%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM464+1 : TPTP v8.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n028.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 : Mon Jun 24 12:24:23 EDT 2024 % Result : Theorem 0.52s 0.83s % Output : CNFRefutation 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM464+1 : TPTP v8.2.0. Released v4.0.0. % 0.06/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.32 % Computer : n028.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Sat Jun 22 20:10:09 EDT 2024 % 0.11/0.33 % CPUTime : % 0.52/0.63 start to proof:theBenchmark % 0.52/0.81 %------------------------------------------- % 0.52/0.81 % File :CSE---1.7 % 0.52/0.81 % Problem :theBenchmark % 0.52/0.81 % Transform :cnf % 0.52/0.81 % Format :tptp:raw % 0.52/0.82 % Command :java -jar mcs_scs.jar %d %s % 0.52/0.82 % 0.52/0.82 % Result :Theorem 0.140000s % 0.52/0.82 % Output :CNFRefutation 0.140000s % 0.52/0.82 %------------------------------------------- % 0.52/0.82 %------------------------------------------------------------------------------ % 0.52/0.82 % File : NUM464+1 : TPTP v8.2.0. Released v4.0.0. % 0.52/0.82 % Domain : Number Theory % 0.52/0.82 % Problem : Square root of a prime is irrational 07_01, 00 expansion % 0.52/0.82 % Version : Especial. % 0.52/0.82 % English : % 0.52/0.82 % 0.52/0.82 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista % 0.52/0.82 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.52/0.82 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.52/0.82 % Source : [Pas08] % 0.52/0.82 % Names : primes_07_01.00 [Pas08] % 0.52/0.82 % 0.52/0.82 % Status : Theorem % 0.52/0.82 % 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, 0.15 v5.4.0, 0.18 v5.3.0, 0.19 v5.2.0, 0.15 v5.1.0, 0.29 v4.1.0, 0.35 v4.0.1, 0.74 v4.0.0 % 0.52/0.82 % Syntax : Number of formulae : 28 ( 1 unt; 2 def) % 0.52/0.82 % Number of atoms : 119 ( 42 equ) % 0.52/0.82 % Maximal formula atoms : 10 ( 4 avg) % 0.52/0.82 % Number of connectives : 103 ( 12 ~; 6 |; 46 &) % 0.52/0.82 % ( 2 <=>; 37 =>; 0 <=; 0 <~>) % 0.52/0.82 % Maximal formula depth : 11 ( 6 avg) % 0.52/0.82 % Maximal term depth : 3 ( 1 avg) % 0.52/0.82 % Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty) % 0.52/0.82 % Number of functors : 7 ( 7 usr; 4 con; 0-2 aty) % 0.52/0.82 % Number of variables : 52 ( 51 !; 1 ?) % 0.52/0.82 % SPC : FOF_THM_RFO_SEQ % 0.52/0.82 % 0.52/0.82 % Comments : Problem generated by the SAD system [VLP07] % 0.52/0.82 %------------------------------------------------------------------------------ % 0.52/0.82 fof(mNatSort,axiom, % 0.52/0.82 ! [W0] : % 0.52/0.82 ( aNaturalNumber0(W0) % 0.52/0.82 => $true ) ). % 0.52/0.82 % 0.52/0.82 fof(mSortsC,axiom, % 0.52/0.82 aNaturalNumber0(sz00) ). % 0.52/0.82 % 0.52/0.82 fof(mSortsC_01,axiom, % 0.52/0.82 ( aNaturalNumber0(sz10) % 0.52/0.82 & sz10 != sz00 ) ). % 0.52/0.82 % 0.52/0.82 fof(mSortsB,axiom, % 0.52/0.82 ! [W0,W1] : % 0.52/0.82 ( ( aNaturalNumber0(W0) % 0.52/0.82 & aNaturalNumber0(W1) ) % 0.52/0.82 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ). % 0.52/0.82 % 0.52/0.82 fof(mSortsB_02,axiom, % 0.52/0.82 ! [W0,W1] : % 0.52/0.82 ( ( aNaturalNumber0(W0) % 0.52/0.82 & aNaturalNumber0(W1) ) % 0.52/0.82 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ). % 0.52/0.82 % 0.52/0.82 fof(mAddComm,axiom, % 0.52/0.82 ! [W0,W1] : % 0.52/0.82 ( ( aNaturalNumber0(W0) % 0.52/0.82 & aNaturalNumber0(W1) ) % 0.52/0.82 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.52/0.82 % 0.52/0.82 fof(mAddAsso,axiom, % 0.52/0.82 ! [W0,W1,W2] : % 0.52/0.82 ( ( aNaturalNumber0(W0) % 0.52/0.82 & aNaturalNumber0(W1) % 0.52/0.82 & aNaturalNumber0(W2) ) % 0.52/0.82 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ). % 0.52/0.82 % 0.52/0.82 fof(m_AddZero,axiom, % 0.52/0.82 ! [W0] : % 0.52/0.82 ( aNaturalNumber0(W0) % 0.52/0.82 => ( sdtpldt0(W0,sz00) = W0 % 0.52/0.82 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.52/0.82 % 0.52/0.82 fof(mMulComm,axiom, % 0.52/0.82 ! [W0,W1] : % 0.52/0.82 ( ( aNaturalNumber0(W0) % 0.52/0.82 & aNaturalNumber0(W1) ) % 0.52/0.82 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.52/0.82 % 0.52/0.82 fof(mMulAsso,axiom, % 0.52/0.82 ! [W0,W1,W2] : % 0.52/0.82 ( ( aNaturalNumber0(W0) % 0.52/0.82 & aNaturalNumber0(W1) % 0.52/0.82 & aNaturalNumber0(W2) ) % 0.52/0.82 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ). % 0.52/0.82 % 0.52/0.82 fof(m_MulUnit,axiom, % 0.52/0.82 ! [W0] : % 0.52/0.82 ( aNaturalNumber0(W0) % 0.52/0.82 => ( sdtasdt0(W0,sz10) = W0 % 0.52/0.82 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.52/0.82 % 0.52/0.82 fof(m_MulZero,axiom, % 0.52/0.82 ! [W0] : % 0.52/0.82 ( aNaturalNumber0(W0) % 0.52/0.82 => ( sdtasdt0(W0,sz00) = sz00 % 0.52/0.82 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.52/0.82 % 0.52/0.82 fof(mAMDistr,axiom, % 0.52/0.82 ! [W0,W1,W2] : % 0.52/0.82 ( ( aNaturalNumber0(W0) % 0.52/0.82 & aNaturalNumber0(W1) % 0.52/0.82 & aNaturalNumber0(W2) ) % 0.52/0.82 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.52/0.82 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ). % 0.52/0.82 % 0.52/0.82 fof(mAddCanc,axiom, % 0.52/0.82 ! [W0,W1,W2] : % 0.52/0.82 ( ( aNaturalNumber0(W0) % 0.52/0.82 & aNaturalNumber0(W1) % 0.52/0.82 & aNaturalNumber0(W2) ) % 0.52/0.82 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) % 0.52/0.82 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) % 0.52/0.82 => W1 = W2 ) ) ). % 0.52/0.82 % 0.52/0.82 fof(mMulCanc,axiom, % 0.52/0.82 ! [W0] : % 0.52/0.82 ( aNaturalNumber0(W0) % 0.52/0.82 => ( W0 != sz00 % 0.52/0.82 => ! [W1,W2] : % 0.52/0.82 ( ( aNaturalNumber0(W1) % 0.52/0.82 & aNaturalNumber0(W2) ) % 0.52/0.82 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) % 0.52/0.82 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) % 0.52/0.82 => W1 = W2 ) ) ) ) ). % 0.52/0.82 % 0.52/0.82 fof(mZeroAdd,axiom, % 0.52/0.82 ! [W0,W1] : % 0.52/0.82 ( ( aNaturalNumber0(W0) % 0.52/0.82 & aNaturalNumber0(W1) ) % 0.52/0.82 => ( sdtpldt0(W0,W1) = sz00 % 0.52/0.82 => ( W0 = sz00 % 0.52/0.82 & W1 = sz00 ) ) ) ). % 0.52/0.82 % 0.52/0.82 fof(mZeroMul,axiom, % 0.52/0.82 ! [W0,W1] : % 0.52/0.82 ( ( aNaturalNumber0(W0) % 0.52/0.82 & aNaturalNumber0(W1) ) % 0.52/0.83 => ( sdtasdt0(W0,W1) = sz00 % 0.52/0.83 => ( W0 = sz00 % 0.52/0.83 | W1 = sz00 ) ) ) ). % 0.52/0.83 % 0.52/0.83 fof(mDefLE,definition, % 0.52/0.83 ! [W0,W1] : % 0.52/0.83 ( ( aNaturalNumber0(W0) % 0.52/0.83 & aNaturalNumber0(W1) ) % 0.52/0.83 => ( sdtlseqdt0(W0,W1) % 0.52/0.83 <=> ? [W2] : % 0.52/0.83 ( aNaturalNumber0(W2) % 0.52/0.83 & sdtpldt0(W0,W2) = W1 ) ) ) ). % 0.52/0.83 % 0.52/0.83 fof(mDefDiff,definition, % 0.52/0.83 ! [W0,W1] : % 0.52/0.83 ( ( aNaturalNumber0(W0) % 0.52/0.83 & aNaturalNumber0(W1) ) % 0.52/0.83 => ( sdtlseqdt0(W0,W1) % 0.52/0.83 => ! [W2] : % 0.52/0.83 ( W2 = sdtmndt0(W1,W0) % 0.52/0.83 <=> ( aNaturalNumber0(W2) % 0.52/0.83 & sdtpldt0(W0,W2) = W1 ) ) ) ) ). % 0.52/0.83 % 0.52/0.83 fof(mLERefl,axiom, % 0.52/0.83 ! [W0] : % 0.52/0.83 ( aNaturalNumber0(W0) % 0.52/0.83 => sdtlseqdt0(W0,W0) ) ). % 0.52/0.83 % 0.52/0.83 fof(mLEAsym,axiom, % 0.52/0.83 ! [W0,W1] : % 0.52/0.83 ( ( aNaturalNumber0(W0) % 0.52/0.83 & aNaturalNumber0(W1) ) % 0.52/0.83 => ( ( sdtlseqdt0(W0,W1) % 0.52/0.83 & sdtlseqdt0(W1,W0) ) % 0.52/0.83 => W0 = W1 ) ) ). % 0.52/0.83 % 0.52/0.83 fof(mLETran,axiom, % 0.52/0.83 ! [W0,W1,W2] : % 0.52/0.83 ( ( aNaturalNumber0(W0) % 0.52/0.83 & aNaturalNumber0(W1) % 0.52/0.83 & aNaturalNumber0(W2) ) % 0.52/0.83 => ( ( sdtlseqdt0(W0,W1) % 0.52/0.83 & sdtlseqdt0(W1,W2) ) % 0.52/0.83 => sdtlseqdt0(W0,W2) ) ) ). % 0.52/0.83 % 0.52/0.83 fof(mLETotal,axiom, % 0.52/0.83 ! [W0,W1] : % 0.52/0.83 ( ( aNaturalNumber0(W0) % 0.52/0.83 & aNaturalNumber0(W1) ) % 0.52/0.83 => ( sdtlseqdt0(W0,W1) % 0.52/0.83 | ( W1 != W0 % 0.52/0.83 & sdtlseqdt0(W1,W0) ) ) ) ). % 0.52/0.83 % 0.52/0.83 fof(mMonAdd,axiom, % 0.52/0.83 ! [W0,W1] : % 0.52/0.83 ( ( aNaturalNumber0(W0) % 0.52/0.83 & aNaturalNumber0(W1) ) % 0.52/0.83 => ( ( W0 != W1 % 0.52/0.83 & sdtlseqdt0(W0,W1) ) % 0.52/0.83 => ! [W2] : % 0.52/0.83 ( aNaturalNumber0(W2) % 0.52/0.83 => ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) % 0.52/0.83 & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)) % 0.52/0.83 & sdtpldt0(W0,W2) != sdtpldt0(W1,W2) % 0.52/0.83 & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) ). % 0.52/0.83 % 0.52/0.83 fof(mMonMul,axiom, % 0.52/0.83 ! [W0,W1,W2] : % 0.52/0.83 ( ( aNaturalNumber0(W0) % 0.52/0.83 & aNaturalNumber0(W1) % 0.52/0.83 & aNaturalNumber0(W2) ) % 0.52/0.83 => ( ( W0 != sz00 % 0.52/0.83 & W1 != W2 % 0.52/0.83 & sdtlseqdt0(W1,W2) ) % 0.52/0.83 => ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) % 0.52/0.83 & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.52/0.83 & sdtasdt0(W1,W0) != sdtasdt0(W2,W0) % 0.52/0.83 & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ). % 0.52/0.83 % 0.52/0.83 fof(mLENTr,axiom, % 0.52/0.83 ! [W0] : % 0.52/0.83 ( aNaturalNumber0(W0) % 0.52/0.83 => ( W0 = sz00 % 0.52/0.83 | W0 = sz10 % 0.52/0.83 | ( sz10 != W0 % 0.52/0.83 & sdtlseqdt0(sz10,W0) ) ) ) ). % 0.52/0.83 % 0.52/0.83 fof(m__987,hypothesis, % 0.52/0.83 ( aNaturalNumber0(xm) % 0.52/0.83 & aNaturalNumber0(xn) ) ). % 0.52/0.83 % 0.52/0.83 fof(m__,conjecture, % 0.52/0.83 ( xm != sz00 % 0.52/0.83 => sdtlseqdt0(sz10,xm) ) ). % 0.52/0.83 % 0.52/0.83 %------------------------------------------------------------------------------ % 0.52/0.83 %------------------------------------------- % 0.52/0.83 % Proof found % 0.52/0.83 % SZS status Theorem for theBenchmark % 0.52/0.83 % SZS output start Proof % 0.52/0.83 %ClaNum:62(EqnAxiom:14) % 0.52/0.83 %VarNum:261(SingletonVarNum:83) % 0.52/0.83 %MaxLitNum:7 % 0.52/0.83 %MaxfuncDepth:2 % 0.52/0.83 %SharedTerms:11 % 0.52/0.83 %goalClause: 20 21 % 0.52/0.83 %singleGoalClaCount:2 % 0.52/0.83 [15]P1(a1) % 0.52/0.83 [16]P1(a6) % 0.52/0.83 [17]P1(a7) % 0.52/0.83 [18]P1(a8) % 0.52/0.83 [19]~E(a1,a6) % 0.52/0.83 [20]~E(a1,a7) % 0.52/0.83 [21]~P2(a6,a7) % 0.52/0.83 [28]~P1(x281)+P2(x281,x281) % 0.52/0.83 [22]~P1(x221)+E(f2(a1,x221),a1) % 0.52/0.83 [23]~P1(x231)+E(f2(x231,a1),a1) % 0.52/0.83 [24]~P1(x241)+E(f4(a1,x241),x241) % 0.52/0.83 [25]~P1(x251)+E(f2(a6,x251),x251) % 0.52/0.83 [26]~P1(x261)+E(f4(x261,a1),x261) % 0.52/0.83 [27]~P1(x271)+E(f2(x271,a6),x271) % 0.52/0.83 [34]~P1(x342)+~P1(x341)+E(f4(x341,x342),f4(x342,x341)) % 0.52/0.83 [35]~P1(x352)+~P1(x351)+E(f2(x351,x352),f2(x352,x351)) % 0.52/0.83 [37]~P1(x372)+~P1(x371)+P1(f4(x371,x372)) % 0.52/0.83 [38]~P1(x382)+~P1(x381)+P1(f2(x381,x382)) % 0.52/0.83 [29]~P1(x291)+E(x291,a6)+P2(a6,x291)+E(x291,a1) % 0.52/0.83 [30]~E(x302,x301)+~P1(x301)+~P1(x302)+P2(x301,x302) % 0.52/0.83 [36]P2(x362,x361)+~P1(x361)+~P1(x362)+P2(x361,x362) % 0.52/0.83 [31]~P1(x312)+~P1(x311)+E(x311,a1)+~E(f4(x312,x311),a1) % 0.52/0.83 [32]~P1(x322)+~P1(x321)+E(x321,a1)+~E(f4(x321,x322),a1) % 0.52/0.83 [42]~P1(x422)+~P1(x421)+~P2(x421,x422)+P1(f3(x421,x422)) % 0.52/0.83 [48]~P1(x482)+~P1(x481)+~P2(x481,x482)+E(f4(x481,f3(x481,x482)),x482) % 0.52/0.83 [55]~P1(x553)+~P1(x552)+~P1(x551)+E(f4(f4(x551,x552),x553),f4(x551,f4(x552,x553))) % 0.52/0.83 [56]~P1(x563)+~P1(x562)+~P1(x561)+E(f2(f2(x561,x562),x563),f2(x561,f2(x562,x563))) % 0.52/0.83 [61]~P1(x613)+~P1(x612)+~P1(x611)+E(f4(f2(x611,x612),f2(x611,x613)),f2(x611,f4(x612,x613))) % 0.52/0.83 [62]~P1(x622)+~P1(x623)+~P1(x621)+E(f4(f2(x621,x622),f2(x623,x622)),f2(f4(x621,x623),x622)) % 0.52/0.83 [40]~P1(x402)+~P1(x401)+~P2(x402,x401)+~P2(x401,x402)+E(x401,x402) % 0.52/0.83 [33]~P1(x331)+~P1(x332)+E(x331,a1)+E(x332,a1)+~E(f2(x332,x331),a1) % 0.52/0.83 [39]~P1(x392)+~P1(x391)+~P1(x393)+P2(x391,x392)+~E(f4(x391,x393),x392) % 0.52/0.83 [41]~P1(x413)+~P1(x412)+~P2(x413,x412)+P1(x411)+~E(x411,f5(x412,x413)) % 0.52/0.83 [43]~P1(x432)+~P1(x431)+~P1(x433)+E(x431,x432)+~E(f4(x433,x431),f4(x433,x432)) % 0.52/0.83 [44]~P1(x442)+~P1(x443)+~P1(x441)+E(x441,x442)+~E(f4(x441,x443),f4(x442,x443)) % 0.52/0.83 [47]~P1(x473)+~P1(x471)+~P2(x471,x473)+~E(x472,f5(x473,x471))+E(f4(x471,x472),x473) % 0.52/0.83 [49]~P1(x492)+~P1(x491)+~P2(x493,x492)+~P2(x491,x493)+P2(x491,x492)+~P1(x493) % 0.52/0.83 [45]~P1(x452)+~P1(x451)+~P1(x453)+E(x451,x452)+~E(f2(x453,x451),f2(x453,x452))+E(x453,a1) % 0.52/0.83 [46]~P1(x462)+~P1(x463)+~P1(x461)+E(x461,x462)+~E(f2(x461,x463),f2(x462,x463))+E(x463,a1) % 0.52/0.83 [50]~P1(x502)+~P1(x503)+~P1(x501)+~P2(x503,x502)+~E(f4(x503,x501),x502)+E(x501,f5(x502,x503)) % 0.52/0.83 [57]~P1(x572)+~P1(x571)+~P1(x573)+~P2(x571,x572)+E(x571,x572)+P2(f4(x573,x571),f4(x573,x572)) % 0.52/0.83 [58]~P1(x582)+~P1(x583)+~P1(x581)+~P2(x581,x582)+E(x581,x582)+P2(f4(x581,x583),f4(x582,x583)) % 0.52/0.83 [59]~P1(x592)+~P1(x591)+~P1(x593)+~P2(x591,x592)+E(x591,x592)+P2(f2(x593,x591),f2(x593,x592))+E(x593,a1) % 0.52/0.83 [60]~P1(x602)+~P1(x603)+~P1(x601)+~P2(x601,x602)+E(x601,x602)+P2(f2(x601,x603),f2(x602,x603))+E(x603,a1) % 0.52/0.83 %EqnAxiom % 0.52/0.83 [1]E(x11,x11) % 0.52/0.83 [2]E(x22,x21)+~E(x21,x22) % 0.52/0.83 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.52/0.83 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.52/0.83 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.52/0.83 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63)) % 0.52/0.83 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72)) % 0.52/0.83 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83)) % 0.52/0.83 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92)) % 0.52/0.83 [10]~E(x101,x102)+E(f3(x101,x103),f3(x102,x103)) % 0.52/0.83 [11]~E(x111,x112)+E(f3(x113,x111),f3(x113,x112)) % 0.52/0.83 [12]~P1(x121)+P1(x122)+~E(x121,x122) % 0.52/0.83 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133) % 0.52/0.83 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141) % 0.52/0.83 % 0.52/0.83 %------------------------------------------- % 0.52/0.83 cnf(64,plain, % 0.52/0.83 (P2(x641,f4(x641,x642))+~P1(f4(x641,x642))+~P1(x641)+~P1(x642)), % 0.52/0.83 inference(equality_inference,[],[39])). % 0.52/0.83 cnf(65,plain, % 0.52/0.83 (~P2(x651,x652)+~P1(x651)+~P1(x652)+P1(f5(x652,x651))), % 0.52/0.83 inference(equality_inference,[],[41])). % 0.52/0.83 cnf(70,plain, % 0.52/0.83 (~P2(x701,x702)+~P1(x702)+~P1(x701)+E(f4(x701,f5(x702,x701)),x702)), % 0.52/0.83 inference(equality_inference,[],[47])). % 0.52/0.83 cnf(72,plain, % 0.52/0.83 (P2(a1,a1)), % 0.52/0.83 inference(scs_inference,[],[15,36])). % 0.52/0.83 cnf(74,plain, % 0.52/0.83 (P1(f5(a1,a1))), % 0.52/0.83 inference(scs_inference,[],[15,36,65])). % 0.52/0.83 cnf(76,plain, % 0.52/0.83 (E(f4(a1,f5(a1,a1)),a1)), % 0.52/0.83 inference(scs_inference,[],[15,36,65,70])). % 0.52/0.83 cnf(78,plain, % 0.52/0.83 (E(a1,f4(a1,f5(a1,a1)))), % 0.52/0.83 inference(scs_inference,[],[15,36,65,70,2])). % 0.52/0.83 cnf(79,plain, % 0.52/0.83 (P1(f4(a1,f5(a1,a1)))), % 0.52/0.83 inference(scs_inference,[],[15,36,65,70,2,12])). % 0.52/0.83 cnf(80,plain, % 0.52/0.83 (P2(f4(a1,f5(a1,a1)),a1)), % 0.52/0.83 inference(scs_inference,[],[15,36,65,70,2,12,13])). % 0.52/0.83 cnf(81,plain, % 0.52/0.83 (P2(a1,f4(a1,f5(a1,a1)))), % 0.52/0.83 inference(scs_inference,[],[15,36,65,70,2,12,13,14])). % 0.52/0.83 cnf(82,plain, % 0.52/0.83 (P2(a6,a6)), % 0.52/0.83 inference(scs_inference,[],[15,16,36,65,70,2,12,13,14,30])). % 0.52/0.83 cnf(84,plain, % 0.52/0.83 (E(f5(a1,a1),a1)), % 0.52/0.83 inference(scs_inference,[],[15,16,36,65,70,2,12,13,14,30,31])). % 0.52/0.83 cnf(91,plain, % 0.52/0.83 (E(a1,f5(a1,a1))), % 0.52/0.83 inference(scs_inference,[],[84,2])). % 0.52/0.83 cnf(92,plain, % 0.52/0.83 (E(f4(a1,f5(a1,a1)),f5(a1,a1))), % 0.52/0.83 inference(scs_inference,[],[76,84,2,3])). % 0.52/0.83 cnf(96,plain, % 0.52/0.83 (P1(f5(f5(a1,a1),f5(a1,a1)))), % 0.52/0.83 inference(scs_inference,[],[78,76,84,80,74,2,3,14,36,65])). % 0.52/0.83 cnf(98,plain, % 0.52/0.83 (E(f4(f5(a1,a1),f5(f5(a1,a1),f5(a1,a1))),f5(a1,a1))), % 0.52/0.83 inference(scs_inference,[],[78,76,84,80,74,2,3,14,36,65,70])). % 0.52/0.83 cnf(104,plain, % 0.52/0.83 (E(f5(a1,a1),f5(f5(a1,a1),a1))), % 0.52/0.83 inference(scs_inference,[],[78,15,72,76,84,80,74,2,3,14,36,65,70,41,39,50])). % 0.52/0.83 cnf(106,plain, % 0.52/0.83 (P1(f5(f5(a1,a1),a1))), % 0.52/0.83 inference(scs_inference,[],[78,15,72,76,84,80,74,2,3,14,36,65,70,41,39,50,12])). % 0.52/0.83 cnf(110,plain, % 0.52/0.83 (P2(a7,a7)), % 0.52/0.83 inference(scs_inference,[],[78,15,72,76,84,80,74,17,82,2,3,14,36,65,70,41,39,50,12,13,64,30])). % 0.52/0.83 cnf(116,plain, % 0.52/0.83 (E(f4(a1,f5(a1,a1)),f5(f5(a1,a1),a1))), % 0.52/0.83 inference(scs_inference,[],[92,104,2,3])). % 0.52/0.83 cnf(121,plain, % 0.52/0.83 (P1(f5(a6,a6))), % 0.52/0.83 inference(scs_inference,[],[92,91,81,80,82,96,104,16,2,3,13,14,36,65])). % 0.52/0.83 cnf(123,plain, % 0.52/0.83 (E(f4(a6,f5(a6,a6)),a6)), % 0.52/0.83 inference(scs_inference,[],[92,91,81,80,82,96,104,16,2,3,13,14,36,65,70])). % 0.52/0.83 cnf(125,plain, % 0.52/0.83 (P2(a1,f5(f5(a1,a1),a1))), % 0.52/0.83 inference(scs_inference,[],[92,91,81,80,15,82,74,96,106,104,16,2,3,13,14,36,65,70,39])). % 0.52/0.83 cnf(134,plain, % 0.52/0.83 (P2(f5(f5(a1,a1),a1),f5(f5(a1,a1),a1))), % 0.52/0.83 inference(scs_inference,[],[92,91,81,80,15,79,82,74,96,106,104,18,16,2,3,13,14,36,65,70,39,49,50,12,64,30])). % 0.52/0.83 cnf(136,plain, % 0.52/0.83 (~P2(f5(f5(a1,a1),a1),a1)+E(f5(f5(a1,a1),a1),a1)), % 0.52/0.83 inference(scs_inference,[],[92,91,81,80,15,79,82,74,96,106,104,18,16,2,3,13,14,36,65,70,39,49,50,12,64,30,40])). % 0.52/0.83 cnf(139,plain, % 0.52/0.83 (E(f5(f5(a1,a1),a1),f4(a1,f5(a1,a1)))), % 0.52/0.83 inference(scs_inference,[],[116,2])). % 0.52/0.83 cnf(145,plain, % 0.52/0.83 (P1(f5(f5(a6,a6),f5(a6,a6)))), % 0.52/0.83 inference(scs_inference,[],[21,116,82,134,121,123,19,2,3,14,13,36,65])). % 0.52/0.83 cnf(147,plain, % 0.52/0.83 (E(f4(f5(a6,a6),f5(f5(a6,a6),f5(a6,a6))),f5(a6,a6))), % 0.52/0.83 inference(scs_inference,[],[21,116,82,134,121,123,19,2,3,14,13,36,65,70])). % 0.52/0.83 cnf(158,plain, % 0.52/0.83 (P2(f5(f5(a1,a1),a1),f4(a1,f5(a1,a1)))), % 0.52/0.83 inference(scs_inference,[],[91,139,98,125,134,2,13,14])). % 0.52/0.83 cnf(163,plain, % 0.52/0.83 (E(f4(a7,f5(a7,a7)),a7)), % 0.52/0.83 inference(scs_inference,[],[91,139,98,125,17,145,110,134,2,13,14,36,65,70])). % 0.52/0.83 cnf(167,plain, % 0.52/0.83 (E(f5(f5(a1,a1),a1),a1)), % 0.52/0.83 inference(scs_inference,[],[91,139,80,15,98,79,125,17,145,110,134,106,2,13,14,36,65,70,49,136])). % 0.52/0.83 cnf(187,plain, % 0.52/0.83 (E(a7,a1)), % 0.52/0.83 inference(scs_inference,[],[21,92,91,167,17,158,110,2,3,13,14,29])). % 0.52/0.83 cnf(223,plain, % 0.52/0.83 (~E(a1,f4(a7,f5(a7,a7)))), % 0.52/0.84 inference(scs_inference,[],[20,147,163,2,3])). % 0.52/0.84 cnf(241,plain, % 0.52/0.84 (E(f4(a7,f5(a7,a7)),a1)), % 0.52/0.84 inference(scs_inference,[],[163,17,187,2,12,3])). % 0.52/0.84 cnf(255,plain, % 0.52/0.84 ($false), % 0.52/0.84 inference(scs_inference,[],[241,223,2]), % 0.52/0.84 ['proof']). % 0.52/0.84 % SZS output end Proof % 0.52/0.84 % Total time :0.140000s %------------------------------------------------------------------------------