TSTP Solution File: NUM458+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM458+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 : n032.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 10:22:14 EDT 2023
% Result : Theorem 0.13s 0.55s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM458+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Fri Aug 25 09:20:57 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.13/0.46 start to proof:theBenchmark
% 0.13/0.54 %-------------------------------------------
% 0.13/0.54 % File :CSE---1.6
% 0.13/0.54 % Problem :theBenchmark
% 0.13/0.54 % Transform :cnf
% 0.13/0.54 % Format :tptp:raw
% 0.13/0.54 % Command :java -jar mcs_scs.jar %d %s
% 0.13/0.54
% 0.13/0.54 % Result :Theorem 0.020000s
% 0.13/0.54 % Output :CNFRefutation 0.020000s
% 0.13/0.54 %-------------------------------------------
% 0.13/0.54 %------------------------------------------------------------------------------
% 0.13/0.54 % File : NUM458+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.54 % Domain : Number Theory
% 0.13/0.54 % Problem : Square root of a prime is irrational 02, 01 expansion
% 0.13/0.54 % Version : Especial.
% 0.13/0.54 % English :
% 0.13/0.54
% 0.13/0.54 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista
% 0.13/0.54 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.13/0.54 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.13/0.54 % Source : [Pas08]
% 0.13/0.54 % Names : primes_02.01 [Pas08]
% 0.13/0.54
% 0.13/0.54 % Status : Theorem
% 0.13/0.54 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.1.0, 0.03 v6.0.0, 0.04 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.1.0, 0.19 v5.0.0, 0.25 v4.1.0, 0.30 v4.0.1, 0.57 v4.0.0
% 0.13/0.54 % Syntax : Number of formulae : 21 ( 2 unt; 2 def)
% 0.13/0.54 % Number of atoms : 77 ( 30 equ)
% 0.13/0.54 % Maximal formula atoms : 7 ( 3 avg)
% 0.13/0.54 % Number of connectives : 58 ( 2 ~; 4 |; 26 &)
% 0.13/0.54 % ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% 0.13/0.54 % Maximal formula depth : 9 ( 5 avg)
% 0.13/0.54 % Maximal term depth : 3 ( 1 avg)
% 0.13/0.54 % Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% 0.13/0.54 % Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% 0.13/0.54 % Number of variables : 38 ( 36 !; 2 ?)
% 0.13/0.54 % SPC : FOF_THM_RFO_SEQ
% 0.13/0.54
% 0.13/0.54 % Comments : Problem generated by the SAD system [VLP07]
% 0.13/0.54 %------------------------------------------------------------------------------
% 0.13/0.54 fof(mNatSort,axiom,
% 0.13/0.54 ! [W0] :
% 0.13/0.54 ( aNaturalNumber0(W0)
% 0.13/0.54 => $true ) ).
% 0.13/0.54
% 0.13/0.54 fof(mSortsC,axiom,
% 0.13/0.54 aNaturalNumber0(sz00) ).
% 0.13/0.54
% 0.13/0.54 fof(mSortsC_01,axiom,
% 0.13/0.54 ( aNaturalNumber0(sz10)
% 0.13/0.54 & sz10 != sz00 ) ).
% 0.13/0.54
% 0.13/0.54 fof(mSortsB,axiom,
% 0.13/0.54 ! [W0,W1] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1) )
% 0.13/0.54 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mSortsB_02,axiom,
% 0.13/0.54 ! [W0,W1] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1) )
% 0.13/0.54 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mAddComm,axiom,
% 0.13/0.54 ! [W0,W1] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1) )
% 0.13/0.54 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mAddAsso,axiom,
% 0.13/0.54 ! [W0,W1,W2] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1)
% 0.13/0.54 & aNaturalNumber0(W2) )
% 0.13/0.54 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.13/0.54
% 0.13/0.54 fof(m_AddZero,axiom,
% 0.13/0.54 ! [W0] :
% 0.13/0.54 ( aNaturalNumber0(W0)
% 0.13/0.54 => ( sdtpldt0(W0,sz00) = W0
% 0.13/0.54 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mMulComm,axiom,
% 0.13/0.54 ! [W0,W1] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1) )
% 0.13/0.54 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mMulAsso,axiom,
% 0.13/0.54 ! [W0,W1,W2] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1)
% 0.13/0.54 & aNaturalNumber0(W2) )
% 0.13/0.54 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.13/0.54
% 0.13/0.54 fof(m_MulUnit,axiom,
% 0.13/0.54 ! [W0] :
% 0.13/0.54 ( aNaturalNumber0(W0)
% 0.13/0.54 => ( sdtasdt0(W0,sz10) = W0
% 0.13/0.54 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.13/0.54
% 0.13/0.54 fof(m_MulZero,axiom,
% 0.13/0.54 ! [W0] :
% 0.13/0.54 ( aNaturalNumber0(W0)
% 0.13/0.54 => ( sdtasdt0(W0,sz00) = sz00
% 0.13/0.54 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mAMDistr,axiom,
% 0.13/0.54 ! [W0,W1,W2] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1)
% 0.13/0.54 & aNaturalNumber0(W2) )
% 0.13/0.54 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.13/0.54 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mAddCanc,axiom,
% 0.13/0.54 ! [W0,W1,W2] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1)
% 0.13/0.54 & aNaturalNumber0(W2) )
% 0.13/0.54 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
% 0.13/0.54 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
% 0.13/0.54 => W1 = W2 ) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mMulCanc,axiom,
% 0.13/0.54 ! [W0] :
% 0.13/0.54 ( aNaturalNumber0(W0)
% 0.13/0.54 => ( W0 != sz00
% 0.13/0.54 => ! [W1,W2] :
% 0.13/0.54 ( ( aNaturalNumber0(W1)
% 0.13/0.54 & aNaturalNumber0(W2) )
% 0.13/0.54 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2)
% 0.13/0.54 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
% 0.13/0.54 => W1 = W2 ) ) ) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mZeroAdd,axiom,
% 0.13/0.54 ! [W0,W1] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1) )
% 0.13/0.54 => ( sdtpldt0(W0,W1) = sz00
% 0.13/0.54 => ( W0 = sz00
% 0.13/0.54 & W1 = sz00 ) ) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mZeroMul,axiom,
% 0.13/0.54 ! [W0,W1] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1) )
% 0.13/0.54 => ( sdtasdt0(W0,W1) = sz00
% 0.13/0.54 => ( W0 = sz00
% 0.13/0.54 | W1 = sz00 ) ) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mDefLE,definition,
% 0.13/0.54 ! [W0,W1] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1) )
% 0.13/0.54 => ( sdtlseqdt0(W0,W1)
% 0.13/0.54 <=> ? [W2] :
% 0.13/0.54 ( aNaturalNumber0(W2)
% 0.13/0.54 & sdtpldt0(W0,W2) = W1 ) ) ) ).
% 0.13/0.54
% 0.13/0.54 fof(mDefDiff,definition,
% 0.13/0.54 ! [W0,W1] :
% 0.13/0.54 ( ( aNaturalNumber0(W0)
% 0.13/0.54 & aNaturalNumber0(W1) )
% 0.13/0.54 => ( sdtlseqdt0(W0,W1)
% 0.13/0.54 => ! [W2] :
% 0.13/0.54 ( W2 = sdtmndt0(W1,W0)
% 0.13/0.54 <=> ( aNaturalNumber0(W2)
% 0.13/0.54 & sdtpldt0(W0,W2) = W1 ) ) ) ) ).
% 0.13/0.54
% 0.13/0.54 fof(m__718,hypothesis,
% 0.13/0.54 aNaturalNumber0(xm) ).
% 0.13/0.54
% 0.13/0.54 fof(m__,conjecture,
% 0.13/0.54 ( ? [W0] :
% 0.13/0.54 ( aNaturalNumber0(W0)
% 0.13/0.54 & sdtpldt0(xm,W0) = xm )
% 0.13/0.54 | sdtlseqdt0(xm,xm) ) ).
% 0.13/0.54
% 0.13/0.54 %------------------------------------------------------------------------------
% 0.13/0.54 %-------------------------------------------
% 0.13/0.55 % Proof found
% 0.13/0.55 % SZS status Theorem for theBenchmark
% 0.13/0.55 % SZS output start Proof
% 0.13/0.55 %ClaNum:47(EqnAxiom:14)
% 0.13/0.55 %VarNum:181(SingletonVarNum:61)
% 0.13/0.55 %MaxLitNum:6
% 0.13/0.55 %MaxfuncDepth:2
% 0.13/0.55 %SharedTerms:8
% 0.13/0.55 %goalClause: 19 26
% 0.13/0.55 %singleGoalClaCount:1
% 0.13/0.55 [15]P1(a1)
% 0.13/0.55 [16]P1(a6)
% 0.13/0.55 [17]P1(a7)
% 0.13/0.55 [18]~E(a1,a6)
% 0.13/0.55 [19]~P2(a7,a7)
% 0.13/0.55 [20]~P1(x201)+E(f2(a1,x201),a1)
% 0.13/0.55 [21]~P1(x211)+E(f2(x211,a1),a1)
% 0.13/0.55 [22]~P1(x221)+E(f4(a1,x221),x221)
% 0.13/0.55 [23]~P1(x231)+E(f2(a6,x231),x231)
% 0.13/0.55 [24]~P1(x241)+E(f4(x241,a1),x241)
% 0.13/0.55 [25]~P1(x251)+E(f2(x251,a6),x251)
% 0.13/0.55 [26]~P1(x261)+~E(f4(a7,x261),a7)
% 0.13/0.55 [30]~P1(x302)+~P1(x301)+E(f4(x301,x302),f4(x302,x301))
% 0.13/0.55 [31]~P1(x312)+~P1(x311)+E(f2(x311,x312),f2(x312,x311))
% 0.13/0.55 [32]~P1(x322)+~P1(x321)+P1(f4(x321,x322))
% 0.13/0.55 [33]~P1(x332)+~P1(x331)+P1(f2(x331,x332))
% 0.13/0.55 [27]~P1(x272)+~P1(x271)+E(x271,a1)+~E(f4(x272,x271),a1)
% 0.13/0.55 [28]~P1(x282)+~P1(x281)+E(x281,a1)+~E(f4(x281,x282),a1)
% 0.13/0.55 [36]~P1(x362)+~P1(x361)+~P2(x361,x362)+P1(f3(x361,x362))
% 0.13/0.55 [42]~P1(x422)+~P1(x421)+~P2(x421,x422)+E(f4(x421,f3(x421,x422)),x422)
% 0.13/0.55 [44]~P1(x443)+~P1(x442)+~P1(x441)+E(f4(f4(x441,x442),x443),f4(x441,f4(x442,x443)))
% 0.13/0.55 [45]~P1(x453)+~P1(x452)+~P1(x451)+E(f2(f2(x451,x452),x453),f2(x451,f2(x452,x453)))
% 0.13/0.55 [46]~P1(x463)+~P1(x462)+~P1(x461)+E(f4(f2(x461,x462),f2(x461,x463)),f2(x461,f4(x462,x463)))
% 0.13/0.55 [47]~P1(x472)+~P1(x473)+~P1(x471)+E(f4(f2(x471,x472),f2(x473,x472)),f2(f4(x471,x473),x472))
% 0.13/0.55 [29]~P1(x291)+~P1(x292)+E(x291,a1)+E(x292,a1)+~E(f2(x292,x291),a1)
% 0.13/0.55 [34]~P1(x342)+~P1(x341)+~P1(x343)+P2(x341,x342)+~E(f4(x341,x343),x342)
% 0.13/0.55 [35]~P1(x353)+~P1(x352)+~P2(x353,x352)+P1(x351)+~E(x351,f5(x352,x353))
% 0.13/0.55 [37]~P1(x372)+~P1(x371)+~P1(x373)+E(x371,x372)+~E(f4(x373,x371),f4(x373,x372))
% 0.13/0.55 [38]~P1(x382)+~P1(x383)+~P1(x381)+E(x381,x382)+~E(f4(x381,x383),f4(x382,x383))
% 0.13/0.55 [41]~P1(x413)+~P1(x411)+~P2(x411,x413)+~E(x412,f5(x413,x411))+E(f4(x411,x412),x413)
% 0.13/0.55 [39]~P1(x392)+~P1(x391)+~P1(x393)+E(x391,x392)+~E(f2(x393,x391),f2(x393,x392))+E(x393,a1)
% 0.13/0.55 [40]~P1(x402)+~P1(x403)+~P1(x401)+E(x401,x402)+~E(f2(x401,x403),f2(x402,x403))+E(x403,a1)
% 0.13/0.55 [43]~P1(x432)+~P1(x433)+~P1(x431)+~P2(x433,x432)+~E(f4(x433,x431),x432)+E(x431,f5(x432,x433))
% 0.13/0.55 %EqnAxiom
% 0.13/0.55 [1]E(x11,x11)
% 0.13/0.55 [2]E(x22,x21)+~E(x21,x22)
% 0.13/0.55 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.13/0.55 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.13/0.55 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.13/0.55 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.13/0.55 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.13/0.55 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83))
% 0.13/0.55 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92))
% 0.13/0.55 [10]~E(x101,x102)+E(f5(x101,x103),f5(x102,x103))
% 0.13/0.55 [11]~E(x111,x112)+E(f5(x113,x111),f5(x113,x112))
% 0.13/0.55 [12]~P1(x121)+P1(x122)+~E(x121,x122)
% 0.13/0.55 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133)
% 0.13/0.55 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141)
% 0.13/0.55
% 0.13/0.55 %-------------------------------------------
% 0.13/0.55 cnf(48,plain,
% 0.13/0.55 (~E(a6,a1)),
% 0.13/0.55 inference(scs_inference,[],[18,2])).
% 0.13/0.55 cnf(49,plain,
% 0.13/0.55 (~E(f4(a7,a1),a7)),
% 0.13/0.55 inference(scs_inference,[],[15,18,2,26])).
% 0.13/0.55 cnf(63,plain,
% 0.13/0.55 (E(f5(x631,f2(a1,a6)),f5(x631,a1))),
% 0.13/0.55 inference(scs_inference,[],[15,16,17,18,2,26,25,24,23,22,21,20,11])).
% 0.13/0.55 cnf(64,plain,
% 0.13/0.55 (E(f5(f2(a1,a6),x641),f5(a1,x641))),
% 0.13/0.55 inference(scs_inference,[],[15,16,17,18,2,26,25,24,23,22,21,20,11,10])).
% 0.13/0.55 cnf(70,plain,
% 0.13/0.55 (E(f2(f2(a1,a6),x701),f2(a1,x701))),
% 0.13/0.55 inference(scs_inference,[],[15,16,17,18,2,26,25,24,23,22,21,20,11,10,9,8,7,6,5,4])).
% 0.13/0.55 cnf(100,plain,
% 0.13/0.55 (~P2(a1,a1)+P1(f3(a1,a1))),
% 0.13/0.55 inference(scs_inference,[],[19,15,16,17,18,2,26,25,24,23,22,21,20,11,10,9,8,7,6,5,4,14,3,33,32,28,27,45,44,47,46,29,38,37,40,39,13,36])).
% 0.13/0.55 cnf(104,plain,
% 0.13/0.55 (P2(a1,a1)),
% 0.13/0.55 inference(scs_inference,[],[19,15,16,17,18,2,26,25,24,23,22,21,20,11,10,9,8,7,6,5,4,14,3,33,32,28,27,45,44,47,46,29,38,37,40,39,13,36,42,34])).
% 0.13/0.55 cnf(106,plain,
% 0.13/0.55 (P1(f5(a1,f2(a1,a6)))),
% 0.13/0.55 inference(scs_inference,[],[19,15,16,17,18,2,26,25,24,23,22,21,20,11,10,9,8,7,6,5,4,14,3,33,32,28,27,45,44,47,46,29,38,37,40,39,13,36,42,34,35])).
% 0.13/0.55 cnf(136,plain,
% 0.13/0.55 ($false),
% 0.13/0.55 inference(scs_inference,[],[19,17,16,15,70,64,63,106,49,48,104,100,12,32,28,45,44,42,47,46,34,35,2,24]),
% 0.13/0.55 ['proof']).
% 0.13/0.55 % SZS output end Proof
% 0.13/0.55 % Total time :0.020000s
%------------------------------------------------------------------------------