TSTP Solution File: NUM430+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM430+3 : 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 : n022.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 10:22:04 EDT 2023
% Result : Theorem 0.21s 0.83s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.16 % Problem : NUM430+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.17 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.39 % Computer : n022.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8042.1875MB
% 0.13/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.39 % CPULimit : 300
% 0.21/0.39 % WCLimit : 300
% 0.21/0.39 % DateTime : Fri Aug 25 10:34:10 EDT 2023
% 0.21/0.39 % CPUTime :
% 0.21/0.65 start to proof:theBenchmark
% 0.21/0.81 %-------------------------------------------
% 0.21/0.81 % File :CSE---1.6
% 0.21/0.81 % Problem :theBenchmark
% 0.21/0.82 % Transform :cnf
% 0.21/0.82 % Format :tptp:raw
% 0.21/0.82 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.82
% 0.21/0.82 % Result :Theorem 0.090000s
% 0.21/0.82 % Output :CNFRefutation 0.090000s
% 0.21/0.82 %-------------------------------------------
% 0.21/0.82 %------------------------------------------------------------------------------
% 0.21/0.82 % File : NUM430+3 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.82 % Domain : Number Theory
% 0.21/0.82 % Problem : Fuerstenberg's infinitude of primes 05_02, 02 expansion
% 0.21/0.82 % Version : Especial.
% 0.21/0.82 % English :
% 0.21/0.82
% 0.21/0.82 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.21/0.82 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.21/0.82 % Source : [Pas08]
% 0.21/0.82 % Names : fuerst_05_02.02 [Pas08]
% 0.21/0.82
% 0.21/0.82 % Status : Theorem
% 0.21/0.82 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.08 v6.3.0, 0.04 v6.1.0, 0.13 v6.0.0, 0.09 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
% 0.21/0.82 % Syntax : Number of formulae : 25 ( 2 unt; 2 def)
% 0.21/0.82 % Number of atoms : 90 ( 29 equ)
% 0.21/0.82 % Maximal formula atoms : 8 ( 3 avg)
% 0.21/0.82 % Number of connectives : 70 ( 5 ~; 1 |; 41 &)
% 0.21/0.82 % ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% 0.21/0.82 % Maximal formula depth : 9 ( 5 avg)
% 0.21/0.82 % Maximal term depth : 3 ( 1 avg)
% 0.21/0.82 % Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% 0.21/0.82 % Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% 0.21/0.82 % Number of variables : 40 ( 36 !; 4 ?)
% 0.21/0.82 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.82
% 0.21/0.82 % Comments : Problem generated by the SAD system [VLP07]
% 0.21/0.82 %------------------------------------------------------------------------------
% 0.21/0.82 fof(mIntegers,axiom,
% 0.21/0.82 ! [W0] :
% 0.21/0.82 ( aInteger0(W0)
% 0.21/0.82 => $true ) ).
% 0.21/0.82
% 0.21/0.82 fof(mIntZero,axiom,
% 0.21/0.82 aInteger0(sz00) ).
% 0.21/0.82
% 0.21/0.82 fof(mIntOne,axiom,
% 0.21/0.82 aInteger0(sz10) ).
% 0.21/0.82
% 0.21/0.82 fof(mIntNeg,axiom,
% 0.21/0.82 ! [W0] :
% 0.21/0.82 ( aInteger0(W0)
% 0.21/0.82 => aInteger0(smndt0(W0)) ) ).
% 0.21/0.82
% 0.21/0.82 fof(mIntPlus,axiom,
% 0.21/0.82 ! [W0,W1] :
% 0.21/0.82 ( ( aInteger0(W0)
% 0.21/0.82 & aInteger0(W1) )
% 0.21/0.82 => aInteger0(sdtpldt0(W0,W1)) ) ).
% 0.21/0.82
% 0.21/0.82 fof(mIntMult,axiom,
% 0.21/0.82 ! [W0,W1] :
% 0.21/0.82 ( ( aInteger0(W0)
% 0.21/0.82 & aInteger0(W1) )
% 0.21/0.82 => aInteger0(sdtasdt0(W0,W1)) ) ).
% 0.21/0.82
% 0.21/0.82 fof(mAddAsso,axiom,
% 0.21/0.82 ! [W0,W1,W2] :
% 0.21/0.82 ( ( aInteger0(W0)
% 0.21/0.82 & aInteger0(W1)
% 0.21/0.82 & aInteger0(W2) )
% 0.21/0.82 => sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ).
% 0.21/0.82
% 0.21/0.82 fof(mAddComm,axiom,
% 0.21/0.82 ! [W0,W1] :
% 0.21/0.82 ( ( aInteger0(W0)
% 0.21/0.82 & aInteger0(W1) )
% 0.21/0.83 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mAddZero,axiom,
% 0.21/0.83 ! [W0] :
% 0.21/0.83 ( aInteger0(W0)
% 0.21/0.83 => ( sdtpldt0(W0,sz00) = W0
% 0.21/0.83 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mAddNeg,axiom,
% 0.21/0.83 ! [W0] :
% 0.21/0.83 ( aInteger0(W0)
% 0.21/0.83 => ( sdtpldt0(W0,smndt0(W0)) = sz00
% 0.21/0.83 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mMulAsso,axiom,
% 0.21/0.83 ! [W0,W1,W2] :
% 0.21/0.83 ( ( aInteger0(W0)
% 0.21/0.83 & aInteger0(W1)
% 0.21/0.83 & aInteger0(W2) )
% 0.21/0.83 => sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mMulComm,axiom,
% 0.21/0.83 ! [W0,W1] :
% 0.21/0.83 ( ( aInteger0(W0)
% 0.21/0.83 & aInteger0(W1) )
% 0.21/0.83 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mMulOne,axiom,
% 0.21/0.83 ! [W0] :
% 0.21/0.83 ( aInteger0(W0)
% 0.21/0.83 => ( sdtasdt0(W0,sz10) = W0
% 0.21/0.83 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mDistrib,axiom,
% 0.21/0.83 ! [W0,W1,W2] :
% 0.21/0.83 ( ( aInteger0(W0)
% 0.21/0.83 & aInteger0(W1)
% 0.21/0.83 & aInteger0(W2) )
% 0.21/0.83 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.21/0.83 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mMulZero,axiom,
% 0.21/0.83 ! [W0] :
% 0.21/0.83 ( aInteger0(W0)
% 0.21/0.83 => ( sdtasdt0(W0,sz00) = sz00
% 0.21/0.83 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mMulMinOne,axiom,
% 0.21/0.83 ! [W0] :
% 0.21/0.83 ( aInteger0(W0)
% 0.21/0.83 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
% 0.21/0.83 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mZeroDiv,axiom,
% 0.21/0.83 ! [W0,W1] :
% 0.21/0.83 ( ( aInteger0(W0)
% 0.21/0.83 & aInteger0(W1) )
% 0.21/0.83 => ( sdtasdt0(W0,W1) = sz00
% 0.21/0.83 => ( W0 = sz00
% 0.21/0.83 | W1 = sz00 ) ) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mDivisor,definition,
% 0.21/0.83 ! [W0] :
% 0.21/0.83 ( aInteger0(W0)
% 0.21/0.83 => ! [W1] :
% 0.21/0.83 ( aDivisorOf0(W1,W0)
% 0.21/0.83 <=> ( aInteger0(W1)
% 0.21/0.83 & W1 != sz00
% 0.21/0.83 & ? [W2] :
% 0.21/0.83 ( aInteger0(W2)
% 0.21/0.83 & sdtasdt0(W1,W2) = W0 ) ) ) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mEquMod,definition,
% 0.21/0.83 ! [W0,W1,W2] :
% 0.21/0.83 ( ( aInteger0(W0)
% 0.21/0.83 & aInteger0(W1)
% 0.21/0.83 & aInteger0(W2)
% 0.21/0.83 & W2 != sz00 )
% 0.21/0.83 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.21/0.83 <=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mEquModRef,axiom,
% 0.21/0.83 ! [W0,W1] :
% 0.21/0.83 ( ( aInteger0(W0)
% 0.21/0.83 & aInteger0(W1)
% 0.21/0.83 & W1 != sz00 )
% 0.21/0.83 => sdteqdtlpzmzozddtrp0(W0,W0,W1) ) ).
% 0.21/0.83
% 0.21/0.83 fof(mEquModSym,axiom,
% 0.21/0.83 ! [W0,W1,W2] :
% 0.21/0.83 ( ( aInteger0(W0)
% 0.21/0.83 & aInteger0(W1)
% 0.21/0.83 & aInteger0(W2)
% 0.21/0.83 & W2 != sz00 )
% 0.21/0.83 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.21/0.83 => sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ) ).
% 0.21/0.83
% 0.21/0.83 fof(m__818,hypothesis,
% 0.21/0.83 ( aInteger0(xa)
% 0.21/0.83 & aInteger0(xb)
% 0.21/0.83 & aInteger0(xq)
% 0.21/0.83 & xq != sz00
% 0.21/0.83 & aInteger0(xc) ) ).
% 0.21/0.83
% 0.21/0.83 fof(m__853,hypothesis,
% 0.21/0.83 ( ? [W0] :
% 0.21/0.83 ( aInteger0(W0)
% 0.21/0.83 & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) )
% 0.21/0.83 & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
% 0.21/0.83 & sdteqdtlpzmzozddtrp0(xa,xb,xq)
% 0.21/0.83 & ? [W0] :
% 0.21/0.83 ( aInteger0(W0)
% 0.21/0.83 & sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) )
% 0.21/0.83 & aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
% 0.21/0.83 & sdteqdtlpzmzozddtrp0(xb,xc,xq) ) ).
% 0.21/0.83
% 0.21/0.83 fof(m__876,hypothesis,
% 0.21/0.83 ( aInteger0(xn)
% 0.21/0.83 & sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ).
% 0.21/0.83
% 0.21/0.83 fof(m__,conjecture,
% 0.21/0.83 ? [W0] :
% 0.21/0.83 ( aInteger0(W0)
% 0.21/0.83 & sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) ).
% 0.21/0.83
% 0.21/0.83 %------------------------------------------------------------------------------
% 0.21/0.83 %-------------------------------------------
% 0.21/0.83 % Proof found
% 0.21/0.83 % SZS status Theorem for theBenchmark
% 0.21/0.83 % SZS output start Proof
% 0.21/0.83 %ClaNum:63(EqnAxiom:16)
% 0.21/0.83 %VarNum:161(SingletonVarNum:56)
% 0.21/0.83 %MaxLitNum:6
% 0.21/0.83 %MaxfuncDepth:2
% 0.21/0.83 %SharedTerms:34
% 0.21/0.83 %goalClause: 52
% 0.21/0.83 [17]P1(a1)
% 0.21/0.83 [18]P1(a8)
% 0.21/0.83 [19]P1(a9)
% 0.21/0.83 [20]P1(a10)
% 0.21/0.83 [21]P1(a11)
% 0.21/0.83 [22]P1(a12)
% 0.21/0.83 [23]P1(a13)
% 0.21/0.83 [24]P1(a2)
% 0.21/0.83 [25]P1(a4)
% 0.21/0.83 [31]P3(a9,a10,a11)
% 0.21/0.83 [32]P3(a10,a12,a11)
% 0.21/0.83 [33]~E(a1,a11)
% 0.21/0.83 [26]E(f6(a9,f5(a10)),f7(a11,a13))
% 0.21/0.83 [27]E(f6(a9,f5(a10)),f7(a11,a2))
% 0.21/0.83 [28]E(f6(a10,f5(a12)),f7(a11,a4))
% 0.21/0.83 [29]P2(a11,f6(a9,f5(a10)))
% 0.21/0.83 [30]P2(a11,f6(a10,f5(a12)))
% 0.21/0.83 [34]~P1(x341)+P1(f5(x341))
% 0.21/0.83 [35]~P1(x351)+E(f7(a1,x351),a1)
% 0.21/0.83 [36]~P1(x361)+E(f7(x361,a1),a1)
% 0.21/0.83 [37]~P1(x371)+E(f6(a1,x371),x371)
% 0.21/0.83 [38]~P1(x381)+E(f7(a8,x381),x381)
% 0.21/0.83 [39]~P1(x391)+E(f6(x391,a1),x391)
% 0.21/0.83 [40]~P1(x401)+E(f7(x401,a8),x401)
% 0.21/0.83 [41]~P1(x411)+E(f6(f5(x411),x411),a1)
% 0.21/0.83 [42]~P1(x421)+E(f6(x421,f5(x421)),a1)
% 0.21/0.83 [43]~P1(x431)+E(f7(x431,f5(a8)),f5(x431))
% 0.21/0.83 [44]~P1(x441)+E(f7(f5(a8),x441),f5(x441))
% 0.21/0.83 [52]~P1(x521)+~E(f7(a11,x521),f6(a10,f5(a12)))
% 0.21/0.83 [45]~P2(x451,x452)+~P1(x452)+~E(x451,a1)
% 0.21/0.83 [46]~P2(x461,x462)+P1(x461)+~P1(x462)
% 0.21/0.83 [48]~P1(x482)+~P1(x481)+E(f6(x481,x482),f6(x482,x481))
% 0.21/0.83 [49]~P1(x492)+~P1(x491)+E(f7(x491,x492),f7(x492,x491))
% 0.21/0.83 [50]~P1(x502)+~P1(x501)+P1(f6(x501,x502))
% 0.21/0.83 [51]~P1(x512)+~P1(x511)+P1(f7(x511,x512))
% 0.21/0.83 [53]~P1(x531)+~P2(x532,x531)+P1(f3(x531,x532))
% 0.21/0.83 [56]~P1(x562)+~P2(x561,x562)+E(f7(x561,f3(x562,x561)),x562)
% 0.21/0.83 [55]~P1(x551)+~P1(x552)+P3(x552,x552,x551)+E(x551,a1)
% 0.21/0.83 [57]~P1(x573)+~P1(x572)+~P1(x571)+E(f6(f6(x571,x572),x573),f6(x571,f6(x572,x573)))
% 0.21/0.83 [58]~P1(x583)+~P1(x582)+~P1(x581)+E(f7(f7(x581,x582),x583),f7(x581,f7(x582,x583)))
% 0.21/0.84 [59]~P1(x593)+~P1(x592)+~P1(x591)+E(f6(f7(x591,x592),f7(x591,x593)),f7(x591,f6(x592,x593)))
% 0.21/0.84 [60]~P1(x602)+~P1(x603)+~P1(x601)+E(f6(f7(x601,x602),f7(x603,x602)),f7(f6(x601,x603),x602))
% 0.21/0.84 [47]~P1(x471)+~P1(x472)+E(x471,a1)+E(x472,a1)+~E(f7(x472,x471),a1)
% 0.21/0.84 [63]~P1(x631)+~P1(x632)+~P1(x633)+~P3(x633,x632,x631)+P3(x632,x633,x631)+E(x631,a1)
% 0.21/0.84 [54]~P1(x542)+~P1(x543)+~P1(x541)+P2(x541,x542)+E(x541,a1)+~E(f7(x541,x543),x542)
% 0.21/0.84 [61]~P1(x613)+~P1(x612)+~P1(x611)+P3(x612,x613,x611)+E(x611,a1)+~P2(x611,f6(x612,f5(x613)))
% 0.21/0.84 [62]~P1(x621)+~P1(x623)+~P1(x622)+~P3(x622,x623,x621)+E(x621,a1)+P2(x621,f6(x622,f5(x623)))
% 0.21/0.84 %EqnAxiom
% 0.21/0.84 [1]E(x11,x11)
% 0.21/0.84 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.84 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.84 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.21/0.84 [5]~E(x51,x52)+E(f6(x51,x53),f6(x52,x53))
% 0.21/0.84 [6]~E(x61,x62)+E(f6(x63,x61),f6(x63,x62))
% 0.21/0.84 [7]~E(x71,x72)+E(f7(x71,x73),f7(x72,x73))
% 0.21/0.84 [8]~E(x81,x82)+E(f7(x83,x81),f7(x83,x82))
% 0.21/0.84 [9]~E(x91,x92)+E(f3(x91,x93),f3(x92,x93))
% 0.21/0.84 [10]~E(x101,x102)+E(f3(x103,x101),f3(x103,x102))
% 0.21/0.84 [11]~P1(x111)+P1(x112)+~E(x111,x112)
% 0.21/0.84 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124)
% 0.21/0.84 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134)
% 0.21/0.84 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141)
% 0.21/0.84 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153)
% 0.21/0.84 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161)
% 0.21/0.84
% 0.21/0.84 %-------------------------------------------
% 0.21/0.84 cnf(173,plain,
% 0.21/0.84 (E(f7(a11,a4),f6(a10,f5(a12)))),
% 0.21/0.84 inference(scs_inference,[],[18,28,57,60,58,59,2])).
% 0.21/0.84 cnf(213,plain,
% 0.21/0.84 ($false),
% 0.21/0.84 inference(scs_inference,[],[25,173,52]),
% 0.21/0.84 ['proof']).
% 0.21/0.84 % SZS output end Proof
% 0.21/0.84 % Total time :0.090000s
%------------------------------------------------------------------------------