TSTP Solution File: SEU424+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU424+1 : TPTP v8.1.2. Released v3.4.0.
% 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 16:19:55 EDT 2023
% Result : Theorem 0.20s 0.66s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU424+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 01:25:50 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.59 start to proof:theBenchmark
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % File :CSE---1.6
% 0.20/0.65 % Problem :theBenchmark
% 0.20/0.65 % Transform :cnf
% 0.20/0.65 % Format :tptp:raw
% 0.20/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.65
% 0.20/0.65 % Result :Theorem 0.000000s
% 0.20/0.65 % Output :CNFRefutation 0.000000s
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 % File : SEU424+1 : TPTP v8.1.2. Released v3.4.0.
% 0.20/0.66 % Domain : Set Theory
% 0.20/0.66 % Problem : First and Second Order Cutting of Binary Relations T18
% 0.20/0.66 % Version : [Urb08] axioms : Especial.
% 0.20/0.66 % English :
% 0.20/0.66
% 0.20/0.66 % Refs : [Ret05] Retel (2005), Properties of First and Second Order Cut
% 0.20/0.66 % : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% 0.20/0.66 % : [Urb08] Urban (2006), Email to G. Sutcliffe
% 0.20/0.66 % Source : [Urb08]
% 0.20/0.66 % Names : t18_relset_2 [Urb08]
% 0.20/0.66
% 0.20/0.66 % Status : Theorem
% 0.20/0.66 % Rating : 0.11 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.1.0, 0.13 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.10 v5.1.0, 0.14 v5.0.0, 0.17 v4.1.0, 0.22 v4.0.1, 0.26 v4.0.0, 0.29 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0
% 0.20/0.66 % Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% 0.20/0.66 % Number of atoms : 91 ( 6 equ)
% 0.20/0.66 % Maximal formula atoms : 7 ( 2 avg)
% 0.20/0.66 % Number of connectives : 64 ( 16 ~; 1 |; 22 &)
% 0.20/0.66 % ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% 0.20/0.66 % Maximal formula depth : 11 ( 4 avg)
% 0.20/0.66 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.66 % Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% 0.20/0.66 % Number of functors : 8 ( 8 usr; 1 con; 0-4 aty)
% 0.20/0.66 % Number of variables : 85 ( 76 !; 9 ?)
% 0.20/0.66 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.66
% 0.20/0.66 % Comments : Normal version: includes the axioms (which may be theorems from
% 0.20/0.66 % other articles) and background that are possibly necessary.
% 0.20/0.66 % : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% 0.20/0.66 % : The problem encoding is based on set theory.
% 0.20/0.66 %------------------------------------------------------------------------------
% 0.20/0.66 fof(t18_relset_2,conjecture,
% 0.20/0.66 ! [A] :
% 0.20/0.66 ( ~ v1_xboole_0(A)
% 0.20/0.66 => ! [B,C] :
% 0.20/0.66 ( m1_subset_1(C,k1_zfmisc_1(A))
% 0.20/0.66 => ! [D] :
% 0.20/0.66 ( m2_relset_1(D,A,B)
% 0.20/0.66 => m1_subset_1(a_4_0_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(antisymmetry_r2_hidden,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( r2_hidden(A,B)
% 0.20/0.66 => ~ r2_hidden(B,A) ) ).
% 0.20/0.66
% 0.20/0.66 fof(cc1_relat_1,axiom,
% 0.20/0.66 ! [A] :
% 0.20/0.66 ( v1_xboole_0(A)
% 0.20/0.66 => v1_relat_1(A) ) ).
% 0.20/0.66
% 0.20/0.66 fof(cc1_relset_1,axiom,
% 0.20/0.66 ! [A,B,C] :
% 0.20/0.66 ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
% 0.20/0.66 => v1_relat_1(C) ) ).
% 0.20/0.66
% 0.20/0.66 fof(d1_relset_2,axiom,
% 0.20/0.66 ! [A,B,C] :
% 0.20/0.66 ( m2_relset_1(C,A,B)
% 0.20/0.66 => ! [D] :
% 0.20/0.66 ( m1_subset_1(D,A)
% 0.20/0.66 => k2_relset_2(A,B,C,D) = k10_relset_1(A,B,C,k1_tarski(D)) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(dt_k10_relset_1,axiom,
% 0.20/0.66 ! [A,B,C,D] :
% 0.20/0.66 ( m1_relset_1(C,A,B)
% 0.20/0.66 => m1_subset_1(k10_relset_1(A,B,C,D),k1_zfmisc_1(B)) ) ).
% 0.20/0.66
% 0.20/0.66 fof(dt_k1_tarski,axiom,
% 0.20/0.66 $true ).
% 0.20/0.66
% 0.20/0.66 fof(dt_k1_xboole_0,axiom,
% 0.20/0.66 $true ).
% 0.20/0.66
% 0.20/0.66 fof(dt_k1_zfmisc_1,axiom,
% 0.20/0.66 $true ).
% 0.20/0.66
% 0.20/0.66 fof(dt_k2_relset_2,axiom,
% 0.20/0.66 ! [A,B,C,D] :
% 0.20/0.66 ( ( m1_relset_1(C,A,B)
% 0.20/0.66 & m1_subset_1(D,A) )
% 0.20/0.66 => m1_subset_1(k2_relset_2(A,B,C,D),k1_zfmisc_1(B)) ) ).
% 0.20/0.66
% 0.20/0.66 fof(dt_k2_zfmisc_1,axiom,
% 0.20/0.66 $true ).
% 0.20/0.66
% 0.20/0.66 fof(dt_k9_relat_1,axiom,
% 0.20/0.66 $true ).
% 0.20/0.66
% 0.20/0.66 fof(dt_m1_relset_1,axiom,
% 0.20/0.66 $true ).
% 0.20/0.66
% 0.20/0.66 fof(dt_m1_subset_1,axiom,
% 0.20/0.66 $true ).
% 0.20/0.66
% 0.20/0.66 fof(dt_m2_relset_1,axiom,
% 0.20/0.66 ! [A,B,C] :
% 0.20/0.66 ( m2_relset_1(C,A,B)
% 0.20/0.66 => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ).
% 0.20/0.66
% 0.20/0.66 fof(existence_m1_relset_1,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ? [C] : m1_relset_1(C,A,B) ).
% 0.20/0.66
% 0.20/0.66 fof(existence_m1_subset_1,axiom,
% 0.20/0.66 ! [A] :
% 0.20/0.66 ? [B] : m1_subset_1(B,A) ).
% 0.20/0.66
% 0.20/0.66 fof(existence_m2_relset_1,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ? [C] : m2_relset_1(C,A,B) ).
% 0.20/0.66
% 0.20/0.66 fof(fc12_relat_1,axiom,
% 0.20/0.66 ( v1_xboole_0(k1_xboole_0)
% 0.20/0.66 & v1_relat_1(k1_xboole_0)
% 0.20/0.66 & v3_relat_1(k1_xboole_0) ) ).
% 0.20/0.66
% 0.20/0.66 fof(fc1_subset_1,axiom,
% 0.20/0.66 ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ).
% 0.20/0.66
% 0.20/0.66 fof(fc1_sysrel,axiom,
% 0.20/0.66 ! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)) ).
% 0.20/0.66
% 0.20/0.66 fof(fc2_subset_1,axiom,
% 0.20/0.66 ! [A] : ~ v1_xboole_0(k1_tarski(A)) ).
% 0.20/0.66
% 0.20/0.66 fof(fc4_relat_1,axiom,
% 0.20/0.66 ( v1_xboole_0(k1_xboole_0)
% 0.20/0.66 & v1_relat_1(k1_xboole_0) ) ).
% 0.20/0.66
% 0.20/0.66 fof(fc4_subset_1,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( ( ~ v1_xboole_0(A)
% 0.20/0.66 & ~ v1_xboole_0(B) )
% 0.20/0.66 => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ).
% 0.20/0.66
% 0.20/0.66 fof(fraenkel_a_4_0_relset_2,axiom,
% 0.20/0.66 ! [A,B,C,D,E] :
% 0.20/0.66 ( ( ~ v1_xboole_0(B)
% 0.20/0.66 & m1_subset_1(D,k1_zfmisc_1(B))
% 0.20/0.66 & m2_relset_1(E,B,C) )
% 0.20/0.66 => ( r2_hidden(A,a_4_0_relset_2(B,C,D,E))
% 0.20/0.66 <=> ? [F] :
% 0.20/0.66 ( m1_subset_1(F,B)
% 0.20/0.66 & A = k2_relset_2(B,C,E,F)
% 0.20/0.66 & r2_hidden(F,D) ) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(rc1_relat_1,axiom,
% 0.20/0.66 ? [A] :
% 0.20/0.66 ( v1_xboole_0(A)
% 0.20/0.66 & v1_relat_1(A) ) ).
% 0.20/0.66
% 0.20/0.66 fof(rc1_subset_1,axiom,
% 0.20/0.66 ! [A] :
% 0.20/0.66 ( ~ v1_xboole_0(A)
% 0.20/0.66 => ? [B] :
% 0.20/0.66 ( m1_subset_1(B,k1_zfmisc_1(A))
% 0.20/0.66 & ~ v1_xboole_0(B) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(rc2_relat_1,axiom,
% 0.20/0.66 ? [A] :
% 0.20/0.66 ( ~ v1_xboole_0(A)
% 0.20/0.66 & v1_relat_1(A) ) ).
% 0.20/0.66
% 0.20/0.66 fof(rc2_subset_1,axiom,
% 0.20/0.66 ! [A] :
% 0.20/0.66 ? [B] :
% 0.20/0.66 ( m1_subset_1(B,k1_zfmisc_1(A))
% 0.20/0.66 & v1_xboole_0(B) ) ).
% 0.20/0.66
% 0.20/0.66 fof(rc3_relat_1,axiom,
% 0.20/0.66 ? [A] :
% 0.20/0.66 ( v1_relat_1(A)
% 0.20/0.66 & v3_relat_1(A) ) ).
% 0.20/0.66
% 0.20/0.66 fof(redefinition_k10_relset_1,axiom,
% 0.20/0.66 ! [A,B,C,D] :
% 0.20/0.66 ( m1_relset_1(C,A,B)
% 0.20/0.66 => k10_relset_1(A,B,C,D) = k9_relat_1(C,D) ) ).
% 0.20/0.66
% 0.20/0.66 fof(redefinition_m2_relset_1,axiom,
% 0.20/0.66 ! [A,B,C] :
% 0.20/0.66 ( m2_relset_1(C,A,B)
% 0.20/0.66 <=> m1_relset_1(C,A,B) ) ).
% 0.20/0.66
% 0.20/0.66 fof(reflexivity_r1_tarski,axiom,
% 0.20/0.66 ! [A,B] : r1_tarski(A,A) ).
% 0.20/0.66
% 0.20/0.66 fof(s8_domain_1__e1_22__relset_2,axiom,
% 0.20/0.66 ! [A,B,C,D] :
% 0.20/0.66 ( ( ~ v1_xboole_0(A)
% 0.20/0.66 & m1_subset_1(C,k1_zfmisc_1(A))
% 0.20/0.66 & m2_relset_1(D,A,B) )
% 0.20/0.66 => m1_subset_1(a_4_0_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) ).
% 0.20/0.66
% 0.20/0.66 fof(t1_subset,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( r2_hidden(A,B)
% 0.20/0.66 => m1_subset_1(A,B) ) ).
% 0.20/0.66
% 0.20/0.66 fof(t2_subset,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( m1_subset_1(A,B)
% 0.20/0.66 => ( v1_xboole_0(B)
% 0.20/0.66 | r2_hidden(A,B) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(t2_tarski,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( ! [C] :
% 0.20/0.66 ( r2_hidden(C,A)
% 0.20/0.66 <=> r2_hidden(C,B) )
% 0.20/0.66 => A = B ) ).
% 0.20/0.66
% 0.20/0.66 fof(t3_subset,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( m1_subset_1(A,k1_zfmisc_1(B))
% 0.20/0.66 <=> r1_tarski(A,B) ) ).
% 0.20/0.66
% 0.20/0.66 fof(t4_subset,axiom,
% 0.20/0.66 ! [A,B,C] :
% 0.20/0.66 ( ( r2_hidden(A,B)
% 0.20/0.66 & m1_subset_1(B,k1_zfmisc_1(C)) )
% 0.20/0.66 => m1_subset_1(A,C) ) ).
% 0.20/0.66
% 0.20/0.66 fof(t5_subset,axiom,
% 0.20/0.66 ! [A,B,C] :
% 0.20/0.66 ~ ( r2_hidden(A,B)
% 0.20/0.66 & m1_subset_1(B,k1_zfmisc_1(C))
% 0.20/0.66 & v1_xboole_0(C) ) ).
% 0.20/0.66
% 0.20/0.66 fof(t6_boole,axiom,
% 0.20/0.66 ! [A] :
% 0.20/0.66 ( v1_xboole_0(A)
% 0.20/0.66 => A = k1_xboole_0 ) ).
% 0.20/0.66
% 0.20/0.66 fof(t7_boole,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ~ ( r2_hidden(A,B)
% 0.20/0.66 & v1_xboole_0(B) ) ).
% 0.20/0.66
% 0.20/0.66 fof(t8_boole,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ~ ( v1_xboole_0(A)
% 0.20/0.66 & A != B
% 0.20/0.66 & v1_xboole_0(B) ) ).
% 0.20/0.66
% 0.20/0.66 %------------------------------------------------------------------------------
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % Proof found
% 0.20/0.66 % SZS status Theorem for theBenchmark
% 0.20/0.66 % SZS output start Proof
% 0.20/0.66 %ClaNum:103(EqnAxiom:50)
% 0.20/0.66 %VarNum:234(SingletonVarNum:95)
% 0.20/0.66 %MaxLitNum:7
% 0.20/0.66 %MaxfuncDepth:2
% 0.20/0.66 %SharedTerms:25
% 0.20/0.66 %goalClause: 63 67 70 74
% 0.20/0.66 %singleGoalClaCount:4
% 0.20/0.66 [52]P1(a1)
% 0.20/0.66 [53]P1(a2)
% 0.20/0.66 [55]P2(a1)
% 0.20/0.66 [56]P2(a2)
% 0.20/0.66 [57]P2(a3)
% 0.20/0.66 [58]P2(a6)
% 0.20/0.66 [59]P8(a1)
% 0.20/0.66 [60]P8(a6)
% 0.20/0.66 [67]P6(a13,a9,a11)
% 0.20/0.66 [70]~P1(a9)
% 0.20/0.66 [71]~P1(a3)
% 0.20/0.66 [63]P4(a8,f19(a9))
% 0.20/0.66 [74]~P4(f4(a9,a11,a8,a13),f19(f19(a11)))
% 0.20/0.66 [62]P3(x621,x621)
% 0.20/0.66 [61]P1(f7(x611))
% 0.20/0.66 [64]P4(f12(x641),x641)
% 0.20/0.67 [65]P4(f7(x651),f19(x651))
% 0.20/0.67 [72]~P1(f19(x721))
% 0.20/0.67 [73]~P1(f17(x731))
% 0.20/0.67 [66]P2(f20(x661,x662))
% 0.20/0.67 [68]P6(f15(x681,x682),x681,x682)
% 0.20/0.67 [69]P5(f14(x691,x692),x691,x692)
% 0.20/0.67 [75]~P1(x751)+E(x751,a1)
% 0.20/0.67 [76]~P1(x761)+P2(x761)
% 0.20/0.67 [78]P1(x781)+~P1(f5(x781))
% 0.20/0.67 [80]P1(x801)+P4(f5(x801),f19(x801))
% 0.20/0.67 [79]~P1(x791)+~P7(x792,x791)
% 0.20/0.67 [81]~P7(x811,x812)+P4(x811,x812)
% 0.20/0.67 [84]~P7(x842,x841)+~P7(x841,x842)
% 0.20/0.67 [83]~P3(x831,x832)+P4(x831,f19(x832))
% 0.20/0.67 [85]P3(x851,x852)+~P4(x851,f19(x852))
% 0.20/0.67 [92]~P5(x921,x922,x923)+P6(x921,x922,x923)
% 0.20/0.67 [93]~P6(x931,x932,x933)+P5(x931,x932,x933)
% 0.20/0.67 [90]P2(x901)+~P4(x901,f19(f20(x902,x903)))
% 0.20/0.67 [94]~P6(x941,x942,x943)+P4(x941,f19(f20(x942,x943)))
% 0.20/0.67 [95]~P5(x953,x951,x952)+E(f18(x951,x952,x953,x954),f22(x953,x954))
% 0.20/0.67 [96]~P5(x963,x961,x962)+P4(f18(x961,x962,x963,x964),f19(x962))
% 0.20/0.67 [77]~P1(x772)+~P1(x771)+E(x771,x772)
% 0.20/0.67 [82]~P4(x822,x821)+P1(x821)+P7(x822,x821)
% 0.20/0.67 [86]P1(x861)+P1(x862)+~P1(f20(x862,x861))
% 0.20/0.67 [89]E(x891,x892)+P7(f10(x891,x892),x892)+P7(f10(x891,x892),x891)
% 0.20/0.67 [91]E(x911,x912)+~P7(f10(x911,x912),x912)+~P7(f10(x911,x912),x911)
% 0.20/0.67 [87]~P1(x871)+~P7(x872,x873)+~P4(x873,f19(x871))
% 0.20/0.67 [88]P4(x881,x882)+~P7(x881,x883)+~P4(x883,f19(x882))
% 0.20/0.67 [98]~P4(x984,x981)+~P5(x983,x981,x982)+P4(f21(x981,x982,x983,x984),f19(x982))
% 0.20/0.67 [97]~P4(x974,x971)+~P6(x973,x971,x972)+E(f21(x971,x972,x973,x974),f18(x971,x972,x973,f17(x974)))
% 0.20/0.67 [99]~P6(x994,x991,x992)+P1(x991)+~P4(x993,f19(x991))+P4(f4(x991,x992,x993,x994),f19(f19(x992)))
% 0.20/0.67 [101]~P6(x1015,x1011,x1013)+P1(x1011)+~P4(x1014,f19(x1011))+~P7(x1012,f4(x1011,x1013,x1014,x1015))+P4(f16(x1012,x1011,x1013,x1014,x1015),x1011)
% 0.20/0.67 [102]~P6(x1025,x1021,x1023)+P1(x1021)+~P4(x1024,f19(x1021))+~P7(x1022,f4(x1021,x1023,x1024,x1025))+P7(f16(x1022,x1021,x1023,x1024,x1025),x1024)
% 0.20/0.67 [103]P1(x1031)+~P6(x1033,x1031,x1032)+~P4(x1035,f19(x1031))+~P7(x1034,f4(x1031,x1032,x1035,x1033))+E(f21(x1031,x1032,x1033,f16(x1034,x1031,x1032,x1035,x1033)),x1034)
% 0.20/0.67 [100]~P4(x1006,x1001)+~P7(x1006,x1004)+~P6(x1005,x1001,x1003)+P1(x1001)+~P4(x1004,f19(x1001))+P7(x1002,f4(x1001,x1003,x1004,x1005))+~E(x1002,f21(x1001,x1003,x1005,x1006))
% 0.20/0.67 %EqnAxiom
% 0.20/0.67 [1]E(x11,x11)
% 0.20/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.67 [4]~E(x41,x42)+E(f7(x41),f7(x42))
% 0.20/0.67 [5]~E(x51,x52)+E(f19(x51),f19(x52))
% 0.20/0.67 [6]~E(x61,x62)+E(f12(x61),f12(x62))
% 0.20/0.67 [7]~E(x71,x72)+E(f4(x71,x73,x74,x75),f4(x72,x73,x74,x75))
% 0.20/0.67 [8]~E(x81,x82)+E(f4(x83,x81,x84,x85),f4(x83,x82,x84,x85))
% 0.20/0.67 [9]~E(x91,x92)+E(f4(x93,x94,x91,x95),f4(x93,x94,x92,x95))
% 0.20/0.67 [10]~E(x101,x102)+E(f4(x103,x104,x105,x101),f4(x103,x104,x105,x102))
% 0.20/0.67 [11]~E(x111,x112)+E(f21(x111,x113,x114,x115),f21(x112,x113,x114,x115))
% 0.20/0.67 [12]~E(x121,x122)+E(f21(x123,x121,x124,x125),f21(x123,x122,x124,x125))
% 0.20/0.67 [13]~E(x131,x132)+E(f21(x133,x134,x131,x135),f21(x133,x134,x132,x135))
% 0.20/0.67 [14]~E(x141,x142)+E(f21(x143,x144,x145,x141),f21(x143,x144,x145,x142))
% 0.20/0.67 [15]~E(x151,x152)+E(f20(x151,x153),f20(x152,x153))
% 0.20/0.67 [16]~E(x161,x162)+E(f20(x163,x161),f20(x163,x162))
% 0.20/0.67 [17]~E(x171,x172)+E(f15(x171,x173),f15(x172,x173))
% 0.20/0.67 [18]~E(x181,x182)+E(f15(x183,x181),f15(x183,x182))
% 0.20/0.67 [19]~E(x191,x192)+E(f14(x191,x193),f14(x192,x193))
% 0.20/0.67 [20]~E(x201,x202)+E(f14(x203,x201),f14(x203,x202))
% 0.20/0.67 [21]~E(x211,x212)+E(f16(x211,x213,x214,x215,x216),f16(x212,x213,x214,x215,x216))
% 0.20/0.67 [22]~E(x221,x222)+E(f16(x223,x221,x224,x225,x226),f16(x223,x222,x224,x225,x226))
% 0.20/0.67 [23]~E(x231,x232)+E(f16(x233,x234,x231,x235,x236),f16(x233,x234,x232,x235,x236))
% 0.20/0.67 [24]~E(x241,x242)+E(f16(x243,x244,x245,x241,x246),f16(x243,x244,x245,x242,x246))
% 0.20/0.67 [25]~E(x251,x252)+E(f16(x253,x254,x255,x256,x251),f16(x253,x254,x255,x256,x252))
% 0.20/0.67 [26]~E(x261,x262)+E(f17(x261),f17(x262))
% 0.20/0.67 [27]~E(x271,x272)+E(f18(x271,x273,x274,x275),f18(x272,x273,x274,x275))
% 0.20/0.67 [28]~E(x281,x282)+E(f18(x283,x281,x284,x285),f18(x283,x282,x284,x285))
% 0.20/0.67 [29]~E(x291,x292)+E(f18(x293,x294,x291,x295),f18(x293,x294,x292,x295))
% 0.20/0.67 [30]~E(x301,x302)+E(f18(x303,x304,x305,x301),f18(x303,x304,x305,x302))
% 0.20/0.67 [31]~E(x311,x312)+E(f22(x311,x313),f22(x312,x313))
% 0.20/0.67 [32]~E(x321,x322)+E(f22(x323,x321),f22(x323,x322))
% 0.20/0.67 [33]~E(x331,x332)+E(f10(x331,x333),f10(x332,x333))
% 0.20/0.67 [34]~E(x341,x342)+E(f10(x343,x341),f10(x343,x342))
% 0.20/0.67 [35]~E(x351,x352)+E(f5(x351),f5(x352))
% 0.20/0.67 [36]~P1(x361)+P1(x362)+~E(x361,x362)
% 0.20/0.67 [37]P7(x372,x373)+~E(x371,x372)+~P7(x371,x373)
% 0.20/0.67 [38]P7(x383,x382)+~E(x381,x382)+~P7(x383,x381)
% 0.20/0.67 [39]P4(x392,x393)+~E(x391,x392)+~P4(x391,x393)
% 0.20/0.67 [40]P4(x403,x402)+~E(x401,x402)+~P4(x403,x401)
% 0.20/0.67 [41]~P2(x411)+P2(x412)+~E(x411,x412)
% 0.20/0.67 [42]P5(x422,x423,x424)+~E(x421,x422)+~P5(x421,x423,x424)
% 0.20/0.67 [43]P5(x433,x432,x434)+~E(x431,x432)+~P5(x433,x431,x434)
% 0.20/0.67 [44]P5(x443,x444,x442)+~E(x441,x442)+~P5(x443,x444,x441)
% 0.20/0.67 [45]P6(x452,x453,x454)+~E(x451,x452)+~P6(x451,x453,x454)
% 0.20/0.67 [46]P6(x463,x462,x464)+~E(x461,x462)+~P6(x463,x461,x464)
% 0.20/0.67 [47]P6(x473,x474,x472)+~E(x471,x472)+~P6(x473,x474,x471)
% 0.20/0.67 [48]P3(x482,x483)+~E(x481,x482)+~P3(x481,x483)
% 0.20/0.67 [49]P3(x493,x492)+~E(x491,x492)+~P3(x493,x491)
% 0.20/0.67 [50]~P8(x501)+P8(x502)+~E(x501,x502)
% 0.20/0.67
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 cnf(104,plain,
% 0.20/0.67 ($false),
% 0.20/0.67 inference(scs_inference,[],[67,70,63,74,99]),
% 0.20/0.67 ['proof']).
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67 % Total time :0.000000s
%------------------------------------------------------------------------------