TSTP Solution File: NUM464+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM464+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 : n006.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 10:22:16 EDT 2023
% Result : Theorem 0.19s 0.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM464+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n006.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 : Fri Aug 25 15:40:52 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.53 start to proof:theBenchmark
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 % File :CSE---1.6
% 0.19/0.61 % Problem :theBenchmark
% 0.19/0.61 % Transform :cnf
% 0.19/0.61 % Format :tptp:raw
% 0.19/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.61
% 0.19/0.61 % Result :Theorem 0.020000s
% 0.19/0.61 % Output :CNFRefutation 0.020000s
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 % File : NUM464+2 : TPTP v8.1.2. Released v4.0.0.
% 0.19/0.61 % Domain : Number Theory
% 0.19/0.61 % Problem : Square root of a prime is irrational 07_01, 01 expansion
% 0.19/0.61 % Version : Especial.
% 0.19/0.61 % English :
% 0.19/0.61
% 0.19/0.61 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista
% 0.19/0.61 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.19/0.61 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.19/0.61 % Source : [Pas08]
% 0.19/0.61 % Names : primes_07_01.01 [Pas08]
% 0.19/0.61
% 0.19/0.61 % Status : Theorem
% 0.19/0.61 % Rating : 0.14 v8.1.0, 0.11 v7.5.0, 0.12 v7.4.0, 0.13 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.19 v5.4.0, 0.18 v5.3.0, 0.19 v5.2.0, 0.15 v5.1.0, 0.24 v5.0.0, 0.25 v4.1.0, 0.30 v4.0.1, 0.61 v4.0.0
% 0.19/0.61 % Syntax : Number of formulae : 28 ( 1 unt; 2 def)
% 0.19/0.61 % Number of atoms : 121 ( 43 equ)
% 0.19/0.61 % Maximal formula atoms : 10 ( 4 avg)
% 0.19/0.61 % Number of connectives : 105 ( 12 ~; 7 |; 47 &)
% 0.19/0.61 % ( 2 <=>; 37 =>; 0 <=; 0 <~>)
% 0.19/0.61 % Maximal formula depth : 11 ( 6 avg)
% 0.19/0.61 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.61 % Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% 0.19/0.61 % Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% 0.19/0.61 % Number of variables : 53 ( 51 !; 2 ?)
% 0.19/0.61 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.61
% 0.19/0.61 % Comments : Problem generated by the SAD system [VLP07]
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 fof(mNatSort,axiom,
% 0.19/0.61 ! [W0] :
% 0.19/0.61 ( aNaturalNumber0(W0)
% 0.19/0.61 => $true ) ).
% 0.19/0.61
% 0.19/0.61 fof(mSortsC,axiom,
% 0.19/0.61 aNaturalNumber0(sz00) ).
% 0.19/0.61
% 0.19/0.61 fof(mSortsC_01,axiom,
% 0.19/0.61 ( aNaturalNumber0(sz10)
% 0.19/0.61 & sz10 != sz00 ) ).
% 0.19/0.61
% 0.19/0.61 fof(mSortsB,axiom,
% 0.19/0.61 ! [W0,W1] :
% 0.19/0.61 ( ( aNaturalNumber0(W0)
% 0.19/0.61 & aNaturalNumber0(W1) )
% 0.19/0.61 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ).
% 0.19/0.61
% 0.19/0.61 fof(mSortsB_02,axiom,
% 0.19/0.61 ! [W0,W1] :
% 0.19/0.61 ( ( aNaturalNumber0(W0)
% 0.19/0.61 & aNaturalNumber0(W1) )
% 0.19/0.61 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ).
% 0.19/0.61
% 0.19/0.61 fof(mAddComm,axiom,
% 0.19/0.61 ! [W0,W1] :
% 0.19/0.61 ( ( aNaturalNumber0(W0)
% 0.19/0.61 & aNaturalNumber0(W1) )
% 0.19/0.61 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.19/0.61
% 0.19/0.61 fof(mAddAsso,axiom,
% 0.19/0.61 ! [W0,W1,W2] :
% 0.19/0.61 ( ( aNaturalNumber0(W0)
% 0.19/0.61 & aNaturalNumber0(W1)
% 0.19/0.61 & aNaturalNumber0(W2) )
% 0.19/0.61 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.19/0.61
% 0.19/0.61 fof(m_AddZero,axiom,
% 0.19/0.61 ! [W0] :
% 0.19/0.61 ( aNaturalNumber0(W0)
% 0.19/0.61 => ( sdtpldt0(W0,sz00) = W0
% 0.19/0.61 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.19/0.61
% 0.19/0.61 fof(mMulComm,axiom,
% 0.19/0.61 ! [W0,W1] :
% 0.19/0.61 ( ( aNaturalNumber0(W0)
% 0.19/0.61 & aNaturalNumber0(W1) )
% 0.19/0.61 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.19/0.61
% 0.19/0.61 fof(mMulAsso,axiom,
% 0.19/0.61 ! [W0,W1,W2] :
% 0.19/0.61 ( ( aNaturalNumber0(W0)
% 0.19/0.61 & aNaturalNumber0(W1)
% 0.19/0.61 & aNaturalNumber0(W2) )
% 0.19/0.61 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.19/0.61
% 0.19/0.61 fof(m_MulUnit,axiom,
% 0.19/0.61 ! [W0] :
% 0.19/0.61 ( aNaturalNumber0(W0)
% 0.19/0.61 => ( sdtasdt0(W0,sz10) = W0
% 0.19/0.61 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.19/0.61
% 0.19/0.61 fof(m_MulZero,axiom,
% 0.19/0.61 ! [W0] :
% 0.19/0.61 ( aNaturalNumber0(W0)
% 0.19/0.61 => ( sdtasdt0(W0,sz00) = sz00
% 0.19/0.61 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.19/0.61
% 0.19/0.61 fof(mAMDistr,axiom,
% 0.19/0.61 ! [W0,W1,W2] :
% 0.19/0.61 ( ( aNaturalNumber0(W0)
% 0.19/0.61 & aNaturalNumber0(W1)
% 0.19/0.61 & aNaturalNumber0(W2) )
% 0.19/0.61 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.19/0.61 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.19/0.61
% 0.19/0.61 fof(mAddCanc,axiom,
% 0.19/0.61 ! [W0,W1,W2] :
% 0.19/0.61 ( ( aNaturalNumber0(W0)
% 0.19/0.61 & aNaturalNumber0(W1)
% 0.19/0.61 & aNaturalNumber0(W2) )
% 0.19/0.61 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
% 0.19/0.61 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
% 0.19/0.61 => W1 = W2 ) ) ).
% 0.19/0.61
% 0.19/0.62 fof(mMulCanc,axiom,
% 0.19/0.62 ! [W0] :
% 0.19/0.62 ( aNaturalNumber0(W0)
% 0.19/0.62 => ( W0 != sz00
% 0.19/0.62 => ! [W1,W2] :
% 0.19/0.62 ( ( aNaturalNumber0(W1)
% 0.19/0.62 & aNaturalNumber0(W2) )
% 0.19/0.62 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2)
% 0.19/0.62 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
% 0.19/0.62 => W1 = W2 ) ) ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mZeroAdd,axiom,
% 0.19/0.62 ! [W0,W1] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1) )
% 0.19/0.62 => ( sdtpldt0(W0,W1) = sz00
% 0.19/0.62 => ( W0 = sz00
% 0.19/0.62 & W1 = sz00 ) ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mZeroMul,axiom,
% 0.19/0.62 ! [W0,W1] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1) )
% 0.19/0.62 => ( sdtasdt0(W0,W1) = sz00
% 0.19/0.62 => ( W0 = sz00
% 0.19/0.62 | W1 = sz00 ) ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mDefLE,definition,
% 0.19/0.62 ! [W0,W1] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1) )
% 0.19/0.62 => ( sdtlseqdt0(W0,W1)
% 0.19/0.62 <=> ? [W2] :
% 0.19/0.62 ( aNaturalNumber0(W2)
% 0.19/0.62 & sdtpldt0(W0,W2) = W1 ) ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mDefDiff,definition,
% 0.19/0.62 ! [W0,W1] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1) )
% 0.19/0.62 => ( sdtlseqdt0(W0,W1)
% 0.19/0.62 => ! [W2] :
% 0.19/0.62 ( W2 = sdtmndt0(W1,W0)
% 0.19/0.62 <=> ( aNaturalNumber0(W2)
% 0.19/0.62 & sdtpldt0(W0,W2) = W1 ) ) ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mLERefl,axiom,
% 0.19/0.62 ! [W0] :
% 0.19/0.62 ( aNaturalNumber0(W0)
% 0.19/0.62 => sdtlseqdt0(W0,W0) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mLEAsym,axiom,
% 0.19/0.62 ! [W0,W1] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1) )
% 0.19/0.62 => ( ( sdtlseqdt0(W0,W1)
% 0.19/0.62 & sdtlseqdt0(W1,W0) )
% 0.19/0.62 => W0 = W1 ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mLETran,axiom,
% 0.19/0.62 ! [W0,W1,W2] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1)
% 0.19/0.62 & aNaturalNumber0(W2) )
% 0.19/0.62 => ( ( sdtlseqdt0(W0,W1)
% 0.19/0.62 & sdtlseqdt0(W1,W2) )
% 0.19/0.62 => sdtlseqdt0(W0,W2) ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mLETotal,axiom,
% 0.19/0.62 ! [W0,W1] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1) )
% 0.19/0.62 => ( sdtlseqdt0(W0,W1)
% 0.19/0.62 | ( W1 != W0
% 0.19/0.62 & sdtlseqdt0(W1,W0) ) ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mMonAdd,axiom,
% 0.19/0.62 ! [W0,W1] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1) )
% 0.19/0.62 => ( ( W0 != W1
% 0.19/0.62 & sdtlseqdt0(W0,W1) )
% 0.19/0.62 => ! [W2] :
% 0.19/0.62 ( aNaturalNumber0(W2)
% 0.19/0.62 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
% 0.19/0.62 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
% 0.19/0.62 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
% 0.19/0.62 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mMonMul,axiom,
% 0.19/0.62 ! [W0,W1,W2] :
% 0.19/0.62 ( ( aNaturalNumber0(W0)
% 0.19/0.62 & aNaturalNumber0(W1)
% 0.19/0.62 & aNaturalNumber0(W2) )
% 0.19/0.62 => ( ( W0 != sz00
% 0.19/0.62 & W1 != W2
% 0.19/0.62 & sdtlseqdt0(W1,W2) )
% 0.19/0.62 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2)
% 0.19/0.62 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.19/0.62 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
% 0.19/0.62 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(mLENTr,axiom,
% 0.19/0.62 ! [W0] :
% 0.19/0.62 ( aNaturalNumber0(W0)
% 0.19/0.62 => ( W0 = sz00
% 0.19/0.62 | W0 = sz10
% 0.19/0.62 | ( sz10 != W0
% 0.19/0.62 & sdtlseqdt0(sz10,W0) ) ) ) ).
% 0.19/0.62
% 0.19/0.62 fof(m__987,hypothesis,
% 0.19/0.62 ( aNaturalNumber0(xm)
% 0.19/0.62 & aNaturalNumber0(xn) ) ).
% 0.19/0.62
% 0.19/0.62 fof(m__,conjecture,
% 0.19/0.62 ( xm != sz00
% 0.19/0.62 => ( ? [W0] :
% 0.19/0.62 ( aNaturalNumber0(W0)
% 0.19/0.62 & sdtpldt0(sz10,W0) = xm )
% 0.19/0.62 | sdtlseqdt0(sz10,xm) ) ) ).
% 0.19/0.62
% 0.19/0.62 %------------------------------------------------------------------------------
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % Proof found
% 0.19/0.62 % SZS status Theorem for theBenchmark
% 0.19/0.62 % SZS output start Proof
% 0.19/0.62 %ClaNum:63(EqnAxiom:14)
% 0.19/0.62 %VarNum:263(SingletonVarNum:84)
% 0.19/0.62 %MaxLitNum:7
% 0.19/0.62 %MaxfuncDepth:2
% 0.19/0.62 %SharedTerms:11
% 0.19/0.62 %goalClause: 20 21 30
% 0.19/0.62 %singleGoalClaCount:2
% 0.19/0.62 [15]P1(a1)
% 0.19/0.62 [16]P1(a6)
% 0.19/0.62 [17]P1(a7)
% 0.19/0.62 [18]P1(a8)
% 0.19/0.62 [19]~E(a1,a6)
% 0.19/0.62 [20]~E(a1,a7)
% 0.19/0.62 [21]~P2(a6,a7)
% 0.19/0.62 [28]~P1(x281)+P2(x281,x281)
% 0.19/0.62 [22]~P1(x221)+E(f2(a1,x221),a1)
% 0.19/0.62 [23]~P1(x231)+E(f2(x231,a1),a1)
% 0.19/0.62 [24]~P1(x241)+E(f4(a1,x241),x241)
% 0.19/0.62 [25]~P1(x251)+E(f2(a6,x251),x251)
% 0.19/0.62 [26]~P1(x261)+E(f4(x261,a1),x261)
% 0.19/0.62 [27]~P1(x271)+E(f2(x271,a6),x271)
% 0.19/0.62 [30]~P1(x301)+~E(f4(a6,x301),a7)
% 0.19/0.62 [35]~P1(x352)+~P1(x351)+E(f4(x351,x352),f4(x352,x351))
% 0.19/0.62 [36]~P1(x362)+~P1(x361)+E(f2(x361,x362),f2(x362,x361))
% 0.19/0.62 [38]~P1(x382)+~P1(x381)+P1(f4(x381,x382))
% 0.19/0.62 [39]~P1(x392)+~P1(x391)+P1(f2(x391,x392))
% 0.19/0.62 [29]~P1(x291)+E(x291,a6)+P2(a6,x291)+E(x291,a1)
% 0.19/0.62 [31]~E(x312,x311)+~P1(x311)+~P1(x312)+P2(x311,x312)
% 0.19/0.62 [37]P2(x372,x371)+~P1(x371)+~P1(x372)+P2(x371,x372)
% 0.19/0.62 [32]~P1(x322)+~P1(x321)+E(x321,a1)+~E(f4(x322,x321),a1)
% 0.19/0.62 [33]~P1(x332)+~P1(x331)+E(x331,a1)+~E(f4(x331,x332),a1)
% 0.19/0.62 [43]~P1(x432)+~P1(x431)+~P2(x431,x432)+P1(f3(x431,x432))
% 0.19/0.62 [49]~P1(x492)+~P1(x491)+~P2(x491,x492)+E(f4(x491,f3(x491,x492)),x492)
% 0.19/0.62 [56]~P1(x563)+~P1(x562)+~P1(x561)+E(f4(f4(x561,x562),x563),f4(x561,f4(x562,x563)))
% 0.19/0.62 [57]~P1(x573)+~P1(x572)+~P1(x571)+E(f2(f2(x571,x572),x573),f2(x571,f2(x572,x573)))
% 0.19/0.62 [62]~P1(x623)+~P1(x622)+~P1(x621)+E(f4(f2(x621,x622),f2(x621,x623)),f2(x621,f4(x622,x623)))
% 0.19/0.62 [63]~P1(x632)+~P1(x633)+~P1(x631)+E(f4(f2(x631,x632),f2(x633,x632)),f2(f4(x631,x633),x632))
% 0.19/0.62 [41]~P1(x412)+~P1(x411)+~P2(x412,x411)+~P2(x411,x412)+E(x411,x412)
% 0.19/0.62 [34]~P1(x341)+~P1(x342)+E(x341,a1)+E(x342,a1)+~E(f2(x342,x341),a1)
% 0.19/0.62 [40]~P1(x402)+~P1(x401)+~P1(x403)+P2(x401,x402)+~E(f4(x401,x403),x402)
% 0.19/0.62 [42]~P1(x423)+~P1(x422)+~P2(x423,x422)+P1(x421)+~E(x421,f5(x422,x423))
% 0.19/0.62 [44]~P1(x442)+~P1(x441)+~P1(x443)+E(x441,x442)+~E(f4(x443,x441),f4(x443,x442))
% 0.19/0.62 [45]~P1(x452)+~P1(x453)+~P1(x451)+E(x451,x452)+~E(f4(x451,x453),f4(x452,x453))
% 0.19/0.62 [48]~P1(x483)+~P1(x481)+~P2(x481,x483)+~E(x482,f5(x483,x481))+E(f4(x481,x482),x483)
% 0.19/0.62 [50]~P1(x502)+~P1(x501)+~P2(x503,x502)+~P2(x501,x503)+P2(x501,x502)+~P1(x503)
% 0.19/0.62 [46]~P1(x462)+~P1(x461)+~P1(x463)+E(x461,x462)+~E(f2(x463,x461),f2(x463,x462))+E(x463,a1)
% 0.19/0.62 [47]~P1(x472)+~P1(x473)+~P1(x471)+E(x471,x472)+~E(f2(x471,x473),f2(x472,x473))+E(x473,a1)
% 0.19/0.62 [51]~P1(x512)+~P1(x513)+~P1(x511)+~P2(x513,x512)+~E(f4(x513,x511),x512)+E(x511,f5(x512,x513))
% 0.19/0.62 [58]~P1(x582)+~P1(x581)+~P1(x583)+~P2(x581,x582)+E(x581,x582)+P2(f4(x583,x581),f4(x583,x582))
% 0.19/0.62 [59]~P1(x592)+~P1(x593)+~P1(x591)+~P2(x591,x592)+E(x591,x592)+P2(f4(x591,x593),f4(x592,x593))
% 0.19/0.62 [60]~P1(x602)+~P1(x601)+~P1(x603)+~P2(x601,x602)+E(x601,x602)+P2(f2(x603,x601),f2(x603,x602))+E(x603,a1)
% 0.19/0.62 [61]~P1(x612)+~P1(x613)+~P1(x611)+~P2(x611,x612)+E(x611,x612)+P2(f2(x611,x613),f2(x612,x613))+E(x613,a1)
% 0.19/0.62 %EqnAxiom
% 0.19/0.62 [1]E(x11,x11)
% 0.19/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.62 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.19/0.62 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.19/0.62 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.19/0.62 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.19/0.62 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83))
% 0.19/0.62 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92))
% 0.19/0.62 [10]~E(x101,x102)+E(f3(x101,x103),f3(x102,x103))
% 0.19/0.62 [11]~E(x111,x112)+E(f3(x113,x111),f3(x113,x112))
% 0.19/0.62 [12]~P1(x121)+P1(x122)+~E(x121,x122)
% 0.19/0.62 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133)
% 0.19/0.62 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141)
% 0.19/0.62
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 cnf(64,plain,
% 0.19/0.62 (P2(a1,a1)),
% 0.19/0.62 inference(scs_inference,[],[15,37])).
% 0.19/0.62 cnf(65,plain,
% 0.19/0.62 (~E(a7,a1)),
% 0.19/0.62 inference(scs_inference,[],[20,15,37,2])).
% 0.19/0.62 cnf(66,plain,
% 0.19/0.62 (P2(a6,a6)),
% 0.19/0.62 inference(scs_inference,[],[20,15,16,37,2,28])).
% 0.19/0.62 cnf(72,plain,
% 0.19/0.62 (E(f4(a1,a1),a1)),
% 0.19/0.62 inference(scs_inference,[],[20,15,16,37,2,28,30,27,26])).
% 0.19/0.62 cnf(85,plain,
% 0.19/0.62 (E(f5(f2(a1,a6),x851),f5(a1,x851))),
% 0.19/0.62 inference(scs_inference,[],[20,15,16,17,37,2,28,30,27,26,25,24,23,22,11,10,9,8])).
% 0.19/0.62 cnf(172,plain,
% 0.19/0.62 ($false),
% 0.19/0.62 inference(scs_inference,[],[18,16,21,17,15,64,85,66,72,65,51,39,38,29,43,57,49,48,37,31]),
% 0.19/0.62 ['proof']).
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time :0.020000s
%------------------------------------------------------------------------------