TSTP Solution File: COM018+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COM018+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 : Wed Aug 30 18:35:13 EDT 2023
% Result : Theorem 0.51s 0.63s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM018+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n003.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 : Tue Aug 29 13:06:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.51/0.61 %-------------------------------------------
% 0.51/0.61 % File :CSE---1.6
% 0.51/0.61 % Problem :theBenchmark
% 0.51/0.61 % Transform :cnf
% 0.51/0.61 % Format :tptp:raw
% 0.51/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.51/0.61
% 0.51/0.61 % Result :Theorem 0.000000s
% 0.51/0.61 % Output :CNFRefutation 0.000000s
% 0.51/0.61 %-------------------------------------------
% 0.51/0.62 %------------------------------------------------------------------------------
% 0.51/0.62 % File : COM018+1 : TPTP v8.1.2. Released v4.0.0.
% 0.51/0.62 % Domain : Computing Theory
% 0.51/0.62 % Problem : Newman's lemma on rewriting systems 03_01_04, 00 expansion
% 0.51/0.62 % Version : Especial.
% 0.51/0.62 % English :
% 0.51/0.62
% 0.51/0.62 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.51/0.62 % : [PV+07] Paskevich et al. (2007), Reasoning Inside a Formula an
% 0.51/0.62 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.51/0.62 % Source : [Pas08]
% 0.51/0.62 % Names : newman_03_01_04.00 [Pas08]
% 0.51/0.62
% 0.51/0.62 % Status : Theorem
% 0.51/0.62 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.05 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.1, 0.57 v4.0.0
% 0.51/0.62 % Syntax : Number of formulae : 23 ( 2 unt; 6 def)
% 0.51/0.62 % Number of atoms : 108 ( 1 equ)
% 0.51/0.62 % Maximal formula atoms : 10 ( 4 avg)
% 0.51/0.62 % Number of connectives : 86 ( 1 ~; 2 |; 51 &)
% 0.51/0.62 % ( 6 <=>; 26 =>; 0 <=; 0 <~>)
% 0.51/0.62 % Maximal formula depth : 12 ( 6 avg)
% 0.51/0.62 % Maximal term depth : 1 ( 1 avg)
% 0.51/0.62 % Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% 0.51/0.62 % Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% 0.51/0.62 % Number of variables : 50 ( 43 !; 7 ?)
% 0.51/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.51/0.62
% 0.51/0.62 % Comments : Problem generated by the SAD system [VLP07]
% 0.51/0.62 %------------------------------------------------------------------------------
% 0.51/0.62 fof(mElmSort,axiom,
% 0.51/0.62 ! [W0] :
% 0.51/0.62 ( aElement0(W0)
% 0.51/0.62 => $true ) ).
% 0.51/0.62
% 0.51/0.62 fof(mRelSort,axiom,
% 0.51/0.62 ! [W0] :
% 0.51/0.62 ( aRewritingSystem0(W0)
% 0.51/0.62 => $true ) ).
% 0.51/0.62
% 0.51/0.62 fof(mReduct,axiom,
% 0.51/0.62 ! [W0,W1] :
% 0.51/0.62 ( ( aElement0(W0)
% 0.51/0.62 & aRewritingSystem0(W1) )
% 0.51/0.62 => ! [W2] :
% 0.51/0.62 ( aReductOfIn0(W2,W0,W1)
% 0.51/0.62 => aElement0(W2) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mWFOrd,axiom,
% 0.51/0.62 ! [W0,W1] :
% 0.51/0.62 ( ( aElement0(W0)
% 0.51/0.62 & aElement0(W1) )
% 0.51/0.62 => ( iLess0(W0,W1)
% 0.51/0.62 => $true ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mTCbr,axiom,
% 0.51/0.62 ! [W0,W1,W2] :
% 0.51/0.62 ( ( aElement0(W0)
% 0.51/0.62 & aRewritingSystem0(W1)
% 0.51/0.62 & aElement0(W2) )
% 0.51/0.62 => ( sdtmndtplgtdt0(W0,W1,W2)
% 0.51/0.62 => $true ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mTCDef,definition,
% 0.51/0.62 ! [W0,W1,W2] :
% 0.51/0.62 ( ( aElement0(W0)
% 0.51/0.62 & aRewritingSystem0(W1)
% 0.51/0.62 & aElement0(W2) )
% 0.51/0.62 => ( sdtmndtplgtdt0(W0,W1,W2)
% 0.51/0.62 <=> ( aReductOfIn0(W2,W0,W1)
% 0.51/0.62 | ? [W3] :
% 0.51/0.62 ( aElement0(W3)
% 0.51/0.62 & aReductOfIn0(W3,W0,W1)
% 0.51/0.62 & sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mTCTrans,axiom,
% 0.51/0.62 ! [W0,W1,W2,W3] :
% 0.51/0.62 ( ( aElement0(W0)
% 0.51/0.62 & aRewritingSystem0(W1)
% 0.51/0.62 & aElement0(W2)
% 0.51/0.62 & aElement0(W3) )
% 0.51/0.62 => ( ( sdtmndtplgtdt0(W0,W1,W2)
% 0.51/0.62 & sdtmndtplgtdt0(W2,W1,W3) )
% 0.51/0.62 => sdtmndtplgtdt0(W0,W1,W3) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mTCRDef,definition,
% 0.51/0.62 ! [W0,W1,W2] :
% 0.51/0.62 ( ( aElement0(W0)
% 0.51/0.62 & aRewritingSystem0(W1)
% 0.51/0.62 & aElement0(W2) )
% 0.51/0.62 => ( sdtmndtasgtdt0(W0,W1,W2)
% 0.51/0.62 <=> ( W0 = W2
% 0.51/0.62 | sdtmndtplgtdt0(W0,W1,W2) ) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mTCRTrans,axiom,
% 0.51/0.62 ! [W0,W1,W2,W3] :
% 0.51/0.62 ( ( aElement0(W0)
% 0.51/0.62 & aRewritingSystem0(W1)
% 0.51/0.62 & aElement0(W2)
% 0.51/0.62 & aElement0(W3) )
% 0.51/0.62 => ( ( sdtmndtasgtdt0(W0,W1,W2)
% 0.51/0.62 & sdtmndtasgtdt0(W2,W1,W3) )
% 0.51/0.62 => sdtmndtasgtdt0(W0,W1,W3) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mCRDef,definition,
% 0.51/0.62 ! [W0] :
% 0.51/0.62 ( aRewritingSystem0(W0)
% 0.51/0.62 => ( isConfluent0(W0)
% 0.51/0.62 <=> ! [W1,W2,W3] :
% 0.51/0.62 ( ( aElement0(W1)
% 0.51/0.62 & aElement0(W2)
% 0.51/0.62 & aElement0(W3)
% 0.51/0.62 & sdtmndtasgtdt0(W1,W0,W2)
% 0.51/0.62 & sdtmndtasgtdt0(W1,W0,W3) )
% 0.51/0.62 => ? [W4] :
% 0.51/0.62 ( aElement0(W4)
% 0.51/0.62 & sdtmndtasgtdt0(W2,W0,W4)
% 0.51/0.62 & sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mWCRDef,definition,
% 0.51/0.62 ! [W0] :
% 0.51/0.62 ( aRewritingSystem0(W0)
% 0.51/0.62 => ( isLocallyConfluent0(W0)
% 0.51/0.62 <=> ! [W1,W2,W3] :
% 0.51/0.62 ( ( aElement0(W1)
% 0.51/0.62 & aElement0(W2)
% 0.51/0.62 & aElement0(W3)
% 0.51/0.62 & aReductOfIn0(W2,W1,W0)
% 0.51/0.62 & aReductOfIn0(W3,W1,W0) )
% 0.51/0.62 => ? [W4] :
% 0.51/0.62 ( aElement0(W4)
% 0.51/0.62 & sdtmndtasgtdt0(W2,W0,W4)
% 0.51/0.62 & sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mTermin,definition,
% 0.51/0.62 ! [W0] :
% 0.51/0.62 ( aRewritingSystem0(W0)
% 0.51/0.62 => ( isTerminating0(W0)
% 0.51/0.62 <=> ! [W1,W2] :
% 0.51/0.62 ( ( aElement0(W1)
% 0.51/0.62 & aElement0(W2) )
% 0.51/0.62 => ( sdtmndtplgtdt0(W1,W0,W2)
% 0.51/0.62 => iLess0(W2,W1) ) ) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mNFRDef,definition,
% 0.51/0.62 ! [W0,W1] :
% 0.51/0.62 ( ( aElement0(W0)
% 0.51/0.62 & aRewritingSystem0(W1) )
% 0.51/0.62 => ! [W2] :
% 0.51/0.62 ( aNormalFormOfIn0(W2,W0,W1)
% 0.51/0.62 <=> ( aElement0(W2)
% 0.51/0.62 & sdtmndtasgtdt0(W0,W1,W2)
% 0.51/0.62 & ~ ? [W3] : aReductOfIn0(W3,W2,W1) ) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mTermNF,axiom,
% 0.51/0.62 ! [W0] :
% 0.51/0.62 ( ( aRewritingSystem0(W0)
% 0.51/0.62 & isTerminating0(W0) )
% 0.51/0.62 => ! [W1] :
% 0.51/0.62 ( aElement0(W1)
% 0.51/0.62 => ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(m__656,hypothesis,
% 0.51/0.62 aRewritingSystem0(xR) ).
% 0.51/0.62
% 0.51/0.62 fof(m__656_01,hypothesis,
% 0.51/0.62 ( isLocallyConfluent0(xR)
% 0.51/0.62 & isTerminating0(xR) ) ).
% 0.51/0.62
% 0.51/0.62 fof(m__731,hypothesis,
% 0.51/0.62 ( aElement0(xa)
% 0.51/0.62 & aElement0(xb)
% 0.51/0.62 & aElement0(xc) ) ).
% 0.51/0.62
% 0.51/0.62 fof(m__715,hypothesis,
% 0.51/0.62 ! [W0,W1,W2] :
% 0.51/0.62 ( ( aElement0(W0)
% 0.51/0.62 & aElement0(W1)
% 0.51/0.62 & aElement0(W2)
% 0.51/0.62 & sdtmndtasgtdt0(W0,xR,W1)
% 0.51/0.62 & sdtmndtasgtdt0(W0,xR,W2) )
% 0.51/0.62 => ( iLess0(W0,xa)
% 0.51/0.62 => ? [W3] :
% 0.51/0.63 ( aElement0(W3)
% 0.51/0.63 & sdtmndtasgtdt0(W1,xR,W3)
% 0.51/0.63 & sdtmndtasgtdt0(W2,xR,W3) ) ) ) ).
% 0.51/0.63
% 0.51/0.63 fof(m__731_02,hypothesis,
% 0.51/0.63 ( sdtmndtplgtdt0(xa,xR,xb)
% 0.51/0.63 & sdtmndtplgtdt0(xa,xR,xc) ) ).
% 0.51/0.63
% 0.51/0.63 fof(m__755,hypothesis,
% 0.51/0.63 ( aElement0(xu)
% 0.51/0.63 & aReductOfIn0(xu,xa,xR)
% 0.51/0.63 & sdtmndtasgtdt0(xu,xR,xb) ) ).
% 0.51/0.63
% 0.51/0.63 fof(m__779,hypothesis,
% 0.51/0.63 ( aElement0(xv)
% 0.51/0.63 & aReductOfIn0(xv,xa,xR)
% 0.51/0.63 & sdtmndtasgtdt0(xv,xR,xc) ) ).
% 0.51/0.63
% 0.51/0.63 fof(m__799,hypothesis,
% 0.51/0.63 ( aElement0(xw)
% 0.51/0.63 & sdtmndtasgtdt0(xu,xR,xw)
% 0.51/0.63 & sdtmndtasgtdt0(xv,xR,xw) ) ).
% 0.51/0.63
% 0.51/0.63 fof(m__,conjecture,
% 0.51/0.63 ? [W0] : aNormalFormOfIn0(W0,xw,xR) ).
% 0.51/0.63
% 0.51/0.63 %------------------------------------------------------------------------------
% 0.51/0.63 %-------------------------------------------
% 0.51/0.63 % Proof found
% 0.51/0.63 % SZS status Theorem for theBenchmark
% 0.51/0.63 % SZS output start Proof
% 0.51/0.63 %ClaNum:109(EqnAxiom:49)
% 0.51/0.63 %VarNum:379(SingletonVarNum:106)
% 0.51/0.63 %MaxLitNum:8
% 0.51/0.63 %MaxfuncDepth:1
% 0.51/0.63 %SharedTerms:24
% 0.51/0.63 %goalClause: 67
% 0.51/0.63 %singleGoalClaCount:1
% 0.51/0.63 [50]P1(a1)
% 0.51/0.63 [51]P1(a17)
% 0.51/0.63 [52]P1(a18)
% 0.51/0.63 [53]P1(a19)
% 0.51/0.63 [54]P1(a20)
% 0.51/0.63 [55]P1(a21)
% 0.51/0.63 [56]P2(a2)
% 0.51/0.63 [57]P5(a2)
% 0.51/0.63 [58]P8(a2)
% 0.51/0.63 [59]P3(a19,a1,a2)
% 0.51/0.63 [60]P3(a20,a1,a2)
% 0.51/0.63 [61]P9(a1,a2,a17)
% 0.51/0.63 [62]P9(a1,a2,a18)
% 0.51/0.63 [63]P10(a19,a2,a17)
% 0.51/0.63 [64]P10(a19,a2,a21)
% 0.51/0.63 [65]P10(a20,a2,a18)
% 0.51/0.63 [66]P10(a20,a2,a21)
% 0.51/0.63 [67]~P4(x671,a21,a2)
% 0.51/0.63 [68]~P2(x681)+P6(x681)+P1(f3(x681))
% 0.51/0.63 [69]~P2(x691)+P6(x691)+P1(f11(x691))
% 0.51/0.63 [70]~P2(x701)+P6(x701)+P1(f12(x701))
% 0.51/0.63 [71]~P2(x711)+P5(x711)+P1(f13(x711))
% 0.51/0.63 [72]~P2(x721)+P5(x721)+P1(f15(x721))
% 0.51/0.63 [73]~P2(x731)+P5(x731)+P1(f16(x731))
% 0.51/0.63 [74]~P2(x741)+P8(x741)+P1(f4(x741))
% 0.51/0.63 [75]~P2(x751)+P8(x751)+P1(f5(x751))
% 0.51/0.63 [76]~P2(x761)+P8(x761)+~P7(f5(x761),f4(x761))
% 0.51/0.63 [77]~P2(x771)+P6(x771)+P10(f3(x771),x771,f11(x771))
% 0.51/0.63 [78]~P2(x781)+P6(x781)+P10(f3(x781),x781,f12(x781))
% 0.51/0.63 [79]~P2(x791)+P8(x791)+P9(f4(x791),x791,f5(x791))
% 0.51/0.63 [80]~P2(x801)+P5(x801)+P3(f15(x801),f13(x801),x801)
% 0.51/0.63 [81]~P2(x811)+P5(x811)+P3(f16(x811),f13(x811),x811)
% 0.51/0.63 [83]~P1(x832)+~P2(x831)+~P8(x831)+P4(f6(x831,x832),x832,x831)
% 0.51/0.63 [84]~P3(x841,x842,x843)+P1(x841)+~P1(x842)+~P2(x843)
% 0.51/0.63 [85]~P4(x851,x852,x853)+P1(x851)+~P1(x852)+~P2(x853)
% 0.51/0.63 [87]~P1(x871)+~P2(x872)+~P4(x873,x871,x872)+P10(x871,x872,x873)
% 0.51/0.63 [91]~P4(x914,x911,x912)+~P1(x911)+~P3(x913,x914,x912)+~P2(x912)
% 0.51/0.63 [92]~P2(x921)+P6(x921)+~P1(x922)+~P10(f11(x921),x921,x922)+~P10(f12(x921),x921,x922)
% 0.51/0.63 [93]~P2(x931)+P5(x931)+~P1(x932)+~P10(f15(x931),x931,x932)+~P10(f16(x931),x931,x932)
% 0.51/0.63 [82]~E(x821,x823)+~P1(x823)+~P1(x821)+~P2(x822)+P10(x821,x822,x823)
% 0.51/0.63 [88]~P1(x881)+~P1(x883)+~P2(x882)+~P3(x883,x881,x882)+P9(x881,x882,x883)
% 0.51/0.63 [89]~P1(x893)+~P1(x891)+~P2(x892)+~P9(x891,x892,x893)+P10(x891,x892,x893)
% 0.51/0.63 [86]~P1(x861)+~P1(x862)+~P8(x863)+~P9(x862,x863,x861)+P7(x861,x862)+~P2(x863)
% 0.51/0.63 [90]~P1(x902)+~P1(x901)+~P2(x903)+~P10(x901,x903,x902)+E(x901,x902)+P9(x901,x903,x902)
% 0.51/0.63 [97]~P1(x971)+~P1(x972)+~P2(x973)+~P9(x972,x973,x971)+P3(x971,x972,x973)+P1(f8(x972,x973,x971))
% 0.51/0.63 [99]~P1(x991)+~P1(x992)+~P2(x993)+~P9(x992,x993,x991)+P3(x991,x992,x993)+P3(f8(x992,x993,x991),x992,x993)
% 0.51/0.63 [100]~P1(x1001)+~P1(x1002)+~P2(x1003)+~P9(x1002,x1003,x1001)+P3(x1001,x1002,x1003)+P9(f8(x1002,x1003,x1001),x1003,x1001)
% 0.51/0.63 [101]~P1(x1012)+~P1(x1011)+~P2(x1013)+~P10(x1012,x1013,x1011)+P4(x1011,x1012,x1013)+P3(f7(x1012,x1013,x1011),x1011,x1013)
% 0.51/0.63 [98]~P1(x983)+~P1(x982)+~P1(x981)+~P10(x981,a2,x983)+~P10(x981,a2,x982)+~P7(x981,a1)+P1(f9(x981,x982,x983))
% 0.51/0.63 [102]~P1(x1023)+~P1(x1022)+~P1(x1021)+~P10(x1022,a2,x1023)+~P10(x1022,a2,x1021)+~P7(x1022,a1)+P10(x1021,a2,f9(x1022,x1023,x1021))
% 0.51/0.63 [103]~P1(x1033)+~P1(x1032)+~P1(x1031)+~P10(x1032,a2,x1033)+~P10(x1032,a2,x1031)+~P7(x1032,a1)+P10(x1031,a2,f9(x1032,x1031,x1033))
% 0.51/0.63 [94]~P1(x943)+~P1(x941)+~P2(x942)+~P3(x944,x941,x942)+~P9(x944,x942,x943)+P9(x941,x942,x943)+~P1(x944)
% 0.51/0.63 [95]~P1(x953)+~P1(x951)+~P2(x952)+~P9(x954,x952,x953)+~P9(x951,x952,x954)+P9(x951,x952,x953)+~P1(x954)
% 0.51/0.63 [96]~P1(x963)+~P1(x961)+~P2(x962)+~P10(x964,x962,x963)+~P10(x961,x962,x964)+P10(x961,x962,x963)+~P1(x964)
% 0.51/0.63 [104]~P1(x1044)+~P1(x1043)+~P1(x1042)+~P2(x1041)+~P6(x1041)+~P10(x1042,x1041,x1044)+~P10(x1042,x1041,x1043)+P1(f10(x1041,x1042,x1043,x1044))
% 0.51/0.63 [105]~P1(x1054)+~P1(x1053)+~P1(x1052)+~P2(x1051)+~P5(x1051)+~P3(x1054,x1052,x1051)+~P3(x1053,x1052,x1051)+P1(f14(x1051,x1052,x1053,x1054))
% 0.51/0.63 [106]~P1(x1064)+~P1(x1063)+~P1(x1061)+~P2(x1062)+~P6(x1062)+~P10(x1063,x1062,x1064)+~P10(x1063,x1062,x1061)+P10(x1061,x1062,f10(x1062,x1063,x1064,x1061))
% 0.51/0.63 [107]~P1(x1074)+~P1(x1073)+~P1(x1071)+~P2(x1072)+~P6(x1072)+~P10(x1073,x1072,x1074)+~P10(x1073,x1072,x1071)+P10(x1071,x1072,f10(x1072,x1073,x1071,x1074))
% 0.51/0.63 [108]~P1(x1084)+~P1(x1083)+~P1(x1081)+~P2(x1082)+~P5(x1082)+~P3(x1084,x1083,x1082)+~P3(x1081,x1083,x1082)+P10(x1081,x1082,f14(x1082,x1083,x1084,x1081))
% 0.51/0.63 [109]~P1(x1094)+~P1(x1093)+~P1(x1091)+~P2(x1092)+~P5(x1092)+~P3(x1094,x1093,x1092)+~P3(x1091,x1093,x1092)+P10(x1091,x1092,f14(x1092,x1093,x1091,x1094))
% 0.51/0.63 %EqnAxiom
% 0.51/0.63 [1]E(x11,x11)
% 0.51/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.51/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.51/0.63 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.51/0.63 [5]~E(x51,x52)+E(f11(x51),f11(x52))
% 0.51/0.63 [6]~E(x61,x62)+E(f12(x61),f12(x62))
% 0.51/0.63 [7]~E(x71,x72)+E(f13(x71),f13(x72))
% 0.51/0.63 [8]~E(x81,x82)+E(f15(x81),f15(x82))
% 0.51/0.63 [9]~E(x91,x92)+E(f16(x91),f16(x92))
% 0.51/0.63 [10]~E(x101,x102)+E(f4(x101),f4(x102))
% 0.51/0.63 [11]~E(x111,x112)+E(f5(x111),f5(x112))
% 0.51/0.63 [12]~E(x121,x122)+E(f8(x121,x123,x124),f8(x122,x123,x124))
% 0.51/0.63 [13]~E(x131,x132)+E(f8(x133,x131,x134),f8(x133,x132,x134))
% 0.51/0.63 [14]~E(x141,x142)+E(f8(x143,x144,x141),f8(x143,x144,x142))
% 0.51/0.63 [15]~E(x151,x152)+E(f10(x151,x153,x154,x155),f10(x152,x153,x154,x155))
% 0.51/0.63 [16]~E(x161,x162)+E(f10(x163,x161,x164,x165),f10(x163,x162,x164,x165))
% 0.51/0.63 [17]~E(x171,x172)+E(f10(x173,x174,x171,x175),f10(x173,x174,x172,x175))
% 0.51/0.63 [18]~E(x181,x182)+E(f10(x183,x184,x185,x181),f10(x183,x184,x185,x182))
% 0.51/0.63 [19]~E(x191,x192)+E(f14(x191,x193,x194,x195),f14(x192,x193,x194,x195))
% 0.51/0.63 [20]~E(x201,x202)+E(f14(x203,x201,x204,x205),f14(x203,x202,x204,x205))
% 0.51/0.63 [21]~E(x211,x212)+E(f14(x213,x214,x211,x215),f14(x213,x214,x212,x215))
% 0.51/0.63 [22]~E(x221,x222)+E(f14(x223,x224,x225,x221),f14(x223,x224,x225,x222))
% 0.51/0.63 [23]~E(x231,x232)+E(f9(x231,x233,x234),f9(x232,x233,x234))
% 0.51/0.63 [24]~E(x241,x242)+E(f9(x243,x241,x244),f9(x243,x242,x244))
% 0.51/0.63 [25]~E(x251,x252)+E(f9(x253,x254,x251),f9(x253,x254,x252))
% 0.51/0.63 [26]~E(x261,x262)+E(f6(x261,x263),f6(x262,x263))
% 0.51/0.63 [27]~E(x271,x272)+E(f6(x273,x271),f6(x273,x272))
% 0.51/0.63 [28]~E(x281,x282)+E(f7(x281,x283,x284),f7(x282,x283,x284))
% 0.51/0.63 [29]~E(x291,x292)+E(f7(x293,x291,x294),f7(x293,x292,x294))
% 0.51/0.63 [30]~E(x301,x302)+E(f7(x303,x304,x301),f7(x303,x304,x302))
% 0.51/0.63 [31]~P1(x311)+P1(x312)+~E(x311,x312)
% 0.51/0.63 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 0.51/0.63 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 0.51/0.63 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 0.51/0.63 [35]P10(x352,x353,x354)+~E(x351,x352)+~P10(x351,x353,x354)
% 0.51/0.63 [36]P10(x363,x362,x364)+~E(x361,x362)+~P10(x363,x361,x364)
% 0.51/0.63 [37]P10(x373,x374,x372)+~E(x371,x372)+~P10(x373,x374,x371)
% 0.51/0.63 [38]~P5(x381)+P5(x382)+~E(x381,x382)
% 0.51/0.63 [39]~P2(x391)+P2(x392)+~E(x391,x392)
% 0.51/0.63 [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404)
% 0.51/0.63 [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414)
% 0.51/0.63 [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421)
% 0.51/0.63 [43]P9(x432,x433,x434)+~E(x431,x432)+~P9(x431,x433,x434)
% 0.51/0.63 [44]P9(x443,x442,x444)+~E(x441,x442)+~P9(x443,x441,x444)
% 0.51/0.63 [45]P9(x453,x454,x452)+~E(x451,x452)+~P9(x453,x454,x451)
% 0.51/0.63 [46]~P8(x461)+P8(x462)+~E(x461,x462)
% 0.51/0.63 [47]~P6(x471)+P6(x472)+~E(x471,x472)
% 0.51/0.63 [48]P7(x482,x483)+~E(x481,x482)+~P7(x481,x483)
% 0.51/0.63 [49]P7(x493,x492)+~E(x491,x492)+~P7(x493,x491)
% 0.51/0.63
% 0.51/0.63 %-------------------------------------------
% 0.51/0.63 cnf(111,plain,
% 0.51/0.63 ($false),
% 0.51/0.63 inference(scs_inference,[],[67,50,55,56,58,59,91,83]),
% 0.51/0.63 ['proof']).
% 0.51/0.63 % SZS output end Proof
% 0.51/0.63 % Total time :0.000000s
%------------------------------------------------------------------------------