 % Total time :0.250000s
%------------------------------------------------------------------------------