TSTP Solution File: RNG101+2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG101+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 : 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 : Thu Aug 31 13:48:10 EDT 2023
% Result : Theorem 0.21s 0.68s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG101+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 01:46:47 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.59 start to proof:theBenchmark
% 0.21/0.66 %-------------------------------------------
% 0.21/0.66 % File :CSE---1.6
% 0.21/0.66 % Problem :theBenchmark
% 0.21/0.66 % Transform :cnf
% 0.21/0.66 % Format :tptp:raw
% 0.21/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.66
% 0.21/0.66 % Result :Theorem 0.000000s
% 0.21/0.66 % Output :CNFRefutation 0.000000s
% 0.21/0.66 %-------------------------------------------
% 0.21/0.67 %------------------------------------------------------------------------------
% 0.21/0.67 % File : RNG101+2 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.67 % Domain : Ring Theory
% 0.21/0.67 % Problem : Chinese remainder theorem in a ring 06_01, 01 expansion
% 0.21/0.67 % Version : Especial.
% 0.21/0.67 % English :
% 0.21/0.67
% 0.21/0.67 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.21/0.67 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.21/0.67 % Source : [Pas08]
% 0.21/0.67 % Names : chines_06_01.01 [Pas08]
% 0.21/0.67
% 0.21/0.67 % Status : Theorem
% 0.21/0.67 % Rating : 0.06 v8.1.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.19 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.10 v5.1.0, 0.19 v5.0.0, 0.25 v4.1.0, 0.35 v4.0.1, 0.70 v4.0.0
% 0.21/0.67 % Syntax : Number of formulae : 40 ( 4 unt; 9 def)
% 0.21/0.67 % Number of atoms : 160 ( 34 equ)
% 0.21/0.67 % Maximal formula atoms : 9 ( 4 avg)
% 0.21/0.67 % Number of connectives : 124 ( 4 ~; 1 |; 60 &)
% 0.21/0.67 % ( 12 <=>; 47 =>; 0 <=; 0 <~>)
% 0.21/0.67 % Maximal formula depth : 13 ( 6 avg)
% 0.21/0.67 % Maximal term depth : 3 ( 1 avg)
% 0.21/0.67 % Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% 0.21/0.67 % Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% 0.21/0.67 % Number of variables : 86 ( 76 !; 10 ?)
% 0.21/0.67 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.67
% 0.21/0.67 % Comments : Problem generated by the SAD system [VLP07]
% 0.21/0.67 %------------------------------------------------------------------------------
% 0.21/0.67 fof(mElmSort,axiom,
% 0.21/0.67 ! [W0] :
% 0.21/0.67 ( aElement0(W0)
% 0.21/0.67 => $true ) ).
% 0.21/0.67
% 0.21/0.67 fof(mSortsC,axiom,
% 0.21/0.67 aElement0(sz00) ).
% 0.21/0.67
% 0.21/0.67 fof(mSortsC_01,axiom,
% 0.21/0.67 aElement0(sz10) ).
% 0.21/0.67
% 0.21/0.67 fof(mSortsU,axiom,
% 0.21/0.67 ! [W0] :
% 0.21/0.67 ( aElement0(W0)
% 0.21/0.67 => aElement0(smndt0(W0)) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mSortsB,axiom,
% 0.21/0.67 ! [W0,W1] :
% 0.21/0.67 ( ( aElement0(W0)
% 0.21/0.67 & aElement0(W1) )
% 0.21/0.67 => aElement0(sdtpldt0(W0,W1)) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mSortsB_02,axiom,
% 0.21/0.67 ! [W0,W1] :
% 0.21/0.67 ( ( aElement0(W0)
% 0.21/0.67 & aElement0(W1) )
% 0.21/0.67 => aElement0(sdtasdt0(W0,W1)) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mAddComm,axiom,
% 0.21/0.67 ! [W0,W1] :
% 0.21/0.67 ( ( aElement0(W0)
% 0.21/0.67 & aElement0(W1) )
% 0.21/0.67 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mAddAsso,axiom,
% 0.21/0.67 ! [W0,W1,W2] :
% 0.21/0.67 ( ( aElement0(W0)
% 0.21/0.67 & aElement0(W1)
% 0.21/0.67 & aElement0(W2) )
% 0.21/0.67 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mAddZero,axiom,
% 0.21/0.67 ! [W0] :
% 0.21/0.67 ( aElement0(W0)
% 0.21/0.67 => ( sdtpldt0(W0,sz00) = W0
% 0.21/0.67 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mAddInvr,axiom,
% 0.21/0.67 ! [W0] :
% 0.21/0.67 ( aElement0(W0)
% 0.21/0.67 => ( sdtpldt0(W0,smndt0(W0)) = sz00
% 0.21/0.67 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mMulComm,axiom,
% 0.21/0.67 ! [W0,W1] :
% 0.21/0.67 ( ( aElement0(W0)
% 0.21/0.67 & aElement0(W1) )
% 0.21/0.67 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mMulAsso,axiom,
% 0.21/0.67 ! [W0,W1,W2] :
% 0.21/0.67 ( ( aElement0(W0)
% 0.21/0.67 & aElement0(W1)
% 0.21/0.67 & aElement0(W2) )
% 0.21/0.67 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mMulUnit,axiom,
% 0.21/0.67 ! [W0] :
% 0.21/0.67 ( aElement0(W0)
% 0.21/0.67 => ( sdtasdt0(W0,sz10) = W0
% 0.21/0.67 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mAMDistr,axiom,
% 0.21/0.67 ! [W0,W1,W2] :
% 0.21/0.67 ( ( aElement0(W0)
% 0.21/0.67 & aElement0(W1)
% 0.21/0.67 & aElement0(W2) )
% 0.21/0.67 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.21/0.67 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mMulMnOne,axiom,
% 0.21/0.67 ! [W0] :
% 0.21/0.67 ( aElement0(W0)
% 0.21/0.67 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
% 0.21/0.67 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mMulZero,axiom,
% 0.21/0.67 ! [W0] :
% 0.21/0.67 ( aElement0(W0)
% 0.21/0.67 => ( sdtasdt0(W0,sz00) = sz00
% 0.21/0.67 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mCancel,axiom,
% 0.21/0.67 ! [W0,W1] :
% 0.21/0.67 ( ( aElement0(W0)
% 0.21/0.67 & aElement0(W1) )
% 0.21/0.67 => ( sdtasdt0(W0,W1) = sz00
% 0.21/0.67 => ( W0 = sz00
% 0.21/0.67 | W1 = sz00 ) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(mUnNeZr,axiom,
% 0.21/0.67 sz10 != sz00 ).
% 0.21/0.67
% 0.21/0.67 fof(mSetSort,axiom,
% 0.21/0.67 ! [W0] :
% 0.21/0.67 ( aSet0(W0)
% 0.21/0.67 => $true ) ).
% 0.21/0.67
% 0.21/0.67 fof(mEOfElem,axiom,
% 0.21/0.67 ! [W0] :
% 0.21/0.67 ( aSet0(W0)
% 0.21/0.67 => ! [W1] :
% 0.21/0.67 ( aElementOf0(W1,W0)
% 0.21/0.67 => aElement0(W1) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mSetEq,axiom,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aSet0(W0)
% 0.21/0.68 & aSet0(W1) )
% 0.21/0.68 => ( ( ! [W2] :
% 0.21/0.68 ( aElementOf0(W2,W0)
% 0.21/0.68 => aElementOf0(W2,W1) )
% 0.21/0.68 & ! [W2] :
% 0.21/0.68 ( aElementOf0(W2,W1)
% 0.21/0.68 => aElementOf0(W2,W0) ) )
% 0.21/0.68 => W0 = W1 ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mDefSSum,definition,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aSet0(W0)
% 0.21/0.68 & aSet0(W1) )
% 0.21/0.68 => ! [W2] :
% 0.21/0.68 ( W2 = sdtpldt1(W0,W1)
% 0.21/0.68 <=> ( aSet0(W2)
% 0.21/0.68 & ! [W3] :
% 0.21/0.68 ( aElementOf0(W3,W2)
% 0.21/0.68 <=> ? [W4,W5] :
% 0.21/0.68 ( aElementOf0(W4,W0)
% 0.21/0.68 & aElementOf0(W5,W1)
% 0.21/0.68 & sdtpldt0(W4,W5) = W3 ) ) ) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mDefSInt,definition,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aSet0(W0)
% 0.21/0.68 & aSet0(W1) )
% 0.21/0.68 => ! [W2] :
% 0.21/0.68 ( W2 = sdtasasdt0(W0,W1)
% 0.21/0.68 <=> ( aSet0(W2)
% 0.21/0.68 & ! [W3] :
% 0.21/0.68 ( aElementOf0(W3,W2)
% 0.21/0.68 <=> ( aElementOf0(W3,W0)
% 0.21/0.68 & aElementOf0(W3,W1) ) ) ) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mDefIdeal,definition,
% 0.21/0.68 ! [W0] :
% 0.21/0.68 ( aIdeal0(W0)
% 0.21/0.68 <=> ( aSet0(W0)
% 0.21/0.68 & ! [W1] :
% 0.21/0.68 ( aElementOf0(W1,W0)
% 0.21/0.68 => ( ! [W2] :
% 0.21/0.68 ( aElementOf0(W2,W0)
% 0.21/0.68 => aElementOf0(sdtpldt0(W1,W2),W0) )
% 0.21/0.68 & ! [W2] :
% 0.21/0.68 ( aElement0(W2)
% 0.21/0.68 => aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mIdeSum,axiom,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aIdeal0(W0)
% 0.21/0.68 & aIdeal0(W1) )
% 0.21/0.68 => aIdeal0(sdtpldt1(W0,W1)) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mIdeInt,axiom,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aIdeal0(W0)
% 0.21/0.68 & aIdeal0(W1) )
% 0.21/0.68 => aIdeal0(sdtasasdt0(W0,W1)) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mDefMod,definition,
% 0.21/0.68 ! [W0,W1,W2] :
% 0.21/0.68 ( ( aElement0(W0)
% 0.21/0.68 & aElement0(W1)
% 0.21/0.68 & aIdeal0(W2) )
% 0.21/0.68 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.21/0.68 <=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mChineseRemainder,axiom,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aIdeal0(W0)
% 0.21/0.68 & aIdeal0(W1) )
% 0.21/0.68 => ( ! [W2] :
% 0.21/0.68 ( aElement0(W2)
% 0.21/0.68 => aElementOf0(W2,sdtpldt1(W0,W1)) )
% 0.21/0.68 => ! [W2,W3] :
% 0.21/0.68 ( ( aElement0(W2)
% 0.21/0.68 & aElement0(W3) )
% 0.21/0.68 => ? [W4] :
% 0.21/0.68 ( aElement0(W4)
% 0.21/0.68 & sdteqdtlpzmzozddtrp0(W4,W2,W0)
% 0.21/0.68 & sdteqdtlpzmzozddtrp0(W4,W3,W1) ) ) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mNatSort,axiom,
% 0.21/0.68 ! [W0] :
% 0.21/0.68 ( aNaturalNumber0(W0)
% 0.21/0.68 => $true ) ).
% 0.21/0.68
% 0.21/0.68 fof(mEucSort,axiom,
% 0.21/0.68 ! [W0] :
% 0.21/0.68 ( ( aElement0(W0)
% 0.21/0.68 & W0 != sz00 )
% 0.21/0.68 => aNaturalNumber0(sbrdtbr0(W0)) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mNatLess,axiom,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aNaturalNumber0(W0)
% 0.21/0.68 & aNaturalNumber0(W1) )
% 0.21/0.68 => ( iLess0(W0,W1)
% 0.21/0.68 => $true ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mDivision,axiom,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aElement0(W0)
% 0.21/0.68 & aElement0(W1)
% 0.21/0.68 & W1 != sz00 )
% 0.21/0.68 => ? [W2,W3] :
% 0.21/0.68 ( aElement0(W2)
% 0.21/0.68 & aElement0(W3)
% 0.21/0.68 & W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
% 0.21/0.68 & ( W3 != sz00
% 0.21/0.68 => iLess0(sbrdtbr0(W3),sbrdtbr0(W1)) ) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mDefDiv,definition,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aElement0(W0)
% 0.21/0.68 & aElement0(W1) )
% 0.21/0.68 => ( doDivides0(W0,W1)
% 0.21/0.68 <=> ? [W2] :
% 0.21/0.68 ( aElement0(W2)
% 0.21/0.68 & sdtasdt0(W0,W2) = W1 ) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mDefDvs,definition,
% 0.21/0.68 ! [W0] :
% 0.21/0.68 ( aElement0(W0)
% 0.21/0.68 => ! [W1] :
% 0.21/0.68 ( aDivisorOf0(W1,W0)
% 0.21/0.68 <=> ( aElement0(W1)
% 0.21/0.68 & doDivides0(W1,W0) ) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mDefGCD,definition,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aElement0(W0)
% 0.21/0.68 & aElement0(W1) )
% 0.21/0.68 => ! [W2] :
% 0.21/0.68 ( aGcdOfAnd0(W2,W0,W1)
% 0.21/0.68 <=> ( aDivisorOf0(W2,W0)
% 0.21/0.68 & aDivisorOf0(W2,W1)
% 0.21/0.68 & ! [W3] :
% 0.21/0.68 ( ( aDivisorOf0(W3,W0)
% 0.21/0.68 & aDivisorOf0(W3,W1) )
% 0.21/0.68 => doDivides0(W3,W2) ) ) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mDefRel,definition,
% 0.21/0.68 ! [W0,W1] :
% 0.21/0.68 ( ( aElement0(W0)
% 0.21/0.68 & aElement0(W1) )
% 0.21/0.68 => ( misRelativelyPrime0(W0,W1)
% 0.21/0.68 <=> aGcdOfAnd0(sz10,W0,W1) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(mDefPrIdeal,definition,
% 0.21/0.68 ! [W0] :
% 0.21/0.68 ( aElement0(W0)
% 0.21/0.68 => ! [W1] :
% 0.21/0.68 ( W1 = slsdtgt0(W0)
% 0.21/0.68 <=> ( aSet0(W1)
% 0.21/0.68 & ! [W2] :
% 0.21/0.68 ( aElementOf0(W2,W1)
% 0.21/0.68 <=> ? [W3] :
% 0.21/0.68 ( aElement0(W3)
% 0.21/0.68 & sdtasdt0(W0,W3) = W2 ) ) ) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(m__1905,hypothesis,
% 0.21/0.68 aElement0(xc) ).
% 0.21/0.68
% 0.21/0.68 fof(m__1933,hypothesis,
% 0.21/0.68 ( ? [W0] :
% 0.21/0.68 ( aElement0(W0)
% 0.21/0.68 & sdtasdt0(xc,W0) = xx )
% 0.21/0.68 & aElementOf0(xx,slsdtgt0(xc))
% 0.21/0.68 & ? [W0] :
% 0.21/0.68 ( aElement0(W0)
% 0.21/0.68 & sdtasdt0(xc,W0) = xy )
% 0.21/0.68 & aElementOf0(xy,slsdtgt0(xc))
% 0.21/0.68 & aElement0(xz) ) ).
% 0.21/0.68
% 0.21/0.68 fof(m__,conjecture,
% 0.21/0.68 ? [W0] :
% 0.21/0.68 ( aElement0(W0)
% 0.21/0.68 & sdtasdt0(xc,W0) = xx ) ).
% 0.21/0.68
% 0.21/0.68 %------------------------------------------------------------------------------
% 0.21/0.68 %-------------------------------------------
% 0.21/0.68 % Proof found
% 0.21/0.68 % SZS status Theorem for theBenchmark
% 0.21/0.68 % SZS output start Proof
% 0.21/0.68 %ClaNum:180(EqnAxiom:83)
% 0.21/0.68 %VarNum:701(SingletonVarNum:213)
% 0.21/0.68 %MaxLitNum:8
% 0.21/0.68 %MaxfuncDepth:2
% 0.21/0.68 %SharedTerms:23
% 0.21/0.68 %goalClause: 105
% 0.21/0.68 [84]P1(a1)
% 0.21/0.68 [85]P1(a31)
% 0.21/0.68 [86]P1(a32)
% 0.21/0.68 [87]P1(a33)
% 0.21/0.68 [88]P1(a2)
% 0.21/0.68 [89]P1(a15)
% 0.21/0.68 [94]~E(a1,a31)
% 0.21/0.68 [90]E(f16(a32,a2),a34)
% 0.21/0.68 [91]E(f16(a32,a15),a35)
% 0.21/0.68 [92]P3(a34,f27(a32))
% 0.21/0.68 [93]P3(a35,f27(a32))
% 0.21/0.68 [95]~P5(x951)+P4(x951)
% 0.21/0.68 [96]~P1(x961)+P1(f30(x961))
% 0.21/0.68 [98]~P1(x981)+E(f16(a1,x981),a1)
% 0.21/0.68 [99]~P1(x991)+E(f16(x991,a1),a1)
% 0.21/0.68 [101]~P1(x1011)+E(f28(a1,x1011),x1011)
% 0.21/0.68 [102]~P1(x1021)+E(f16(a31,x1021),x1021)
% 0.21/0.68 [103]~P1(x1031)+E(f28(x1031,a1),x1031)
% 0.21/0.68 [104]~P1(x1041)+E(f16(x1041,a31),x1041)
% 0.21/0.68 [105]~P1(x1051)+~E(f16(a32,x1051),a34)
% 0.21/0.68 [106]~P1(x1061)+E(f28(f30(x1061),x1061),a1)
% 0.21/0.68 [107]~P1(x1071)+E(f28(x1071,f30(x1071)),a1)
% 0.21/0.68 [108]~P1(x1081)+E(f16(x1081,f30(a31)),f30(x1081))
% 0.21/0.68 [109]~P1(x1091)+E(f16(f30(a31),x1091),f30(x1091))
% 0.21/0.68 [97]~P1(x971)+E(x971,a1)+P7(f17(x971))
% 0.21/0.68 [110]~P4(x1101)+P5(x1101)+P3(f18(x1101),x1101)
% 0.21/0.68 [111]~P3(x1111,x1112)+P1(x1111)+~P4(x1112)
% 0.21/0.68 [112]~P2(x1121,x1122)+P1(x1121)+~P1(x1122)
% 0.21/0.68 [119]~P1(x1192)+~P2(x1191,x1192)+P8(x1191,x1192)
% 0.21/0.68 [100]~P1(x1002)+P4(x1001)+~E(x1001,f27(x1002))
% 0.21/0.68 [114]~P1(x1142)+~P1(x1141)+E(f28(x1141,x1142),f28(x1142,x1141))
% 0.21/0.68 [115]~P1(x1152)+~P1(x1151)+E(f16(x1151,x1152),f16(x1152,x1151))
% 0.21/0.68 [120]~P1(x1202)+~P1(x1201)+P1(f28(x1201,x1202))
% 0.21/0.68 [121]~P1(x1212)+~P1(x1211)+P1(f16(x1211,x1212))
% 0.21/0.68 [122]~P5(x1222)+~P5(x1221)+P5(f29(x1221,x1222))
% 0.21/0.68 [123]~P5(x1232)+~P5(x1231)+P5(f26(x1231,x1232))
% 0.21/0.68 [118]~P4(x1181)+P5(x1181)+P3(f4(x1181),x1181)+P1(f3(x1181))
% 0.21/0.68 [149]~P4(x1491)+P5(x1491)+P1(f3(x1491))+~P3(f28(f18(x1491),f4(x1491)),x1491)
% 0.21/0.68 [152]~P4(x1521)+P5(x1521)+P3(f4(x1521),x1521)+~P3(f16(f3(x1521),f18(x1521)),x1521)
% 0.21/0.68 [161]~P4(x1611)+P5(x1611)+~P3(f28(f18(x1611),f4(x1611)),x1611)+~P3(f16(f3(x1611),f18(x1611)),x1611)
% 0.21/0.68 [126]~P1(x1262)+~P1(x1261)+~P8(x1261,x1262)+P2(x1261,x1262)
% 0.21/0.68 [134]~P1(x1342)+~P1(x1341)+~P9(x1341,x1342)+P6(a31,x1341,x1342)
% 0.21/0.68 [142]~P1(x1422)+~P1(x1421)+P9(x1421,x1422)+~P6(a31,x1421,x1422)
% 0.21/0.68 [124]~P1(x1241)+~P1(x1242)+E(x1241,a1)+P1(f5(x1242,x1241))
% 0.21/0.68 [125]~P1(x1251)+~P1(x1252)+E(x1251,a1)+P1(f8(x1252,x1251))
% 0.21/0.68 [129]~P1(x1292)+~P1(x1291)+~P8(x1291,x1292)+P1(f9(x1291,x1292))
% 0.21/0.68 [133]~P1(x1332)+~P1(x1331)+~P8(x1331,x1332)+E(f16(x1331,f9(x1331,x1332)),x1332)
% 0.21/0.68 [154]~P1(x1541)+~P1(x1542)+E(x1541,a1)+E(f28(f16(f5(x1542,x1541),x1541),f8(x1542,x1541)),x1542)
% 0.21/0.68 [144]~P1(x1442)+~P6(x1441,x1443,x1442)+P2(x1441,x1442)+~P1(x1443)
% 0.21/0.68 [145]~P1(x1452)+~P6(x1451,x1452,x1453)+P2(x1451,x1452)+~P1(x1453)
% 0.21/0.68 [116]~P4(x1163)+~P4(x1162)+P4(x1161)+~E(x1161,f29(x1162,x1163))
% 0.21/0.68 [117]~P4(x1173)+~P4(x1172)+P4(x1171)+~E(x1171,f26(x1172,x1173))
% 0.21/0.68 [132]~P1(x1321)+~P5(x1323)+~P3(x1322,x1323)+P3(f16(x1321,x1322),x1323)
% 0.21/0.68 [136]~P5(x1363)+~P3(x1361,x1363)+~P3(x1362,x1363)+P3(f28(x1361,x1362),x1363)
% 0.21/0.68 [156]~P1(x1561)+~P3(x1563,x1562)+~E(x1562,f27(x1561))+P1(f12(x1561,x1562,x1563))
% 0.21/0.68 [139]~P1(x1393)+~P1(x1392)+~P1(x1391)+E(f28(f28(x1391,x1392),x1393),f28(x1391,f28(x1392,x1393)))
% 0.21/0.68 [140]~P1(x1403)+~P1(x1402)+~P1(x1401)+E(f16(f16(x1401,x1402),x1403),f16(x1401,f16(x1402,x1403)))
% 0.21/0.69 [150]~P1(x1503)+~P1(x1502)+~P1(x1501)+E(f28(f16(x1501,x1502),f16(x1501,x1503)),f16(x1501,f28(x1502,x1503)))
% 0.21/0.69 [151]~P1(x1512)+~P1(x1513)+~P1(x1511)+E(f28(f16(x1511,x1512),f16(x1513,x1512)),f16(f28(x1511,x1513),x1512))
% 0.21/0.69 [158]~P1(x1581)+~P3(x1583,x1582)+~E(x1582,f27(x1581))+E(f16(x1581,f12(x1581,x1582,x1583)),x1583)
% 0.21/0.69 [113]~P1(x1131)+~P1(x1132)+E(x1131,a1)+E(x1132,a1)+~E(f16(x1132,x1131),a1)
% 0.21/0.69 [135]~P1(x1352)+~P4(x1351)+P3(f11(x1352,x1351),x1351)+E(x1351,f27(x1352))+P1(f10(x1352,x1351))
% 0.21/0.69 [137]~P4(x1372)+~P4(x1371)+E(x1371,x1372)+P3(f14(x1371,x1372),x1371)+P3(f19(x1371,x1372),x1372)
% 0.21/0.69 [146]~P4(x1462)+~P4(x1461)+E(x1461,x1462)+P3(f14(x1461,x1462),x1461)+~P3(f19(x1461,x1462),x1461)
% 0.21/0.69 [147]~P4(x1472)+~P4(x1471)+E(x1471,x1472)+P3(f19(x1471,x1472),x1472)+~P3(f14(x1471,x1472),x1472)
% 0.21/0.69 [155]~P4(x1552)+~P4(x1551)+E(x1551,x1552)+~P3(f14(x1551,x1552),x1552)+~P3(f19(x1551,x1552),x1551)
% 0.21/0.69 [141]~P1(x1411)+~P1(x1412)+E(x1411,a1)+P10(f17(f8(x1412,x1411)),f17(x1411))+E(f8(x1412,x1411),a1)
% 0.21/0.69 [143]~P1(x1432)+~P4(x1431)+P3(f11(x1432,x1431),x1431)+E(x1431,f27(x1432))+E(f16(x1432,f10(x1432,x1431)),f11(x1432,x1431))
% 0.21/0.69 [127]~P1(x1272)+~P1(x1271)+~P1(x1273)+P8(x1271,x1272)+~E(f16(x1271,x1273),x1272)
% 0.21/0.69 [157]~P1(x1572)+~P1(x1571)+~P5(x1573)+P11(x1571,x1572,x1573)+~P3(f28(x1571,f30(x1572)),x1573)
% 0.21/0.69 [159]~P1(x1592)+~P1(x1591)+~P5(x1593)+~P11(x1591,x1592,x1593)+P3(f28(x1591,f30(x1592)),x1593)
% 0.21/0.69 [128]~P1(x1283)+~P1(x1284)+P3(x1281,x1282)+~E(f16(x1283,x1284),x1281)+~E(x1282,f27(x1283))
% 0.21/0.69 [130]~P4(x1304)+~P4(x1302)+~P3(x1301,x1303)+P3(x1301,x1302)+~E(x1303,f26(x1304,x1302))
% 0.21/0.69 [131]~P4(x1314)+~P4(x1312)+~P3(x1311,x1313)+P3(x1311,x1312)+~E(x1313,f26(x1312,x1314))
% 0.21/0.69 [172]~P4(x1722)+~P4(x1721)+~P3(x1724,x1723)+~E(x1723,f29(x1721,x1722))+P3(f21(x1721,x1722,x1723,x1724),x1721)
% 0.21/0.69 [173]~P4(x1732)+~P4(x1731)+~P3(x1734,x1733)+~E(x1733,f29(x1731,x1732))+P3(f22(x1731,x1732,x1733,x1734),x1732)
% 0.21/0.69 [180]~P4(x1802)+~P4(x1801)+~P3(x1804,x1803)+~E(x1803,f29(x1801,x1802))+E(f28(f21(x1801,x1802,x1803,x1804),f22(x1801,x1802,x1803,x1804)),x1804)
% 0.21/0.69 [153]~P1(x1533)+~P1(x1532)+~P4(x1531)+~P3(f11(x1532,x1531),x1531)+~E(f11(x1532,x1531),f16(x1532,x1533))+E(x1531,f27(x1532))
% 0.21/0.69 [162]~P1(x1623)+~P1(x1622)+~P2(x1621,x1623)+~P2(x1621,x1622)+P6(x1621,x1622,x1623)+P2(f13(x1622,x1623,x1621),x1623)
% 0.21/0.69 [163]~P1(x1633)+~P1(x1632)+~P2(x1631,x1633)+~P2(x1631,x1632)+P6(x1631,x1632,x1633)+P2(f13(x1632,x1633,x1631),x1632)
% 0.21/0.69 [164]~P4(x1641)+~P4(x1643)+~P4(x1642)+P3(f20(x1642,x1643,x1641),x1641)+P3(f23(x1642,x1643,x1641),x1642)+E(x1641,f29(x1642,x1643))
% 0.21/0.69 [165]~P4(x1651)+~P4(x1653)+~P4(x1652)+P3(f20(x1652,x1653,x1651),x1651)+P3(f24(x1652,x1653,x1651),x1653)+E(x1651,f29(x1652,x1653))
% 0.21/0.69 [166]~P4(x1661)+~P4(x1663)+~P4(x1662)+P3(f25(x1662,x1663,x1661),x1661)+P3(f25(x1662,x1663,x1661),x1663)+E(x1661,f26(x1662,x1663))
% 0.21/0.69 [167]~P4(x1671)+~P4(x1673)+~P4(x1672)+P3(f25(x1672,x1673,x1671),x1671)+P3(f25(x1672,x1673,x1671),x1672)+E(x1671,f26(x1672,x1673))
% 0.21/0.69 [168]~P1(x1683)+~P1(x1682)+~P2(x1681,x1683)+~P2(x1681,x1682)+P6(x1681,x1682,x1683)+~P8(f13(x1682,x1683,x1681),x1681)
% 0.21/0.69 [170]~P4(x1701)+~P4(x1703)+~P4(x1702)+P3(f20(x1702,x1703,x1701),x1701)+E(x1701,f29(x1702,x1703))+E(f28(f23(x1702,x1703,x1701),f24(x1702,x1703,x1701)),f20(x1702,x1703,x1701))
% 0.21/0.69 [160]~P2(x1601,x1603)+~P2(x1601,x1604)+~P6(x1602,x1604,x1603)+P8(x1601,x1602)+~P1(x1603)+~P1(x1604)
% 0.21/0.69 [138]~P4(x1384)+~P4(x1383)+~P3(x1381,x1384)+~P3(x1381,x1383)+P3(x1381,x1382)+~E(x1382,f26(x1383,x1384))
% 0.21/0.69 [171]~P1(x1714)+~P1(x1713)+~P5(x1712)+~P5(x1711)+P1(f6(x1711,x1712))+P1(f7(x1711,x1712,x1713,x1714))
% 0.21/0.69 [174]~P1(x1744)+~P1(x1743)+~P5(x1742)+~P5(x1741)+P11(f7(x1741,x1742,x1743,x1744),x1744,x1742)+P1(f6(x1741,x1742))
% 0.21/0.69 [175]~P1(x1754)+~P1(x1753)+~P5(x1752)+~P5(x1751)+P11(f7(x1751,x1752,x1753,x1754),x1753,x1751)+P1(f6(x1751,x1752))
% 0.21/0.69 [177]~P1(x1774)+~P1(x1773)+~P5(x1772)+~P5(x1771)+~P3(f6(x1771,x1772),f29(x1771,x1772))+P1(f7(x1771,x1772,x1773,x1774))
% 0.21/0.69 [178]~P1(x1784)+~P1(x1783)+~P5(x1782)+~P5(x1781)+P11(f7(x1781,x1782,x1783,x1784),x1784,x1782)+~P3(f6(x1781,x1782),f29(x1781,x1782))
% 0.21/0.69 [179]~P1(x1794)+~P1(x1793)+~P5(x1792)+~P5(x1791)+P11(f7(x1791,x1792,x1793,x1794),x1793,x1791)+~P3(f6(x1791,x1792),f29(x1791,x1792))
% 0.21/0.69 [176]~P4(x1761)+~P4(x1763)+~P4(x1762)+~P3(f25(x1762,x1763,x1761),x1761)+~P3(f25(x1762,x1763,x1761),x1763)+~P3(f25(x1762,x1763,x1761),x1762)+E(x1761,f26(x1762,x1763))
% 0.21/0.69 [148]~P4(x1484)+~P4(x1483)+~P3(x1486,x1484)+~P3(x1485,x1483)+P3(x1481,x1482)+~E(x1482,f29(x1483,x1484))+~E(f28(x1485,x1486),x1481)
% 0.21/0.69 [169]~P4(x1691)+~P4(x1693)+~P4(x1692)+~P3(x1695,x1693)+~P3(x1694,x1692)+~P3(f20(x1692,x1693,x1691),x1691)+E(x1691,f29(x1692,x1693))+~E(f28(x1694,x1695),f20(x1692,x1693,x1691))
% 0.21/0.69 %EqnAxiom
% 0.21/0.69 [1]E(x11,x11)
% 0.21/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.69 [4]~E(x41,x42)+E(f16(x41,x43),f16(x42,x43))
% 0.21/0.69 [5]~E(x51,x52)+E(f16(x53,x51),f16(x53,x52))
% 0.21/0.69 [6]~E(x61,x62)+E(f29(x61,x63),f29(x62,x63))
% 0.21/0.69 [7]~E(x71,x72)+E(f29(x73,x71),f29(x73,x72))
% 0.21/0.69 [8]~E(x81,x82)+E(f27(x81),f27(x82))
% 0.21/0.69 [9]~E(x91,x92)+E(f24(x91,x93,x94),f24(x92,x93,x94))
% 0.21/0.69 [10]~E(x101,x102)+E(f24(x103,x101,x104),f24(x103,x102,x104))
% 0.21/0.69 [11]~E(x111,x112)+E(f24(x113,x114,x111),f24(x113,x114,x112))
% 0.21/0.69 [12]~E(x121,x122)+E(f30(x121),f30(x122))
% 0.21/0.69 [13]~E(x131,x132)+E(f17(x131),f17(x132))
% 0.21/0.69 [14]~E(x141,x142)+E(f28(x141,x143),f28(x142,x143))
% 0.21/0.69 [15]~E(x151,x152)+E(f28(x153,x151),f28(x153,x152))
% 0.21/0.69 [16]~E(x161,x162)+E(f22(x161,x163,x164,x165),f22(x162,x163,x164,x165))
% 0.21/0.69 [17]~E(x171,x172)+E(f22(x173,x171,x174,x175),f22(x173,x172,x174,x175))
% 0.21/0.69 [18]~E(x181,x182)+E(f22(x183,x184,x181,x185),f22(x183,x184,x182,x185))
% 0.21/0.69 [19]~E(x191,x192)+E(f22(x193,x194,x195,x191),f22(x193,x194,x195,x192))
% 0.21/0.69 [20]~E(x201,x202)+E(f20(x201,x203,x204),f20(x202,x203,x204))
% 0.21/0.69 [21]~E(x211,x212)+E(f20(x213,x211,x214),f20(x213,x212,x214))
% 0.21/0.69 [22]~E(x221,x222)+E(f20(x223,x224,x221),f20(x223,x224,x222))
% 0.21/0.69 [23]~E(x231,x232)+E(f13(x231,x233,x234),f13(x232,x233,x234))
% 0.21/0.69 [24]~E(x241,x242)+E(f13(x243,x241,x244),f13(x243,x242,x244))
% 0.21/0.69 [25]~E(x251,x252)+E(f13(x253,x254,x251),f13(x253,x254,x252))
% 0.21/0.69 [26]~E(x261,x262)+E(f21(x261,x263,x264,x265),f21(x262,x263,x264,x265))
% 0.21/0.69 [27]~E(x271,x272)+E(f21(x273,x271,x274,x275),f21(x273,x272,x274,x275))
% 0.21/0.69 [28]~E(x281,x282)+E(f21(x283,x284,x281,x285),f21(x283,x284,x282,x285))
% 0.21/0.69 [29]~E(x291,x292)+E(f21(x293,x294,x295,x291),f21(x293,x294,x295,x292))
% 0.21/0.69 [30]~E(x301,x302)+E(f18(x301),f18(x302))
% 0.21/0.69 [31]~E(x311,x312)+E(f6(x311,x313),f6(x312,x313))
% 0.21/0.69 [32]~E(x321,x322)+E(f6(x323,x321),f6(x323,x322))
% 0.21/0.69 [33]~E(x331,x332)+E(f14(x331,x333),f14(x332,x333))
% 0.21/0.69 [34]~E(x341,x342)+E(f14(x343,x341),f14(x343,x342))
% 0.21/0.69 [35]~E(x351,x352)+E(f25(x351,x353,x354),f25(x352,x353,x354))
% 0.21/0.69 [36]~E(x361,x362)+E(f25(x363,x361,x364),f25(x363,x362,x364))
% 0.21/0.69 [37]~E(x371,x372)+E(f25(x373,x374,x371),f25(x373,x374,x372))
% 0.21/0.69 [38]~E(x381,x382)+E(f12(x381,x383,x384),f12(x382,x383,x384))
% 0.21/0.69 [39]~E(x391,x392)+E(f12(x393,x391,x394),f12(x393,x392,x394))
% 0.21/0.69 [40]~E(x401,x402)+E(f12(x403,x404,x401),f12(x403,x404,x402))
% 0.21/0.69 [41]~E(x411,x412)+E(f3(x411),f3(x412))
% 0.21/0.69 [42]~E(x421,x422)+E(f19(x421,x423),f19(x422,x423))
% 0.21/0.69 [43]~E(x431,x432)+E(f19(x433,x431),f19(x433,x432))
% 0.21/0.69 [44]~E(x441,x442)+E(f4(x441),f4(x442))
% 0.21/0.69 [45]~E(x451,x452)+E(f7(x451,x453,x454,x455),f7(x452,x453,x454,x455))
% 0.21/0.69 [46]~E(x461,x462)+E(f7(x463,x461,x464,x465),f7(x463,x462,x464,x465))
% 0.21/0.69 [47]~E(x471,x472)+E(f7(x473,x474,x471,x475),f7(x473,x474,x472,x475))
% 0.21/0.69 [48]~E(x481,x482)+E(f7(x483,x484,x485,x481),f7(x483,x484,x485,x482))
% 0.21/0.69 [49]~E(x491,x492)+E(f26(x491,x493),f26(x492,x493))
% 0.21/0.69 [50]~E(x501,x502)+E(f26(x503,x501),f26(x503,x502))
% 0.21/0.69 [51]~E(x511,x512)+E(f11(x511,x513),f11(x512,x513))
% 0.21/0.69 [52]~E(x521,x522)+E(f11(x523,x521),f11(x523,x522))
% 0.21/0.69 [53]~E(x531,x532)+E(f8(x531,x533),f8(x532,x533))
% 0.21/0.69 [54]~E(x541,x542)+E(f8(x543,x541),f8(x543,x542))
% 0.21/0.69 [55]~E(x551,x552)+E(f10(x551,x553),f10(x552,x553))
% 0.21/0.69 [56]~E(x561,x562)+E(f10(x563,x561),f10(x563,x562))
% 0.21/0.69 [57]~E(x571,x572)+E(f9(x571,x573),f9(x572,x573))
% 0.21/0.69 [58]~E(x581,x582)+E(f9(x583,x581),f9(x583,x582))
% 0.21/0.69 [59]~E(x591,x592)+E(f5(x591,x593),f5(x592,x593))
% 0.21/0.69 [60]~E(x601,x602)+E(f5(x603,x601),f5(x603,x602))
% 0.21/0.69 [61]~E(x611,x612)+E(f23(x611,x613,x614),f23(x612,x613,x614))
% 0.21/0.69 [62]~E(x621,x622)+E(f23(x623,x621,x624),f23(x623,x622,x624))
% 0.21/0.69 [63]~E(x631,x632)+E(f23(x633,x634,x631),f23(x633,x634,x632))
% 0.21/0.69 [64]~P1(x641)+P1(x642)+~E(x641,x642)
% 0.21/0.69 [65]P3(x652,x653)+~E(x651,x652)+~P3(x651,x653)
% 0.21/0.69 [66]P3(x663,x662)+~E(x661,x662)+~P3(x663,x661)
% 0.21/0.69 [67]~P4(x671)+P4(x672)+~E(x671,x672)
% 0.21/0.69 [68]P10(x682,x683)+~E(x681,x682)+~P10(x681,x683)
% 0.21/0.69 [69]P10(x693,x692)+~E(x691,x692)+~P10(x693,x691)
% 0.21/0.69 [70]~P5(x701)+P5(x702)+~E(x701,x702)
% 0.21/0.69 [71]P2(x712,x713)+~E(x711,x712)+~P2(x711,x713)
% 0.21/0.69 [72]P2(x723,x722)+~E(x721,x722)+~P2(x723,x721)
% 0.21/0.69 [73]P11(x732,x733,x734)+~E(x731,x732)+~P11(x731,x733,x734)
% 0.21/0.69 [74]P11(x743,x742,x744)+~E(x741,x742)+~P11(x743,x741,x744)
% 0.21/0.69 [75]P11(x753,x754,x752)+~E(x751,x752)+~P11(x753,x754,x751)
% 0.21/0.69 [76]P6(x762,x763,x764)+~E(x761,x762)+~P6(x761,x763,x764)
% 0.21/0.69 [77]P6(x773,x772,x774)+~E(x771,x772)+~P6(x773,x771,x774)
% 0.21/0.69 [78]P6(x783,x784,x782)+~E(x781,x782)+~P6(x783,x784,x781)
% 0.21/0.69 [79]P9(x792,x793)+~E(x791,x792)+~P9(x791,x793)
% 0.21/0.69 [80]P9(x803,x802)+~E(x801,x802)+~P9(x803,x801)
% 0.21/0.69 [81]P8(x812,x813)+~E(x811,x812)+~P8(x811,x813)
% 0.21/0.69 [82]P8(x823,x822)+~E(x821,x822)+~P8(x823,x821)
% 0.21/0.69 [83]~P7(x831)+P7(x832)+~E(x831,x832)
% 0.21/0.69
% 0.21/0.69 %-------------------------------------------
% 0.21/0.69 cnf(182,plain,
% 0.21/0.69 ($false),
% 0.21/0.69 inference(scs_inference,[],[88,90,2,105]),
% 0.21/0.69 ['proof']).
% 0.21/0.69 % SZS output end Proof
% 0.21/0.69 % Total time :0.000000s
%------------------------------------------------------------------------------