TSTP Solution File: NUM429+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM429+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 : n027.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 10:22:03 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM429+3 : 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
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 08:35:48 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % File :CSE---1.6
% 0.20/0.62 % Problem :theBenchmark
% 0.20/0.62 % Transform :cnf
% 0.20/0.62 % Format :tptp:raw
% 0.20/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.62
% 0.20/0.62 % Result :Theorem 0.000000s
% 0.20/0.62 % Output :CNFRefutation 0.000000s
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 % File : NUM429+3 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.62 % Domain : Number Theory
% 0.20/0.62 % Problem : Fuerstenberg's infinitude of primes 05_01, 02 expansion
% 0.20/0.62 % Version : Especial.
% 0.20/0.62 % English :
% 0.20/0.62
% 0.20/0.62 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.20/0.62 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.20/0.62 % Source : [Pas08]
% 0.20/0.62 % Names : fuerst_05_01.02 [Pas08]
% 0.20/0.62
% 0.20/0.62 % Status : Theorem
% 0.20/0.62 % 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, 0.26 v5.2.0, 0.15 v5.1.0, 0.24 v5.0.0, 0.33 v4.1.0, 0.39 v4.0.1, 0.65 v4.0.0
% 0.20/0.62 % Syntax : Number of formulae : 24 ( 2 unt; 2 def)
% 0.20/0.62 % Number of atoms : 88 ( 28 equ)
% 0.20/0.62 % Maximal formula atoms : 8 ( 3 avg)
% 0.20/0.62 % Number of connectives : 69 ( 5 ~; 1 |; 40 &)
% 0.20/0.62 % ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% 0.20/0.62 % Maximal formula depth : 9 ( 5 avg)
% 0.20/0.62 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.62 % Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% 0.20/0.62 % Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% 0.20/0.62 % Number of variables : 40 ( 36 !; 4 ?)
% 0.20/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.62
% 0.20/0.62 % Comments : Problem generated by the SAD system [VLP07]
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 fof(mIntegers,axiom,
% 0.20/0.62 ! [W0] :
% 0.20/0.62 ( aInteger0(W0)
% 0.20/0.62 => $true ) ).
% 0.20/0.62
% 0.20/0.62 fof(mIntZero,axiom,
% 0.20/0.62 aInteger0(sz00) ).
% 0.20/0.62
% 0.20/0.62 fof(mIntOne,axiom,
% 0.20/0.63 aInteger0(sz10) ).
% 0.20/0.63
% 0.20/0.63 fof(mIntNeg,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aInteger0(W0)
% 0.20/0.63 => aInteger0(smndt0(W0)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mIntPlus,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1) )
% 0.20/0.63 => aInteger0(sdtpldt0(W0,W1)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mIntMult,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1) )
% 0.20/0.63 => aInteger0(sdtasdt0(W0,W1)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mAddAsso,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1)
% 0.20/0.63 & aInteger0(W2) )
% 0.20/0.63 => sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mAddComm,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1) )
% 0.20/0.63 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mAddZero,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aInteger0(W0)
% 0.20/0.63 => ( sdtpldt0(W0,sz00) = W0
% 0.20/0.63 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mAddNeg,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aInteger0(W0)
% 0.20/0.63 => ( sdtpldt0(W0,smndt0(W0)) = sz00
% 0.20/0.63 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMulAsso,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1)
% 0.20/0.63 & aInteger0(W2) )
% 0.20/0.63 => sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMulComm,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1) )
% 0.20/0.63 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMulOne,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aInteger0(W0)
% 0.20/0.63 => ( sdtasdt0(W0,sz10) = W0
% 0.20/0.63 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mDistrib,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1)
% 0.20/0.63 & aInteger0(W2) )
% 0.20/0.63 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.20/0.63 & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMulZero,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aInteger0(W0)
% 0.20/0.63 => ( sdtasdt0(W0,sz00) = sz00
% 0.20/0.63 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mMulMinOne,axiom,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aInteger0(W0)
% 0.20/0.63 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
% 0.20/0.63 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mZeroDiv,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1) )
% 0.20/0.63 => ( sdtasdt0(W0,W1) = sz00
% 0.20/0.63 => ( W0 = sz00
% 0.20/0.63 | W1 = sz00 ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mDivisor,definition,
% 0.20/0.63 ! [W0] :
% 0.20/0.63 ( aInteger0(W0)
% 0.20/0.63 => ! [W1] :
% 0.20/0.63 ( aDivisorOf0(W1,W0)
% 0.20/0.63 <=> ( aInteger0(W1)
% 0.20/0.63 & W1 != sz00
% 0.20/0.63 & ? [W2] :
% 0.20/0.63 ( aInteger0(W2)
% 0.20/0.63 & sdtasdt0(W1,W2) = W0 ) ) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mEquMod,definition,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1)
% 0.20/0.63 & aInteger0(W2)
% 0.20/0.63 & W2 != sz00 )
% 0.20/0.63 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.20/0.63 <=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mEquModRef,axiom,
% 0.20/0.63 ! [W0,W1] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1)
% 0.20/0.63 & W1 != sz00 )
% 0.20/0.63 => sdteqdtlpzmzozddtrp0(W0,W0,W1) ) ).
% 0.20/0.63
% 0.20/0.63 fof(mEquModSym,axiom,
% 0.20/0.63 ! [W0,W1,W2] :
% 0.20/0.63 ( ( aInteger0(W0)
% 0.20/0.63 & aInteger0(W1)
% 0.20/0.63 & aInteger0(W2)
% 0.20/0.63 & W2 != sz00 )
% 0.20/0.63 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
% 0.20/0.63 => sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(m__818,hypothesis,
% 0.20/0.63 ( aInteger0(xa)
% 0.20/0.63 & aInteger0(xb)
% 0.20/0.63 & aInteger0(xq)
% 0.20/0.63 & xq != sz00
% 0.20/0.63 & aInteger0(xc) ) ).
% 0.20/0.63
% 0.20/0.63 fof(m__853,hypothesis,
% 0.20/0.63 ( ? [W0] :
% 0.20/0.63 ( aInteger0(W0)
% 0.20/0.63 & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) )
% 0.20/0.63 & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
% 0.20/0.63 & sdteqdtlpzmzozddtrp0(xa,xb,xq)
% 0.20/0.63 & ? [W0] :
% 0.20/0.63 ( aInteger0(W0)
% 0.20/0.63 & sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) )
% 0.20/0.63 & aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
% 0.20/0.63 & sdteqdtlpzmzozddtrp0(xb,xc,xq) ) ).
% 0.20/0.63
% 0.20/0.63 fof(m__,conjecture,
% 0.20/0.63 ? [W0] :
% 0.20/0.63 ( aInteger0(W0)
% 0.20/0.63 & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ) ).
% 0.20/0.63
% 0.20/0.63 %------------------------------------------------------------------------------
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 %ClaNum:61(EqnAxiom:16)
% 0.20/0.63 %VarNum:161(SingletonVarNum:56)
% 0.20/0.63 %MaxLitNum:6
% 0.20/0.63 %MaxfuncDepth:2
% 0.20/0.63 %SharedTerms:30
% 0.20/0.63 %goalClause: 50
% 0.20/0.63 [17]P1(a1)
% 0.20/0.63 [18]P1(a8)
% 0.20/0.63 [19]P1(a9)
% 0.20/0.63 [20]P1(a10)
% 0.20/0.63 [21]P1(a11)
% 0.20/0.63 [22]P1(a12)
% 0.20/0.63 [23]P1(a2)
% 0.20/0.63 [24]P1(a4)
% 0.20/0.63 [29]P3(a9,a10,a11)
% 0.20/0.63 [30]P3(a10,a12,a11)
% 0.20/0.63 [31]~E(a1,a11)
% 0.20/0.63 [25]E(f6(a9,f5(a10)),f7(a11,a2))
% 0.20/0.63 [26]E(f6(a10,f5(a12)),f7(a11,a4))
% 0.20/0.63 [27]P2(a11,f6(a9,f5(a10)))
% 0.20/0.63 [28]P2(a11,f6(a10,f5(a12)))
% 0.20/0.63 [32]~P1(x321)+P1(f5(x321))
% 0.20/0.63 [33]~P1(x331)+E(f7(a1,x331),a1)
% 0.20/0.63 [34]~P1(x341)+E(f7(x341,a1),a1)
% 0.20/0.63 [35]~P1(x351)+E(f6(a1,x351),x351)
% 0.20/0.63 [36]~P1(x361)+E(f7(a8,x361),x361)
% 0.20/0.63 [37]~P1(x371)+E(f6(x371,a1),x371)
% 0.20/0.63 [38]~P1(x381)+E(f7(x381,a8),x381)
% 0.20/0.63 [39]~P1(x391)+E(f6(f5(x391),x391),a1)
% 0.20/0.63 [40]~P1(x401)+E(f6(x401,f5(x401)),a1)
% 0.20/0.63 [41]~P1(x411)+E(f7(x411,f5(a8)),f5(x411))
% 0.20/0.63 [42]~P1(x421)+E(f7(f5(a8),x421),f5(x421))
% 0.20/0.63 [50]~P1(x501)+~E(f7(a11,x501),f6(a9,f5(a10)))
% 0.20/0.63 [43]~P2(x431,x432)+~P1(x432)+~E(x431,a1)
% 0.20/0.63 [44]~P2(x441,x442)+P1(x441)+~P1(x442)
% 0.20/0.63 [46]~P1(x462)+~P1(x461)+E(f6(x461,x462),f6(x462,x461))
% 0.20/0.63 [47]~P1(x472)+~P1(x471)+E(f7(x471,x472),f7(x472,x471))
% 0.20/0.63 [48]~P1(x482)+~P1(x481)+P1(f6(x481,x482))
% 0.20/0.63 [49]~P1(x492)+~P1(x491)+P1(f7(x491,x492))
% 0.20/0.63 [51]~P1(x511)+~P2(x512,x511)+P1(f3(x511,x512))
% 0.20/0.63 [54]~P1(x542)+~P2(x541,x542)+E(f7(x541,f3(x542,x541)),x542)
% 0.20/0.63 [53]~P1(x531)+~P1(x532)+P3(x532,x532,x531)+E(x531,a1)
% 0.20/0.63 [55]~P1(x553)+~P1(x552)+~P1(x551)+E(f6(f6(x551,x552),x553),f6(x551,f6(x552,x553)))
% 0.20/0.63 [56]~P1(x563)+~P1(x562)+~P1(x561)+E(f7(f7(x561,x562),x563),f7(x561,f7(x562,x563)))
% 0.20/0.63 [57]~P1(x573)+~P1(x572)+~P1(x571)+E(f6(f7(x571,x572),f7(x571,x573)),f7(x571,f6(x572,x573)))
% 0.20/0.63 [58]~P1(x582)+~P1(x583)+~P1(x581)+E(f6(f7(x581,x582),f7(x583,x582)),f7(f6(x581,x583),x582))
% 0.20/0.63 [45]~P1(x451)+~P1(x452)+E(x451,a1)+E(x452,a1)+~E(f7(x452,x451),a1)
% 0.20/0.63 [61]~P1(x611)+~P1(x612)+~P1(x613)+~P3(x613,x612,x611)+P3(x612,x613,x611)+E(x611,a1)
% 0.20/0.63 [52]~P1(x522)+~P1(x523)+~P1(x521)+P2(x521,x522)+E(x521,a1)+~E(f7(x521,x523),x522)
% 0.20/0.63 [59]~P1(x593)+~P1(x592)+~P1(x591)+P3(x592,x593,x591)+E(x591,a1)+~P2(x591,f6(x592,f5(x593)))
% 0.20/0.63 [60]~P1(x601)+~P1(x603)+~P1(x602)+~P3(x602,x603,x601)+E(x601,a1)+P2(x601,f6(x602,f5(x603)))
% 0.20/0.63 %EqnAxiom
% 0.20/0.63 [1]E(x11,x11)
% 0.20/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.63 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.20/0.63 [5]~E(x51,x52)+E(f6(x51,x53),f6(x52,x53))
% 0.20/0.63 [6]~E(x61,x62)+E(f6(x63,x61),f6(x63,x62))
% 0.20/0.63 [7]~E(x71,x72)+E(f7(x71,x73),f7(x72,x73))
% 0.20/0.63 [8]~E(x81,x82)+E(f7(x83,x81),f7(x83,x82))
% 0.20/0.63 [9]~E(x91,x92)+E(f3(x91,x93),f3(x92,x93))
% 0.20/0.63 [10]~E(x101,x102)+E(f3(x103,x101),f3(x103,x102))
% 0.20/0.63 [11]~P1(x111)+P1(x112)+~E(x111,x112)
% 0.20/0.63 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124)
% 0.20/0.63 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134)
% 0.20/0.63 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141)
% 0.20/0.63 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153)
% 0.20/0.63 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161)
% 0.20/0.63
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 cnf(63,plain,
% 0.20/0.63 ($false),
% 0.20/0.63 inference(scs_inference,[],[23,25,2,50]),
% 0.20/0.63 ['proof']).
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time :0.000000s
%------------------------------------------------------------------------------