TSTP Solution File: COM017+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COM017+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n020.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 18:35:12 EDT 2023
% Result : Theorem 0.54s 0.83s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COM017+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 13:03:13 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.49/0.57 start to proof:theBenchmark
% 0.54/0.82 %-------------------------------------------
% 0.54/0.82 % File :CSE---1.6
% 0.54/0.82 % Problem :theBenchmark
% 0.54/0.82 % Transform :cnf
% 0.54/0.82 % Format :tptp:raw
% 0.54/0.82 % Command :java -jar mcs_scs.jar %d %s
% 0.54/0.82
% 0.54/0.82 % Result :Theorem 0.190000s
% 0.54/0.82 % Output :CNFRefutation 0.190000s
% 0.54/0.82 %-------------------------------------------
% 0.54/0.82 %------------------------------------------------------------------------------
% 0.54/0.82 % File : COM017+1 : TPTP v8.1.2. Released v4.0.0.
% 0.54/0.83 % Domain : Computing Theory
% 0.54/0.83 % Problem : Newman's lemma on rewriting systems 03_01_03, 00 expansion
% 0.54/0.83 % Version : Especial.
% 0.54/0.83 % English :
% 0.54/0.83
% 0.54/0.83 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.54/0.83 % : [PV+07] Paskevich et al. (2007), Reasoning Inside a Formula an
% 0.54/0.83 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.54/0.83 % Source : [Pas08]
% 0.54/0.83 % Names : newman_03_01_03.00 [Pas08]
% 0.54/0.83
% 0.54/0.83 % Status : Theorem
% 0.54/0.83 % Rating : 0.17 v7.5.0, 0.19 v7.4.0, 0.13 v7.3.0, 0.14 v7.1.0, 0.09 v7.0.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.20 v6.0.0, 0.13 v5.5.0, 0.15 v5.4.0, 0.21 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.24 v5.0.0, 0.33 v4.1.0, 0.39 v4.0.1, 0.70 v4.0.0
% 0.54/0.83 % Syntax : Number of formulae : 22 ( 1 unt; 6 def)
% 0.54/0.83 % Number of atoms : 107 ( 1 equ)
% 0.54/0.83 % Maximal formula atoms : 10 ( 4 avg)
% 0.54/0.83 % Number of connectives : 86 ( 1 ~; 2 |; 51 &)
% 0.54/0.83 % ( 6 <=>; 26 =>; 0 <=; 0 <~>)
% 0.54/0.83 % Maximal formula depth : 12 ( 6 avg)
% 0.54/0.83 % Maximal term depth : 1 ( 1 avg)
% 0.54/0.83 % Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% 0.54/0.83 % Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% 0.54/0.83 % Number of variables : 50 ( 43 !; 7 ?)
% 0.54/0.83 % SPC : FOF_THM_RFO_SEQ
% 0.54/0.83
% 0.54/0.83 % Comments : Problem generated by the SAD system [VLP07]
% 0.54/0.83 %------------------------------------------------------------------------------
% 0.54/0.83 fof(mElmSort,axiom,
% 0.54/0.83 ! [W0] :
% 0.54/0.83 ( aElement0(W0)
% 0.54/0.83 => $true ) ).
% 0.54/0.83
% 0.54/0.83 fof(mRelSort,axiom,
% 0.54/0.83 ! [W0] :
% 0.54/0.83 ( aRewritingSystem0(W0)
% 0.54/0.83 => $true ) ).
% 0.54/0.83
% 0.54/0.83 fof(mReduct,axiom,
% 0.54/0.83 ! [W0,W1] :
% 0.54/0.83 ( ( aElement0(W0)
% 0.54/0.83 & aRewritingSystem0(W1) )
% 0.54/0.83 => ! [W2] :
% 0.54/0.83 ( aReductOfIn0(W2,W0,W1)
% 0.54/0.83 => aElement0(W2) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mWFOrd,axiom,
% 0.54/0.83 ! [W0,W1] :
% 0.54/0.83 ( ( aElement0(W0)
% 0.54/0.83 & aElement0(W1) )
% 0.54/0.83 => ( iLess0(W0,W1)
% 0.54/0.83 => $true ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mTCbr,axiom,
% 0.54/0.83 ! [W0,W1,W2] :
% 0.54/0.83 ( ( aElement0(W0)
% 0.54/0.83 & aRewritingSystem0(W1)
% 0.54/0.83 & aElement0(W2) )
% 0.54/0.83 => ( sdtmndtplgtdt0(W0,W1,W2)
% 0.54/0.83 => $true ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mTCDef,definition,
% 0.54/0.83 ! [W0,W1,W2] :
% 0.54/0.83 ( ( aElement0(W0)
% 0.54/0.83 & aRewritingSystem0(W1)
% 0.54/0.83 & aElement0(W2) )
% 0.54/0.83 => ( sdtmndtplgtdt0(W0,W1,W2)
% 0.54/0.83 <=> ( aReductOfIn0(W2,W0,W1)
% 0.54/0.83 | ? [W3] :
% 0.54/0.83 ( aElement0(W3)
% 0.54/0.83 & aReductOfIn0(W3,W0,W1)
% 0.54/0.83 & sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mTCTrans,axiom,
% 0.54/0.83 ! [W0,W1,W2,W3] :
% 0.54/0.83 ( ( aElement0(W0)
% 0.54/0.83 & aRewritingSystem0(W1)
% 0.54/0.83 & aElement0(W2)
% 0.54/0.83 & aElement0(W3) )
% 0.54/0.83 => ( ( sdtmndtplgtdt0(W0,W1,W2)
% 0.54/0.83 & sdtmndtplgtdt0(W2,W1,W3) )
% 0.54/0.83 => sdtmndtplgtdt0(W0,W1,W3) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mTCRDef,definition,
% 0.54/0.83 ! [W0,W1,W2] :
% 0.54/0.83 ( ( aElement0(W0)
% 0.54/0.83 & aRewritingSystem0(W1)
% 0.54/0.83 & aElement0(W2) )
% 0.54/0.83 => ( sdtmndtasgtdt0(W0,W1,W2)
% 0.54/0.83 <=> ( W0 = W2
% 0.54/0.83 | sdtmndtplgtdt0(W0,W1,W2) ) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mTCRTrans,axiom,
% 0.54/0.83 ! [W0,W1,W2,W3] :
% 0.54/0.83 ( ( aElement0(W0)
% 0.54/0.83 & aRewritingSystem0(W1)
% 0.54/0.83 & aElement0(W2)
% 0.54/0.83 & aElement0(W3) )
% 0.54/0.83 => ( ( sdtmndtasgtdt0(W0,W1,W2)
% 0.54/0.83 & sdtmndtasgtdt0(W2,W1,W3) )
% 0.54/0.83 => sdtmndtasgtdt0(W0,W1,W3) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mCRDef,definition,
% 0.54/0.83 ! [W0] :
% 0.54/0.83 ( aRewritingSystem0(W0)
% 0.54/0.83 => ( isConfluent0(W0)
% 0.54/0.83 <=> ! [W1,W2,W3] :
% 0.54/0.83 ( ( aElement0(W1)
% 0.54/0.83 & aElement0(W2)
% 0.54/0.83 & aElement0(W3)
% 0.54/0.83 & sdtmndtasgtdt0(W1,W0,W2)
% 0.54/0.83 & sdtmndtasgtdt0(W1,W0,W3) )
% 0.54/0.83 => ? [W4] :
% 0.54/0.83 ( aElement0(W4)
% 0.54/0.83 & sdtmndtasgtdt0(W2,W0,W4)
% 0.54/0.83 & sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mWCRDef,definition,
% 0.54/0.83 ! [W0] :
% 0.54/0.83 ( aRewritingSystem0(W0)
% 0.54/0.83 => ( isLocallyConfluent0(W0)
% 0.54/0.83 <=> ! [W1,W2,W3] :
% 0.54/0.83 ( ( aElement0(W1)
% 0.54/0.83 & aElement0(W2)
% 0.54/0.83 & aElement0(W3)
% 0.54/0.83 & aReductOfIn0(W2,W1,W0)
% 0.54/0.83 & aReductOfIn0(W3,W1,W0) )
% 0.54/0.83 => ? [W4] :
% 0.54/0.83 ( aElement0(W4)
% 0.54/0.83 & sdtmndtasgtdt0(W2,W0,W4)
% 0.54/0.83 & sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mTermin,definition,
% 0.54/0.83 ! [W0] :
% 0.54/0.83 ( aRewritingSystem0(W0)
% 0.54/0.83 => ( isTerminating0(W0)
% 0.54/0.83 <=> ! [W1,W2] :
% 0.54/0.83 ( ( aElement0(W1)
% 0.54/0.83 & aElement0(W2) )
% 0.54/0.83 => ( sdtmndtplgtdt0(W1,W0,W2)
% 0.54/0.83 => iLess0(W2,W1) ) ) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mNFRDef,definition,
% 0.54/0.83 ! [W0,W1] :
% 0.54/0.83 ( ( aElement0(W0)
% 0.54/0.83 & aRewritingSystem0(W1) )
% 0.54/0.83 => ! [W2] :
% 0.54/0.83 ( aNormalFormOfIn0(W2,W0,W1)
% 0.54/0.83 <=> ( aElement0(W2)
% 0.54/0.83 & sdtmndtasgtdt0(W0,W1,W2)
% 0.54/0.83 & ~ ? [W3] : aReductOfIn0(W3,W2,W1) ) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(mTermNF,axiom,
% 0.54/0.83 ! [W0] :
% 0.54/0.83 ( ( aRewritingSystem0(W0)
% 0.54/0.83 & isTerminating0(W0) )
% 0.54/0.83 => ! [W1] :
% 0.54/0.83 ( aElement0(W1)
% 0.54/0.83 => ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(m__656,hypothesis,
% 0.54/0.83 aRewritingSystem0(xR) ).
% 0.54/0.83
% 0.54/0.83 fof(m__656_01,hypothesis,
% 0.54/0.83 ( isLocallyConfluent0(xR)
% 0.54/0.83 & isTerminating0(xR) ) ).
% 0.54/0.83
% 0.54/0.83 fof(m__731,hypothesis,
% 0.54/0.83 ( aElement0(xa)
% 0.54/0.83 & aElement0(xb)
% 0.54/0.83 & aElement0(xc) ) ).
% 0.54/0.83
% 0.54/0.83 fof(m__715,hypothesis,
% 0.54/0.83 ! [W0,W1,W2] :
% 0.54/0.83 ( ( aElement0(W0)
% 0.54/0.83 & aElement0(W1)
% 0.54/0.83 & aElement0(W2)
% 0.54/0.83 & sdtmndtasgtdt0(W0,xR,W1)
% 0.54/0.83 & sdtmndtasgtdt0(W0,xR,W2) )
% 0.54/0.83 => ( iLess0(W0,xa)
% 0.54/0.83 => ? [W3] :
% 0.54/0.83 ( aElement0(W3)
% 0.54/0.83 & sdtmndtasgtdt0(W1,xR,W3)
% 0.54/0.83 & sdtmndtasgtdt0(W2,xR,W3) ) ) ) ).
% 0.54/0.83
% 0.54/0.83 fof(m__731_02,hypothesis,
% 0.54/0.83 ( sdtmndtplgtdt0(xa,xR,xb)
% 0.54/0.83 & sdtmndtplgtdt0(xa,xR,xc) ) ).
% 0.54/0.83
% 0.54/0.83 fof(m__755,hypothesis,
% 0.54/0.83 ( aElement0(xu)
% 0.54/0.83 & aReductOfIn0(xu,xa,xR)
% 0.54/0.83 & sdtmndtasgtdt0(xu,xR,xb) ) ).
% 0.54/0.83
% 0.54/0.83 fof(m__779,hypothesis,
% 0.54/0.83 ( aElement0(xv)
% 0.54/0.83 & aReductOfIn0(xv,xa,xR)
% 0.54/0.83 & sdtmndtasgtdt0(xv,xR,xc) ) ).
% 0.54/0.83
% 0.54/0.83 fof(m__,conjecture,
% 0.54/0.83 ? [W0] :
% 0.54/0.83 ( aElement0(W0)
% 0.54/0.83 & sdtmndtasgtdt0(xu,xR,W0)
% 0.54/0.83 & sdtmndtasgtdt0(xv,xR,W0) ) ).
% 0.54/0.83
% 0.54/0.83 %------------------------------------------------------------------------------
% 0.54/0.83 %-------------------------------------------
% 0.54/0.83 % Proof found
% 0.54/0.83 % SZS status Theorem for theBenchmark
% 0.54/0.83 % SZS output start Proof
% 0.54/0.83 %ClaNum:106(EqnAxiom:49)
% 0.54/0.83 %VarNum:381(SingletonVarNum:106)
% 0.54/0.83 %MaxLitNum:8
% 0.54/0.84 %MaxfuncDepth:1
% 0.54/0.84 %SharedTerms:20
% 0.54/0.84 %goalClause: 87
% 0.54/0.84 [50]P1(a1)
% 0.54/0.84 [51]P1(a17)
% 0.54/0.84 [52]P1(a18)
% 0.54/0.84 [53]P1(a19)
% 0.54/0.84 [54]P1(a20)
% 0.54/0.84 [55]P2(a2)
% 0.54/0.84 [56]P5(a2)
% 0.54/0.84 [57]P8(a2)
% 0.54/0.84 [58]P3(a19,a1,a2)
% 0.54/0.84 [59]P3(a20,a1,a2)
% 0.54/0.84 [60]P9(a1,a2,a17)
% 0.54/0.84 [61]P9(a1,a2,a18)
% 0.54/0.84 [62]P10(a19,a2,a17)
% 0.54/0.84 [63]P10(a20,a2,a18)
% 0.54/0.84 [87]~P1(x871)+~P10(a19,a2,x871)+~P10(a20,a2,x871)
% 0.54/0.84 [64]~P2(x641)+P6(x641)+P1(f3(x641))
% 0.54/0.84 [65]~P2(x651)+P6(x651)+P1(f11(x651))
% 0.54/0.84 [66]~P2(x661)+P6(x661)+P1(f12(x661))
% 0.54/0.84 [67]~P2(x671)+P5(x671)+P1(f13(x671))
% 0.54/0.84 [68]~P2(x681)+P5(x681)+P1(f15(x681))
% 0.54/0.84 [69]~P2(x691)+P5(x691)+P1(f16(x691))
% 0.54/0.84 [70]~P2(x701)+P8(x701)+P1(f4(x701))
% 0.54/0.84 [71]~P2(x711)+P8(x711)+P1(f5(x711))
% 0.54/0.84 [72]~P2(x721)+P8(x721)+~P7(f5(x721),f4(x721))
% 0.54/0.84 [73]~P2(x731)+P6(x731)+P10(f3(x731),x731,f11(x731))
% 0.54/0.84 [74]~P2(x741)+P6(x741)+P10(f3(x741),x741,f12(x741))
% 0.54/0.84 [75]~P2(x751)+P8(x751)+P9(f4(x751),x751,f5(x751))
% 0.54/0.84 [76]~P2(x761)+P5(x761)+P3(f15(x761),f13(x761),x761)
% 0.54/0.84 [77]~P2(x771)+P5(x771)+P3(f16(x771),f13(x771),x771)
% 0.54/0.84 [79]~P1(x792)+~P2(x791)+~P8(x791)+P4(f6(x791,x792),x792,x791)
% 0.54/0.84 [80]~P3(x801,x802,x803)+P1(x801)+~P1(x802)+~P2(x803)
% 0.54/0.84 [81]~P4(x811,x812,x813)+P1(x811)+~P1(x812)+~P2(x813)
% 0.54/0.84 [83]~P1(x831)+~P2(x832)+~P4(x833,x831,x832)+P10(x831,x832,x833)
% 0.54/0.84 [88]~P4(x884,x881,x882)+~P1(x881)+~P3(x883,x884,x882)+~P2(x882)
% 0.54/0.84 [89]~P2(x891)+P6(x891)+~P1(x892)+~P10(f11(x891),x891,x892)+~P10(f12(x891),x891,x892)
% 0.54/0.84 [90]~P2(x901)+P5(x901)+~P1(x902)+~P10(f15(x901),x901,x902)+~P10(f16(x901),x901,x902)
% 0.54/0.84 [78]~E(x781,x783)+~P1(x783)+~P1(x781)+~P2(x782)+P10(x781,x782,x783)
% 0.54/0.84 [84]~P1(x841)+~P1(x843)+~P2(x842)+~P3(x843,x841,x842)+P9(x841,x842,x843)
% 0.54/0.84 [85]~P1(x853)+~P1(x851)+~P2(x852)+~P9(x851,x852,x853)+P10(x851,x852,x853)
% 0.54/0.84 [82]~P1(x821)+~P1(x822)+~P8(x823)+~P9(x822,x823,x821)+P7(x821,x822)+~P2(x823)
% 0.54/0.84 [86]~P1(x862)+~P1(x861)+~P2(x863)+~P10(x861,x863,x862)+E(x861,x862)+P9(x861,x863,x862)
% 0.54/0.84 [94]~P1(x941)+~P1(x942)+~P2(x943)+~P9(x942,x943,x941)+P3(x941,x942,x943)+P1(f8(x942,x943,x941))
% 0.54/0.84 [96]~P1(x961)+~P1(x962)+~P2(x963)+~P9(x962,x963,x961)+P3(x961,x962,x963)+P3(f8(x962,x963,x961),x962,x963)
% 0.54/0.84 [97]~P1(x971)+~P1(x972)+~P2(x973)+~P9(x972,x973,x971)+P3(x971,x972,x973)+P9(f8(x972,x973,x971),x973,x971)
% 0.54/0.84 [98]~P1(x982)+~P1(x981)+~P2(x983)+~P10(x982,x983,x981)+P4(x981,x982,x983)+P3(f7(x982,x983,x981),x981,x983)
% 0.54/0.84 [95]~P1(x953)+~P1(x952)+~P1(x951)+~P10(x951,a2,x953)+~P10(x951,a2,x952)+~P7(x951,a1)+P1(f9(x951,x952,x953))
% 0.54/0.84 [99]~P1(x993)+~P1(x992)+~P1(x991)+~P10(x992,a2,x993)+~P10(x992,a2,x991)+~P7(x992,a1)+P10(x991,a2,f9(x992,x993,x991))
% 0.54/0.84 [100]~P1(x1003)+~P1(x1002)+~P1(x1001)+~P10(x1002,a2,x1003)+~P10(x1002,a2,x1001)+~P7(x1002,a1)+P10(x1001,a2,f9(x1002,x1001,x1003))
% 0.54/0.84 [91]~P1(x913)+~P1(x911)+~P2(x912)+~P3(x914,x911,x912)+~P9(x914,x912,x913)+P9(x911,x912,x913)+~P1(x914)
% 0.54/0.84 [92]~P1(x923)+~P1(x921)+~P2(x922)+~P9(x924,x922,x923)+~P9(x921,x922,x924)+P9(x921,x922,x923)+~P1(x924)
% 0.54/0.84 [93]~P1(x933)+~P1(x931)+~P2(x932)+~P10(x934,x932,x933)+~P10(x931,x932,x934)+P10(x931,x932,x933)+~P1(x934)
% 0.54/0.84 [101]~P1(x1014)+~P1(x1013)+~P1(x1012)+~P2(x1011)+~P6(x1011)+~P10(x1012,x1011,x1014)+~P10(x1012,x1011,x1013)+P1(f10(x1011,x1012,x1013,x1014))
% 0.54/0.84 [102]~P1(x1024)+~P1(x1023)+~P1(x1022)+~P2(x1021)+~P5(x1021)+~P3(x1024,x1022,x1021)+~P3(x1023,x1022,x1021)+P1(f14(x1021,x1022,x1023,x1024))
% 0.54/0.84 [103]~P1(x1034)+~P1(x1033)+~P1(x1031)+~P2(x1032)+~P6(x1032)+~P10(x1033,x1032,x1034)+~P10(x1033,x1032,x1031)+P10(x1031,x1032,f10(x1032,x1033,x1034,x1031))
% 0.54/0.84 [104]~P1(x1044)+~P1(x1043)+~P1(x1041)+~P2(x1042)+~P6(x1042)+~P10(x1043,x1042,x1044)+~P10(x1043,x1042,x1041)+P10(x1041,x1042,f10(x1042,x1043,x1041,x1044))
% 0.54/0.84 [105]~P1(x1054)+~P1(x1053)+~P1(x1051)+~P2(x1052)+~P5(x1052)+~P3(x1054,x1053,x1052)+~P3(x1051,x1053,x1052)+P10(x1051,x1052,f14(x1052,x1053,x1054,x1051))
% 0.54/0.84 [106]~P1(x1064)+~P1(x1063)+~P1(x1061)+~P2(x1062)+~P5(x1062)+~P3(x1064,x1063,x1062)+~P3(x1061,x1063,x1062)+P10(x1061,x1062,f14(x1062,x1063,x1061,x1064))
% 0.54/0.84 %EqnAxiom
% 0.54/0.84 [1]E(x11,x11)
% 0.54/0.84 [2]E(x22,x21)+~E(x21,x22)
% 0.54/0.84 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.54/0.84 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.54/0.84 [5]~E(x51,x52)+E(f11(x51),f11(x52))
% 0.54/0.84 [6]~E(x61,x62)+E(f12(x61),f12(x62))
% 0.54/0.84 [7]~E(x71,x72)+E(f13(x71),f13(x72))
% 0.54/0.84 [8]~E(x81,x82)+E(f15(x81),f15(x82))
% 0.54/0.84 [9]~E(x91,x92)+E(f16(x91),f16(x92))
% 0.54/0.84 [10]~E(x101,x102)+E(f4(x101),f4(x102))
% 0.54/0.84 [11]~E(x111,x112)+E(f5(x111),f5(x112))
% 0.54/0.84 [12]~E(x121,x122)+E(f8(x121,x123,x124),f8(x122,x123,x124))
% 0.54/0.84 [13]~E(x131,x132)+E(f8(x133,x131,x134),f8(x133,x132,x134))
% 0.54/0.84 [14]~E(x141,x142)+E(f8(x143,x144,x141),f8(x143,x144,x142))
% 0.54/0.84 [15]~E(x151,x152)+E(f10(x151,x153,x154,x155),f10(x152,x153,x154,x155))
% 0.54/0.84 [16]~E(x161,x162)+E(f10(x163,x161,x164,x165),f10(x163,x162,x164,x165))
% 0.54/0.84 [17]~E(x171,x172)+E(f10(x173,x174,x171,x175),f10(x173,x174,x172,x175))
% 0.54/0.84 [18]~E(x181,x182)+E(f10(x183,x184,x185,x181),f10(x183,x184,x185,x182))
% 0.54/0.84 [19]~E(x191,x192)+E(f14(x191,x193,x194,x195),f14(x192,x193,x194,x195))
% 0.54/0.84 [20]~E(x201,x202)+E(f14(x203,x201,x204,x205),f14(x203,x202,x204,x205))
% 0.54/0.84 [21]~E(x211,x212)+E(f14(x213,x214,x211,x215),f14(x213,x214,x212,x215))
% 0.54/0.84 [22]~E(x221,x222)+E(f14(x223,x224,x225,x221),f14(x223,x224,x225,x222))
% 0.54/0.84 [23]~E(x231,x232)+E(f9(x231,x233,x234),f9(x232,x233,x234))
% 0.54/0.84 [24]~E(x241,x242)+E(f9(x243,x241,x244),f9(x243,x242,x244))
% 0.54/0.84 [25]~E(x251,x252)+E(f9(x253,x254,x251),f9(x253,x254,x252))
% 0.54/0.84 [26]~E(x261,x262)+E(f6(x261,x263),f6(x262,x263))
% 0.54/0.84 [27]~E(x271,x272)+E(f6(x273,x271),f6(x273,x272))
% 0.54/0.84 [28]~E(x281,x282)+E(f7(x281,x283,x284),f7(x282,x283,x284))
% 0.54/0.84 [29]~E(x291,x292)+E(f7(x293,x291,x294),f7(x293,x292,x294))
% 0.54/0.84 [30]~E(x301,x302)+E(f7(x303,x304,x301),f7(x303,x304,x302))
% 0.54/0.84 [31]~P1(x311)+P1(x312)+~E(x311,x312)
% 0.54/0.84 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 0.54/0.84 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 0.54/0.84 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 0.54/0.84 [35]P10(x352,x353,x354)+~E(x351,x352)+~P10(x351,x353,x354)
% 0.54/0.84 [36]P10(x363,x362,x364)+~E(x361,x362)+~P10(x363,x361,x364)
% 0.54/0.84 [37]P10(x373,x374,x372)+~E(x371,x372)+~P10(x373,x374,x371)
% 0.54/0.84 [38]~P5(x381)+P5(x382)+~E(x381,x382)
% 0.54/0.84 [39]~P2(x391)+P2(x392)+~E(x391,x392)
% 0.54/0.84 [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404)
% 0.54/0.84 [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414)
% 0.54/0.84 [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421)
% 0.54/0.84 [43]P9(x432,x433,x434)+~E(x431,x432)+~P9(x431,x433,x434)
% 0.54/0.84 [44]P9(x443,x442,x444)+~E(x441,x442)+~P9(x443,x441,x444)
% 0.54/0.84 [45]P9(x453,x454,x452)+~E(x451,x452)+~P9(x453,x454,x451)
% 0.54/0.84 [46]~P8(x461)+P8(x462)+~E(x461,x462)
% 0.54/0.84 [47]~P6(x471)+P6(x472)+~E(x471,x472)
% 0.54/0.84 [48]P7(x482,x483)+~E(x481,x482)+~P7(x481,x483)
% 0.54/0.84 [49]P7(x493,x492)+~E(x491,x492)+~P7(x493,x491)
% 0.54/0.84
% 0.54/0.84 %-------------------------------------------
% 0.54/0.84 cnf(107,plain,
% 0.54/0.84 (~P10(a20,a2,a17)),
% 0.54/0.84 inference(scs_inference,[],[51,62,87])).
% 0.54/0.84 cnf(108,plain,
% 0.54/0.84 (~P4(a1,a1,a2)),
% 0.54/0.84 inference(scs_inference,[],[50,51,55,58,62,87,88])).
% 0.54/0.84 cnf(110,plain,
% 0.54/0.84 (P10(a1,a2,a17)),
% 0.54/0.84 inference(scs_inference,[],[50,51,54,55,58,60,62,87,88,83,85])).
% 0.54/0.84 cnf(115,plain,
% 0.54/0.84 (~P10(a18,a2,a17)),
% 0.54/0.84 inference(scs_inference,[],[50,51,52,53,54,55,57,58,60,62,63,87,88,83,85,84,82,93])).
% 0.54/0.84 cnf(118,plain,
% 0.54/0.84 (~E(a18,a17)),
% 0.54/0.84 inference(scs_inference,[],[50,51,52,53,54,55,57,58,60,62,63,87,88,83,85,84,82,93,46,37])).
% 0.54/0.84 cnf(120,plain,
% 0.54/0.84 (P4(f6(a2,a1),a1,a2)),
% 0.54/0.84 inference(scs_inference,[],[50,51,52,53,54,55,57,58,60,62,63,87,88,83,85,84,82,93,46,37,35,79])).
% 0.54/0.84 cnf(124,plain,
% 0.54/0.84 (P10(a19,a2,f14(a2,a1,a19,a19))),
% 0.54/0.84 inference(scs_inference,[],[50,51,52,53,54,55,56,57,58,60,62,63,87,88,83,85,84,82,93,46,37,35,79,78,106])).
% 0.54/0.84 cnf(126,plain,
% 0.54/0.84 (P1(f14(a2,a1,a19,a19))),
% 0.54/0.84 inference(scs_inference,[],[50,51,52,53,54,55,56,57,58,60,62,63,87,88,83,85,84,82,93,46,37,35,79,78,106,102])).
% 0.54/0.84 cnf(138,plain,
% 0.54/0.84 (P1(f6(a2,a1))),
% 0.54/0.84 inference(scs_inference,[],[50,51,52,53,54,55,56,57,58,60,62,63,87,88,83,85,84,82,93,46,37,35,79,78,106,102,66,65,64,74,73,81])).
% 0.54/0.84 cnf(146,plain,
% 0.54/0.84 (~E(f6(a2,a1),a1)),
% 0.54/0.84 inference(scs_inference,[],[118,120,108,2,40])).
% 0.54/0.84 cnf(149,plain,
% 0.54/0.84 (~P3(x1491,f6(a2,a1),a2)),
% 0.54/0.84 inference(scs_inference,[],[50,52,63,55,118,120,108,2,40,87,88])).
% 0.54/0.84 cnf(155,plain,
% 0.54/0.84 (P1(f14(a2,a1,a20,a20))),
% 0.54/0.84 inference(scs_inference,[],[50,59,52,56,63,53,54,51,55,118,120,107,108,110,2,40,87,88,78,93,102])).
% 0.54/0.84 cnf(157,plain,
% 0.54/0.84 (P10(a20,a2,f14(a2,a1,a20,a20))),
% 0.54/0.84 inference(scs_inference,[],[50,59,52,56,63,53,54,51,55,118,120,107,108,110,2,40,87,88,78,93,102,106])).
% 0.54/0.84 cnf(159,plain,
% 0.54/0.84 (P10(a1,a2,f6(a2,a1))),
% 0.83/0.84 inference(scs_inference,[],[50,59,52,56,63,53,54,51,55,118,120,107,108,110,2,40,87,88,78,93,102,106,83])).
% 0.83/0.84 cnf(161,plain,
% 0.83/0.84 (P4(f6(a2,a18),a18,a2)),
% 0.83/0.84 inference(scs_inference,[],[50,59,52,56,63,57,53,54,51,55,118,120,107,108,110,2,40,87,88,78,93,102,106,83,79])).
% 0.83/0.84 cnf(163,plain,
% 0.83/0.84 (~P9(a20,a2,a17)),
% 0.83/0.84 inference(scs_inference,[],[50,59,52,56,63,57,53,54,51,55,118,120,107,108,110,2,40,87,88,78,93,102,106,83,79,85])).
% 0.83/0.84 cnf(166,plain,
% 0.83/0.84 (~E(a1,a20)),
% 0.83/0.84 inference(scs_inference,[],[50,59,52,60,56,63,57,53,54,51,55,118,120,107,108,110,2,40,87,88,78,93,102,106,83,79,85,45,43])).
% 0.83/0.84 cnf(167,plain,
% 0.83/0.84 (~E(a1,f6(a2,a1))),
% 0.83/0.84 inference(scs_inference,[],[50,59,52,60,56,63,57,53,54,51,55,118,120,107,108,110,2,40,87,88,78,93,102,106,83,79,85,45,43,33])).
% 0.83/0.84 cnf(176,plain,
% 0.83/0.84 (~P9(f6(a2,a1),a2,a20)+P3(f8(f6(a2,a1),a2,a20),f6(a2,a1),a2)),
% 0.83/0.84 inference(scs_inference,[],[50,59,52,60,56,63,57,53,54,51,55,124,138,118,120,107,108,110,2,40,87,88,78,93,102,106,83,79,85,45,43,33,35,81,37,80,97,96])).
% 0.83/0.84 cnf(187,plain,
% 0.83/0.84 (~P9(f6(a2,a1),a2,a20)),
% 0.83/0.84 inference(scs_inference,[],[149,176])).
% 0.83/0.84 cnf(193,plain,
% 0.83/0.84 (~P10(a20,a2,f14(a2,a1,a19,a19))),
% 0.83/0.84 inference(scs_inference,[],[51,60,54,55,126,163,149,124,50,176,84,92,87])).
% 0.83/0.84 cnf(195,plain,
% 0.83/0.84 (~P3(x1951,f6(a2,a18),a2)),
% 0.83/0.84 inference(scs_inference,[],[51,60,52,54,55,126,163,149,161,124,50,176,84,92,87,88])).
% 0.83/0.84 cnf(197,plain,
% 0.83/0.84 (P4(f6(a2,a17),a17,a2)),
% 0.83/0.84 inference(scs_inference,[],[51,60,57,52,54,55,126,163,149,161,124,50,176,84,92,87,88,79])).
% 0.83/0.84 cnf(204,plain,
% 0.83/0.84 (P10(a19,a2,f14(a2,a1,a20,a19))),
% 0.83/0.84 inference(scs_inference,[],[51,60,59,57,53,56,58,52,54,55,126,159,163,149,167,161,124,138,50,176,84,92,87,88,79,83,44,86,105])).
% 0.83/0.84 cnf(208,plain,
% 0.83/0.84 (P1(f6(a2,a17))),
% 0.83/0.84 inference(scs_inference,[],[51,60,59,57,53,56,58,52,54,55,126,159,163,149,167,161,124,138,50,176,84,92,87,88,79,83,44,86,105,91,81])).
% 0.83/0.84 cnf(235,plain,
% 0.83/0.84 (~P10(a19,a2,f14(a2,a1,a20,a20))),
% 0.83/0.84 inference(scs_inference,[],[51,59,54,55,155,157,195,193,126,33,78,88,87])).
% 0.83/0.84 cnf(262,plain,
% 0.83/0.84 (~P3(x2621,f6(a2,a17),a2)),
% 0.83/0.84 inference(scs_inference,[],[55,197,51,88])).
% 0.83/0.84 cnf(268,plain,
% 0.83/0.84 (P9(a1,a2,a20)),
% 0.83/0.84 inference(scs_inference,[],[52,59,62,53,54,55,115,166,197,50,51,88,39,2,93,84])).
% 0.83/0.84 cnf(296,plain,
% 0.83/0.84 (~P9(f6(a2,a1),a2,a1)),
% 0.83/0.84 inference(scs_inference,[],[56,54,55,268,187,138,50,38,92])).
% 0.83/0.84 cnf(311,plain,
% 0.83/0.84 (P10(a20,a2,f14(a2,a1,a20,a19))),
% 0.83/0.84 inference(scs_inference,[],[53,63,56,59,58,62,54,55,235,268,262,187,208,197,138,52,50,38,92,37,41,95,94,100,99,104,106])).
% 0.83/0.84 cnf(319,plain,
% 0.83/0.84 (~P1(f14(a2,a1,a20,a19))),
% 0.83/0.84 inference(scs_inference,[],[55,146,296,311,204,138,50,86,87])).
% 0.83/0.84 cnf(351,plain,
% 0.83/0.84 ($false),
% 0.83/0.84 inference(scs_inference,[],[54,110,56,58,59,55,319,115,53,50,31,35,102]),
% 0.83/0.84 ['proof']).
% 0.83/0.84 % SZS output end Proof
% 0.83/0.84 % Total time :0.190000s
%------------------------------------------------------------------------------