TSTP Solution File: RNG087+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG087+2 : 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 : n023.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 13:48:05 EDT 2023
% Result : Theorem 0.51s 0.62s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG087+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n023.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 : Sun Aug 27 02:34:56 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.48/0.54 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 %-------------------------------------------
% 0.51/0.61 %------------------------------------------------------------------------------
% 0.51/0.61 % File : RNG087+2 : TPTP v8.1.2. Released v4.0.0.
% 0.51/0.61 % Domain : Ring Theory
% 0.51/0.61 % Problem : Chinese remainder theorem in a ring 03_02, 01 expansion
% 0.51/0.61 % Version : Especial.
% 0.51/0.61 % English :
% 0.51/0.61
% 0.51/0.61 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.51/0.61 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.51/0.61 % Source : [Pas08]
% 0.51/0.61 % Names : chines_03_02.01 [Pas08]
% 0.51/0.61
% 0.51/0.61 % Status : Theorem
% 0.51/0.61 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.04 v6.1.0, 0.17 v5.5.0, 0.26 v5.4.0, 0.32 v5.3.0, 0.30 v5.2.0, 0.10 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.39 v4.0.1, 0.78 v4.0.0
% 0.51/0.61 % Syntax : Number of formulae : 28 ( 3 unt; 3 def)
% 0.51/0.61 % Number of atoms : 115 ( 28 equ)
% 0.51/0.61 % Maximal formula atoms : 14 ( 4 avg)
% 0.51/0.61 % Number of connectives : 88 ( 1 ~; 1 |; 47 &)
% 0.51/0.61 % ( 5 <=>; 34 =>; 0 <=; 0 <~>)
% 0.51/0.61 % Maximal formula depth : 13 ( 5 avg)
% 0.51/0.61 % Maximal term depth : 3 ( 1 avg)
% 0.51/0.61 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% 0.51/0.61 % Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% 0.51/0.61 % Number of variables : 59 ( 51 !; 8 ?)
% 0.51/0.61 % SPC : FOF_THM_RFO_SEQ
% 0.51/0.61
% 0.51/0.61 % Comments : Problem generated by the SAD system [VLP07]
% 0.51/0.61 %------------------------------------------------------------------------------
% 0.51/0.61 fof(mElmSort,axiom,
% 0.51/0.61 ! [W0] :
% 0.51/0.61 ( aElement0(W0)
% 0.51/0.61 => $true ) ).
% 0.51/0.61
% 0.51/0.61 fof(mSortsC,axiom,
% 0.51/0.61 aElement0(sz00) ).
% 0.51/0.61
% 0.51/0.61 fof(mSortsC_01,axiom,
% 0.51/0.61 aElement0(sz10) ).
% 0.51/0.61
% 0.51/0.61 fof(mSortsU,axiom,
% 0.51/0.61 ! [W0] :
% 0.51/0.61 ( aElement0(W0)
% 0.51/0.61 => aElement0(smndt0(W0)) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mSortsB,axiom,
% 0.51/0.61 ! [W0,W1] :
% 0.51/0.61 ( ( aElement0(W0)
% 0.51/0.61 & aElement0(W1) )
% 0.51/0.61 => aElement0(sdtpldt0(W0,W1)) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mSortsB_02,axiom,
% 0.51/0.61 ! [W0,W1] :
% 0.51/0.61 ( ( aElement0(W0)
% 0.51/0.61 & aElement0(W1) )
% 0.51/0.61 => aElement0(sdtasdt0(W0,W1)) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mAddComm,axiom,
% 0.51/0.61 ! [W0,W1] :
% 0.51/0.61 ( ( aElement0(W0)
% 0.51/0.61 & aElement0(W1) )
% 0.51/0.61 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mAddAsso,axiom,
% 0.51/0.61 ! [W0,W1,W2] :
% 0.51/0.61 ( ( aElement0(W0)
% 0.51/0.61 & aElement0(W1)
% 0.51/0.61 & aElement0(W2) )
% 0.51/0.61 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mAddZero,axiom,
% 0.51/0.61 ! [W0] :
% 0.51/0.61 ( aElement0(W0)
% 0.51/0.61 => ( sdtpldt0(W0,sz00) = W0
% 0.51/0.61 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mAddInvr,axiom,
% 0.51/0.61 ! [W0] :
% 0.51/0.61 ( aElement0(W0)
% 0.51/0.61 => ( sdtpldt0(W0,smndt0(W0)) = sz00
% 0.51/0.61 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mMulComm,axiom,
% 0.51/0.61 ! [W0,W1] :
% 0.51/0.61 ( ( aElement0(W0)
% 0.51/0.61 & aElement0(W1) )
% 0.51/0.61 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mMulAsso,axiom,
% 0.51/0.61 ! [W0,W1,W2] :
% 0.51/0.61 ( ( aElement0(W0)
% 0.51/0.61 & aElement0(W1)
% 0.51/0.61 & aElement0(W2) )
% 0.51/0.61 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mMulUnit,axiom,
% 0.51/0.61 ! [W0] :
% 0.51/0.61 ( aElement0(W0)
% 0.51/0.61 => ( sdtasdt0(W0,sz10) = W0
% 0.51/0.61 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mAMDistr,axiom,
% 0.51/0.61 ! [W0,W1,W2] :
% 0.51/0.61 ( ( aElement0(W0)
% 0.51/0.61 & aElement0(W1)
% 0.51/0.61 & aElement0(W2) )
% 0.51/0.61 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.51/0.61 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mMulMnOne,axiom,
% 0.51/0.61 ! [W0] :
% 0.51/0.61 ( aElement0(W0)
% 0.51/0.61 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
% 0.51/0.61 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mMulZero,axiom,
% 0.51/0.61 ! [W0] :
% 0.51/0.61 ( aElement0(W0)
% 0.51/0.61 => ( sdtasdt0(W0,sz00) = sz00
% 0.51/0.61 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.51/0.61
% 0.51/0.61 fof(mCancel,axiom,
% 0.51/0.61 ! [W0,W1] :
% 0.51/0.61 ( ( aElement0(W0)
% 0.51/0.61 & aElement0(W1) )
% 0.51/0.62 => ( sdtasdt0(W0,W1) = sz00
% 0.51/0.62 => ( W0 = sz00
% 0.51/0.62 | W1 = sz00 ) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mUnNeZr,axiom,
% 0.51/0.62 sz10 != sz00 ).
% 0.51/0.62
% 0.51/0.62 fof(mSetSort,axiom,
% 0.51/0.62 ! [W0] :
% 0.51/0.62 ( aSet0(W0)
% 0.51/0.62 => $true ) ).
% 0.51/0.62
% 0.51/0.62 fof(mEOfElem,axiom,
% 0.51/0.62 ! [W0] :
% 0.51/0.62 ( aSet0(W0)
% 0.51/0.62 => ! [W1] :
% 0.51/0.62 ( aElementOf0(W1,W0)
% 0.51/0.62 => aElement0(W1) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mSetEq,axiom,
% 0.51/0.62 ! [W0,W1] :
% 0.51/0.62 ( ( aSet0(W0)
% 0.51/0.62 & aSet0(W1) )
% 0.51/0.62 => ( ( ! [W2] :
% 0.51/0.62 ( aElementOf0(W2,W0)
% 0.51/0.62 => aElementOf0(W2,W1) )
% 0.51/0.62 & ! [W2] :
% 0.51/0.62 ( aElementOf0(W2,W1)
% 0.51/0.62 => aElementOf0(W2,W0) ) )
% 0.51/0.62 => W0 = W1 ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mDefSSum,definition,
% 0.51/0.62 ! [W0,W1] :
% 0.51/0.62 ( ( aSet0(W0)
% 0.51/0.62 & aSet0(W1) )
% 0.51/0.62 => ! [W2] :
% 0.51/0.62 ( W2 = sdtpldt1(W0,W1)
% 0.51/0.62 <=> ( aSet0(W2)
% 0.51/0.62 & ! [W3] :
% 0.51/0.62 ( aElementOf0(W3,W2)
% 0.51/0.62 <=> ? [W4,W5] :
% 0.51/0.62 ( aElementOf0(W4,W0)
% 0.51/0.62 & aElementOf0(W5,W1)
% 0.51/0.62 & sdtpldt0(W4,W5) = W3 ) ) ) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mDefSInt,definition,
% 0.51/0.62 ! [W0,W1] :
% 0.51/0.62 ( ( aSet0(W0)
% 0.51/0.62 & aSet0(W1) )
% 0.51/0.62 => ! [W2] :
% 0.51/0.62 ( W2 = sdtasasdt0(W0,W1)
% 0.51/0.62 <=> ( aSet0(W2)
% 0.51/0.62 & ! [W3] :
% 0.51/0.62 ( aElementOf0(W3,W2)
% 0.51/0.62 <=> ( aElementOf0(W3,W0)
% 0.51/0.62 & aElementOf0(W3,W1) ) ) ) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(mDefIdeal,definition,
% 0.51/0.62 ! [W0] :
% 0.51/0.62 ( aIdeal0(W0)
% 0.51/0.62 <=> ( aSet0(W0)
% 0.51/0.62 & ! [W1] :
% 0.51/0.62 ( aElementOf0(W1,W0)
% 0.51/0.62 => ( ! [W2] :
% 0.51/0.62 ( aElementOf0(W2,W0)
% 0.51/0.62 => aElementOf0(sdtpldt0(W1,W2),W0) )
% 0.51/0.62 & ! [W2] :
% 0.51/0.62 ( aElement0(W2)
% 0.51/0.62 => aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(m__870,hypothesis,
% 0.51/0.62 ( aSet0(xI)
% 0.51/0.62 & ! [W0] :
% 0.51/0.62 ( aElementOf0(W0,xI)
% 0.51/0.62 => ( ! [W1] :
% 0.51/0.62 ( aElementOf0(W1,xI)
% 0.51/0.62 => aElementOf0(sdtpldt0(W0,W1),xI) )
% 0.51/0.62 & ! [W1] :
% 0.51/0.62 ( aElement0(W1)
% 0.51/0.62 => aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
% 0.51/0.62 & aIdeal0(xI)
% 0.51/0.62 & aSet0(xJ)
% 0.51/0.62 & ! [W0] :
% 0.51/0.62 ( aElementOf0(W0,xJ)
% 0.51/0.62 => ( ! [W1] :
% 0.51/0.62 ( aElementOf0(W1,xJ)
% 0.51/0.62 => aElementOf0(sdtpldt0(W0,W1),xJ) )
% 0.51/0.62 & ! [W1] :
% 0.51/0.62 ( aElement0(W1)
% 0.51/0.62 => aElementOf0(sdtasdt0(W1,W0),xJ) ) ) )
% 0.51/0.62 & aIdeal0(xJ) ) ).
% 0.51/0.62
% 0.51/0.62 fof(m__901,hypothesis,
% 0.51/0.62 ( ? [W0,W1] :
% 0.51/0.62 ( aElementOf0(W0,xI)
% 0.51/0.62 & aElementOf0(W1,xJ)
% 0.51/0.62 & sdtpldt0(W0,W1) = xx )
% 0.51/0.62 & aElementOf0(xx,sdtpldt1(xI,xJ))
% 0.51/0.62 & ? [W0,W1] :
% 0.51/0.62 ( aElementOf0(W0,xI)
% 0.51/0.62 & aElementOf0(W1,xJ)
% 0.51/0.62 & sdtpldt0(W0,W1) = xy )
% 0.51/0.62 & aElementOf0(xy,sdtpldt1(xI,xJ))
% 0.51/0.62 & aElement0(xz) ) ).
% 0.51/0.62
% 0.51/0.62 fof(m__934,hypothesis,
% 0.51/0.62 ( aElementOf0(xk,xI)
% 0.51/0.62 & aElementOf0(xl,xJ)
% 0.51/0.62 & xx = sdtpldt0(xk,xl) ) ).
% 0.51/0.62
% 0.51/0.62 fof(m__,conjecture,
% 0.51/0.62 ? [W0,W1] :
% 0.51/0.62 ( aElementOf0(W0,xI)
% 0.51/0.62 & aElementOf0(W1,xJ)
% 0.51/0.62 & xy = sdtpldt0(W0,W1) ) ).
% 0.51/0.62
% 0.51/0.62 %------------------------------------------------------------------------------
% 0.51/0.62 %-------------------------------------------
% 0.51/0.62 % Proof found
% 0.51/0.62 % SZS status Theorem for theBenchmark
% 0.51/0.62 % SZS output start Proof
% 0.51/0.62 %ClaNum:117(EqnAxiom:44)
% 0.51/0.62 %VarNum:412(SingletonVarNum:124)
% 0.51/0.62 %MaxLitNum:8
% 0.51/0.62 %MaxfuncDepth:2
% 0.51/0.62 %SharedTerms:37
% 0.51/0.62 %goalClause: 86
% 0.51/0.62 [45]P1(a1)
% 0.51/0.62 [46]P1(a22)
% 0.51/0.62 [47]P1(a23)
% 0.51/0.62 [48]P2(a24)
% 0.51/0.62 [49]P2(a25)
% 0.51/0.62 [50]P3(a24)
% 0.51/0.62 [51]P3(a25)
% 0.51/0.62 [55]P4(a26,a24)
% 0.51/0.62 [56]P4(a27,a25)
% 0.51/0.62 [57]P4(a3,a24)
% 0.51/0.62 [58]P4(a6,a25)
% 0.51/0.62 [59]P4(a7,a24)
% 0.51/0.62 [60]P4(a8,a25)
% 0.51/0.62 [63]~E(a1,a22)
% 0.51/0.62 [52]E(f2(a26,a27),a28)
% 0.51/0.62 [53]E(f2(a3,a6),a28)
% 0.51/0.62 [54]E(f2(a7,a8),a29)
% 0.51/0.62 [61]P4(a28,f20(a24,a25))
% 0.51/0.62 [62]P4(a29,f20(a24,a25))
% 0.51/0.62 [64]~P3(x641)+P2(x641)
% 0.51/0.62 [65]~P1(x651)+P1(f21(x651))
% 0.51/0.62 [66]~P1(x661)+E(f9(a1,x661),a1)
% 0.51/0.62 [67]~P1(x671)+E(f9(x671,a1),a1)
% 0.51/0.62 [68]~P1(x681)+E(f2(a1,x681),x681)
% 0.51/0.62 [69]~P1(x691)+E(f9(a22,x691),x691)
% 0.51/0.62 [70]~P1(x701)+E(f2(x701,a1),x701)
% 0.51/0.62 [71]~P1(x711)+E(f9(x711,a22),x711)
% 0.51/0.62 [72]~P1(x721)+E(f2(f21(x721),x721),a1)
% 0.51/0.62 [73]~P1(x731)+E(f2(x731,f21(x731)),a1)
% 0.51/0.62 [74]~P1(x741)+E(f9(x741,f21(a22)),f21(x741))
% 0.51/0.62 [75]~P1(x751)+E(f9(f21(a22),x751),f21(x751))
% 0.51/0.62 [76]~P2(x761)+P3(x761)+P4(f10(x761),x761)
% 0.51/0.62 [77]~P4(x771,x772)+P1(x771)+~P2(x772)
% 0.51/0.62 [79]~P1(x792)+~P1(x791)+E(f2(x791,x792),f2(x792,x791))
% 0.51/0.62 [80]~P1(x802)+~P1(x801)+E(f9(x801,x802),f9(x802,x801))
% 0.51/0.62 [84]~P1(x842)+~P1(x841)+P1(f2(x841,x842))
% 0.51/0.62 [85]~P1(x852)+~P1(x851)+P1(f9(x851,x852))
% 0.51/0.62 [86]~P4(x862,a25)+~P4(x861,a24)+~E(f2(x861,x862),a29)
% 0.51/0.62 [87]~P1(x871)+~P4(x872,a24)+P4(f9(x871,x872),a24)
% 0.51/0.62 [88]~P1(x881)+~P4(x882,a25)+P4(f9(x881,x882),a25)
% 0.51/0.62 [92]~P4(x921,a24)+~P4(x922,a24)+P4(f2(x921,x922),a24)
% 0.51/0.62 [93]~P4(x931,a25)+~P4(x932,a25)+P4(f2(x931,x932),a25)
% 0.51/0.62 [83]~P2(x831)+P3(x831)+P4(f5(x831),x831)+P1(f4(x831))
% 0.51/0.62 [102]~P2(x1021)+P3(x1021)+P1(f4(x1021))+~P4(f2(f10(x1021),f5(x1021)),x1021)
% 0.51/0.62 [105]~P2(x1051)+P3(x1051)+P4(f5(x1051),x1051)+~P4(f9(f4(x1051),f10(x1051)),x1051)
% 0.51/0.62 [107]~P2(x1071)+P3(x1071)+~P4(f2(f10(x1071),f5(x1071)),x1071)+~P4(f9(f4(x1071),f10(x1071)),x1071)
% 0.51/0.62 [81]~P2(x813)+~P2(x812)+P2(x811)+~E(x811,f20(x812,x813))
% 0.51/0.62 [82]~P2(x823)+~P2(x822)+P2(x821)+~E(x821,f19(x822,x823))
% 0.51/0.62 [91]~P1(x911)+~P3(x913)+~P4(x912,x913)+P4(f9(x911,x912),x913)
% 0.51/0.62 [94]~P3(x943)+~P4(x941,x943)+~P4(x942,x943)+P4(f2(x941,x942),x943)
% 0.51/0.62 [97]~P1(x973)+~P1(x972)+~P1(x971)+E(f2(f2(x971,x972),x973),f2(x971,f2(x972,x973)))
% 0.51/0.62 [98]~P1(x983)+~P1(x982)+~P1(x981)+E(f9(f9(x981,x982),x983),f9(x981,f9(x982,x983)))
% 0.51/0.62 [103]~P1(x1033)+~P1(x1032)+~P1(x1031)+E(f2(f9(x1031,x1032),f9(x1031,x1033)),f9(x1031,f2(x1032,x1033)))
% 0.51/0.62 [104]~P1(x1042)+~P1(x1043)+~P1(x1041)+E(f2(f9(x1041,x1042),f9(x1043,x1042)),f9(f2(x1041,x1043),x1042))
% 0.51/0.62 [78]~P1(x781)+~P1(x782)+E(x781,a1)+E(x782,a1)+~E(f9(x782,x781),a1)
% 0.51/0.62 [95]~P2(x952)+~P2(x951)+E(x951,x952)+P4(f11(x951,x952),x951)+P4(f12(x951,x952),x952)
% 0.51/0.62 [99]~P2(x992)+~P2(x991)+E(x991,x992)+P4(f11(x991,x992),x991)+~P4(f12(x991,x992),x991)
% 0.51/0.62 [100]~P2(x1002)+~P2(x1001)+E(x1001,x1002)+P4(f12(x1001,x1002),x1002)+~P4(f11(x1001,x1002),x1002)
% 0.51/0.62 [106]~P2(x1062)+~P2(x1061)+E(x1061,x1062)+~P4(f11(x1061,x1062),x1062)+~P4(f12(x1061,x1062),x1061)
% 0.51/0.62 [89]~P2(x894)+~P2(x892)+~P4(x891,x893)+P4(x891,x892)+~E(x893,f19(x894,x892))
% 0.51/0.62 [90]~P2(x904)+~P2(x902)+~P4(x901,x903)+P4(x901,x902)+~E(x903,f19(x902,x904))
% 0.51/0.62 [114]~P2(x1142)+~P2(x1141)+~P4(x1144,x1143)+~E(x1143,f20(x1141,x1142))+P4(f14(x1141,x1142,x1143,x1144),x1141)
% 0.51/0.62 [115]~P2(x1152)+~P2(x1151)+~P4(x1154,x1153)+~E(x1153,f20(x1151,x1152))+P4(f15(x1151,x1152,x1153,x1154),x1152)
% 0.51/0.62 [117]~P2(x1172)+~P2(x1171)+~P4(x1174,x1173)+~E(x1173,f20(x1171,x1172))+E(f2(f14(x1171,x1172,x1173,x1174),f15(x1171,x1172,x1173,x1174)),x1174)
% 0.51/0.62 [108]~P2(x1081)+~P2(x1083)+~P2(x1082)+P4(f13(x1082,x1083,x1081),x1081)+P4(f16(x1082,x1083,x1081),x1082)+E(x1081,f20(x1082,x1083))
% 0.51/0.62 [109]~P2(x1091)+~P2(x1093)+~P2(x1092)+P4(f13(x1092,x1093,x1091),x1091)+P4(f17(x1092,x1093,x1091),x1093)+E(x1091,f20(x1092,x1093))
% 0.51/0.62 [110]~P2(x1101)+~P2(x1103)+~P2(x1102)+P4(f18(x1102,x1103,x1101),x1101)+P4(f18(x1102,x1103,x1101),x1103)+E(x1101,f19(x1102,x1103))
% 0.51/0.62 [111]~P2(x1111)+~P2(x1113)+~P2(x1112)+P4(f18(x1112,x1113,x1111),x1111)+P4(f18(x1112,x1113,x1111),x1112)+E(x1111,f19(x1112,x1113))
% 0.51/0.62 [113]~P2(x1131)+~P2(x1133)+~P2(x1132)+P4(f13(x1132,x1133,x1131),x1131)+E(x1131,f20(x1132,x1133))+E(f2(f16(x1132,x1133,x1131),f17(x1132,x1133,x1131)),f13(x1132,x1133,x1131))
% 0.51/0.62 [96]~P2(x964)+~P2(x963)+~P4(x961,x964)+~P4(x961,x963)+P4(x961,x962)+~E(x962,f19(x963,x964))
% 0.51/0.62 [116]~P2(x1161)+~P2(x1163)+~P2(x1162)+~P4(f18(x1162,x1163,x1161),x1161)+~P4(f18(x1162,x1163,x1161),x1163)+~P4(f18(x1162,x1163,x1161),x1162)+E(x1161,f19(x1162,x1163))
% 0.51/0.62 [101]~P2(x1014)+~P2(x1013)+~P4(x1016,x1014)+~P4(x1015,x1013)+P4(x1011,x1012)+~E(x1012,f20(x1013,x1014))+~E(f2(x1015,x1016),x1011)
% 0.51/0.62 [112]~P2(x1121)+~P2(x1123)+~P2(x1122)+~P4(x1125,x1123)+~P4(x1124,x1122)+~P4(f13(x1122,x1123,x1121),x1121)+E(x1121,f20(x1122,x1123))+~E(f2(x1124,x1125),f13(x1122,x1123,x1121))
% 0.51/0.62 %EqnAxiom
% 0.51/0.62 [1]E(x11,x11)
% 0.51/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.51/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.51/0.62 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.51/0.62 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.51/0.62 [6]~E(x61,x62)+E(f20(x61,x63),f20(x62,x63))
% 0.51/0.62 [7]~E(x71,x72)+E(f20(x73,x71),f20(x73,x72))
% 0.51/0.62 [8]~E(x81,x82)+E(f15(x81,x83,x84,x85),f15(x82,x83,x84,x85))
% 0.51/0.62 [9]~E(x91,x92)+E(f15(x93,x91,x94,x95),f15(x93,x92,x94,x95))
% 0.51/0.62 [10]~E(x101,x102)+E(f15(x103,x104,x101,x105),f15(x103,x104,x102,x105))
% 0.51/0.62 [11]~E(x111,x112)+E(f15(x113,x114,x115,x111),f15(x113,x114,x115,x112))
% 0.51/0.62 [12]~E(x121,x122)+E(f19(x121,x123),f19(x122,x123))
% 0.51/0.62 [13]~E(x131,x132)+E(f19(x133,x131),f19(x133,x132))
% 0.51/0.62 [14]~E(x141,x142)+E(f17(x141,x143,x144),f17(x142,x143,x144))
% 0.51/0.62 [15]~E(x151,x152)+E(f17(x153,x151,x154),f17(x153,x152,x154))
% 0.51/0.62 [16]~E(x161,x162)+E(f17(x163,x164,x161),f17(x163,x164,x162))
% 0.51/0.62 [17]~E(x171,x172)+E(f21(x171),f21(x172))
% 0.51/0.62 [18]~E(x181,x182)+E(f9(x181,x183),f9(x182,x183))
% 0.51/0.62 [19]~E(x191,x192)+E(f9(x193,x191),f9(x193,x192))
% 0.51/0.62 [20]~E(x201,x202)+E(f18(x201,x203,x204),f18(x202,x203,x204))
% 0.51/0.62 [21]~E(x211,x212)+E(f18(x213,x211,x214),f18(x213,x212,x214))
% 0.51/0.62 [22]~E(x221,x222)+E(f18(x223,x224,x221),f18(x223,x224,x222))
% 0.51/0.62 [23]~E(x231,x232)+E(f14(x231,x233,x234,x235),f14(x232,x233,x234,x235))
% 0.51/0.62 [24]~E(x241,x242)+E(f14(x243,x241,x244,x245),f14(x243,x242,x244,x245))
% 0.51/0.62 [25]~E(x251,x252)+E(f14(x253,x254,x251,x255),f14(x253,x254,x252,x255))
% 0.51/0.62 [26]~E(x261,x262)+E(f14(x263,x264,x265,x261),f14(x263,x264,x265,x262))
% 0.51/0.62 [27]~E(x271,x272)+E(f12(x271,x273),f12(x272,x273))
% 0.51/0.62 [28]~E(x281,x282)+E(f12(x283,x281),f12(x283,x282))
% 0.51/0.62 [29]~E(x291,x292)+E(f11(x291,x293),f11(x292,x293))
% 0.51/0.62 [30]~E(x301,x302)+E(f11(x303,x301),f11(x303,x302))
% 0.51/0.62 [31]~E(x311,x312)+E(f4(x311),f4(x312))
% 0.51/0.62 [32]~E(x321,x322)+E(f5(x321),f5(x322))
% 0.51/0.62 [33]~E(x331,x332)+E(f13(x331,x333,x334),f13(x332,x333,x334))
% 0.51/0.62 [34]~E(x341,x342)+E(f13(x343,x341,x344),f13(x343,x342,x344))
% 0.51/0.62 [35]~E(x351,x352)+E(f13(x353,x354,x351),f13(x353,x354,x352))
% 0.51/0.62 [36]~E(x361,x362)+E(f16(x361,x363,x364),f16(x362,x363,x364))
% 0.51/0.62 [37]~E(x371,x372)+E(f16(x373,x371,x374),f16(x373,x372,x374))
% 0.51/0.62 [38]~E(x381,x382)+E(f16(x383,x384,x381),f16(x383,x384,x382))
% 0.51/0.62 [39]~E(x391,x392)+E(f10(x391),f10(x392))
% 0.51/0.62 [40]~P1(x401)+P1(x402)+~E(x401,x402)
% 0.51/0.62 [41]P4(x412,x413)+~E(x411,x412)+~P4(x411,x413)
% 0.51/0.62 [42]P4(x423,x422)+~E(x421,x422)+~P4(x423,x421)
% 0.51/0.62 [43]~P2(x431)+P2(x432)+~E(x431,x432)
% 0.51/0.62 [44]~P3(x441)+P3(x442)+~E(x441,x442)
% 0.51/0.62
% 0.51/0.62 %-------------------------------------------
% 0.51/0.62 cnf(120,plain,
% 0.51/0.62 ($false),
% 0.51/0.62 inference(scs_inference,[],[59,60,52,54,61,2,41,86]),
% 0.51/0.62 ['proof']).
% 0.51/0.62 % SZS output end Proof
% 0.51/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------