TSTP Solution File: NUM458+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM458+1 : 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 : 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 : Thu Aug 31 10:22:14 EDT 2023
% Result : Theorem 0.18s 0.65s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM458+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n028.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 09:14:06 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.56 start to proof:theBenchmark
% 0.18/0.64 %-------------------------------------------
% 0.18/0.64 % File :CSE---1.6
% 0.18/0.64 % Problem :theBenchmark
% 0.18/0.64 % Transform :cnf
% 0.18/0.64 % Format :tptp:raw
% 0.18/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.64
% 0.18/0.64 % Result :Theorem 0.020000s
% 0.18/0.64 % Output :CNFRefutation 0.020000s
% 0.18/0.64 %-------------------------------------------
% 0.18/0.64 %------------------------------------------------------------------------------
% 0.18/0.64 % File : NUM458+1 : TPTP v8.1.2. Released v4.0.0.
% 0.18/0.64 % Domain : Number Theory
% 0.18/0.64 % Problem : Square root of a prime is irrational 02, 00 expansion
% 0.18/0.64 % Version : Especial.
% 0.18/0.64 % English :
% 0.18/0.64
% 0.18/0.64 % Refs : [LPV06] Lyaletski et al. (2006), SAD as a Mathematical Assista
% 0.18/0.64 % : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.18/0.64 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.18/0.64 % Source : [Pas08]
% 0.18/0.64 % Names : primes_02.00 [Pas08]
% 0.18/0.64
% 0.18/0.64 % Status : Theorem
% 0.18/0.64 % Rating : 0.14 v8.1.0, 0.06 v7.4.0, 0.10 v7.3.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.19 v5.4.0, 0.25 v5.3.0, 0.26 v5.2.0, 0.15 v5.1.0, 0.33 v5.0.0, 0.29 v4.1.0, 0.39 v4.0.1, 0.70 v4.0.0
% 0.18/0.64 % Syntax : Number of formulae : 21 ( 3 unt; 2 def)
% 0.18/0.64 % Number of atoms : 75 ( 29 equ)
% 0.18/0.64 % Maximal formula atoms : 7 ( 3 avg)
% 0.18/0.64 % Number of connectives : 56 ( 2 ~; 3 |; 25 &)
% 0.18/0.64 % ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% 0.18/0.64 % Maximal formula depth : 9 ( 5 avg)
% 0.18/0.64 % Maximal term depth : 3 ( 1 avg)
% 0.18/0.64 % Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% 0.18/0.64 % Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% 0.18/0.64 % Number of variables : 37 ( 36 !; 1 ?)
% 0.18/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.18/0.64
% 0.18/0.64 % Comments : Problem generated by the SAD system [VLP07]
% 0.18/0.64 %------------------------------------------------------------------------------
% 0.18/0.64 fof(mNatSort,axiom,
% 0.18/0.64 ! [W0] :
% 0.18/0.64 ( aNaturalNumber0(W0)
% 0.18/0.64 => $true ) ).
% 0.18/0.64
% 0.18/0.64 fof(mSortsC,axiom,
% 0.18/0.64 aNaturalNumber0(sz00) ).
% 0.18/0.64
% 0.18/0.64 fof(mSortsC_01,axiom,
% 0.18/0.64 ( aNaturalNumber0(sz10)
% 0.18/0.64 & sz10 != sz00 ) ).
% 0.18/0.64
% 0.18/0.64 fof(mSortsB,axiom,
% 0.18/0.64 ! [W0,W1] :
% 0.18/0.64 ( ( aNaturalNumber0(W0)
% 0.18/0.64 & aNaturalNumber0(W1) )
% 0.18/0.64 => aNaturalNumber0(sdtpldt0(W0,W1)) ) ).
% 0.18/0.64
% 0.18/0.64 fof(mSortsB_02,axiom,
% 0.18/0.64 ! [W0,W1] :
% 0.18/0.64 ( ( aNaturalNumber0(W0)
% 0.18/0.64 & aNaturalNumber0(W1) )
% 0.18/0.64 => aNaturalNumber0(sdtasdt0(W0,W1)) ) ).
% 0.18/0.64
% 0.18/0.64 fof(mAddComm,axiom,
% 0.18/0.64 ! [W0,W1] :
% 0.18/0.64 ( ( aNaturalNumber0(W0)
% 0.18/0.64 & aNaturalNumber0(W1) )
% 0.18/0.64 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
% 0.18/0.64
% 0.18/0.64 fof(mAddAsso,axiom,
% 0.18/0.64 ! [W0,W1,W2] :
% 0.18/0.64 ( ( aNaturalNumber0(W0)
% 0.18/0.64 & aNaturalNumber0(W1)
% 0.18/0.64 & aNaturalNumber0(W2) )
% 0.18/0.64 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
% 0.18/0.64
% 0.18/0.64 fof(m_AddZero,axiom,
% 0.18/0.64 ! [W0] :
% 0.18/0.64 ( aNaturalNumber0(W0)
% 0.18/0.64 => ( sdtpldt0(W0,sz00) = W0
% 0.18/0.64 & W0 = sdtpldt0(sz00,W0) ) ) ).
% 0.18/0.64
% 0.18/0.64 fof(mMulComm,axiom,
% 0.18/0.64 ! [W0,W1] :
% 0.18/0.64 ( ( aNaturalNumber0(W0)
% 0.18/0.64 & aNaturalNumber0(W1) )
% 0.18/0.64 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
% 0.18/0.64
% 0.18/0.64 fof(mMulAsso,axiom,
% 0.18/0.64 ! [W0,W1,W2] :
% 0.18/0.64 ( ( aNaturalNumber0(W0)
% 0.18/0.64 & aNaturalNumber0(W1)
% 0.18/0.65 & aNaturalNumber0(W2) )
% 0.18/0.65 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
% 0.18/0.65
% 0.18/0.65 fof(m_MulUnit,axiom,
% 0.18/0.65 ! [W0] :
% 0.18/0.65 ( aNaturalNumber0(W0)
% 0.18/0.65 => ( sdtasdt0(W0,sz10) = W0
% 0.18/0.65 & W0 = sdtasdt0(sz10,W0) ) ) ).
% 0.18/0.65
% 0.18/0.65 fof(m_MulZero,axiom,
% 0.18/0.65 ! [W0] :
% 0.18/0.65 ( aNaturalNumber0(W0)
% 0.18/0.65 => ( sdtasdt0(W0,sz00) = sz00
% 0.18/0.65 & sz00 = sdtasdt0(sz00,W0) ) ) ).
% 0.18/0.65
% 0.18/0.65 fof(mAMDistr,axiom,
% 0.18/0.65 ! [W0,W1,W2] :
% 0.18/0.65 ( ( aNaturalNumber0(W0)
% 0.18/0.65 & aNaturalNumber0(W1)
% 0.18/0.65 & aNaturalNumber0(W2) )
% 0.18/0.65 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
% 0.18/0.65 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
% 0.18/0.65
% 0.18/0.65 fof(mAddCanc,axiom,
% 0.18/0.65 ! [W0,W1,W2] :
% 0.18/0.65 ( ( aNaturalNumber0(W0)
% 0.18/0.65 & aNaturalNumber0(W1)
% 0.18/0.65 & aNaturalNumber0(W2) )
% 0.18/0.65 => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
% 0.18/0.65 | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
% 0.18/0.65 => W1 = W2 ) ) ).
% 0.18/0.65
% 0.18/0.65 fof(mMulCanc,axiom,
% 0.18/0.65 ! [W0] :
% 0.18/0.65 ( aNaturalNumber0(W0)
% 0.18/0.65 => ( W0 != sz00
% 0.18/0.65 => ! [W1,W2] :
% 0.18/0.65 ( ( aNaturalNumber0(W1)
% 0.18/0.65 & aNaturalNumber0(W2) )
% 0.18/0.65 => ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2)
% 0.18/0.65 | sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
% 0.18/0.65 => W1 = W2 ) ) ) ) ).
% 0.18/0.65
% 0.18/0.65 fof(mZeroAdd,axiom,
% 0.18/0.65 ! [W0,W1] :
% 0.18/0.65 ( ( aNaturalNumber0(W0)
% 0.18/0.65 & aNaturalNumber0(W1) )
% 0.18/0.65 => ( sdtpldt0(W0,W1) = sz00
% 0.18/0.65 => ( W0 = sz00
% 0.18/0.65 & W1 = sz00 ) ) ) ).
% 0.18/0.65
% 0.18/0.65 fof(mZeroMul,axiom,
% 0.18/0.65 ! [W0,W1] :
% 0.18/0.65 ( ( aNaturalNumber0(W0)
% 0.18/0.65 & aNaturalNumber0(W1) )
% 0.18/0.65 => ( sdtasdt0(W0,W1) = sz00
% 0.18/0.65 => ( W0 = sz00
% 0.18/0.65 | W1 = sz00 ) ) ) ).
% 0.18/0.65
% 0.18/0.65 fof(mDefLE,definition,
% 0.18/0.65 ! [W0,W1] :
% 0.18/0.65 ( ( aNaturalNumber0(W0)
% 0.18/0.65 & aNaturalNumber0(W1) )
% 0.18/0.65 => ( sdtlseqdt0(W0,W1)
% 0.18/0.65 <=> ? [W2] :
% 0.18/0.65 ( aNaturalNumber0(W2)
% 0.18/0.65 & sdtpldt0(W0,W2) = W1 ) ) ) ).
% 0.18/0.65
% 0.18/0.65 fof(mDefDiff,definition,
% 0.18/0.65 ! [W0,W1] :
% 0.18/0.65 ( ( aNaturalNumber0(W0)
% 0.18/0.65 & aNaturalNumber0(W1) )
% 0.18/0.65 => ( sdtlseqdt0(W0,W1)
% 0.18/0.65 => ! [W2] :
% 0.18/0.65 ( W2 = sdtmndt0(W1,W0)
% 0.18/0.65 <=> ( aNaturalNumber0(W2)
% 0.18/0.65 & sdtpldt0(W0,W2) = W1 ) ) ) ) ).
% 0.18/0.65
% 0.18/0.65 fof(m__718,hypothesis,
% 0.18/0.65 aNaturalNumber0(xm) ).
% 0.18/0.65
% 0.18/0.65 fof(m__,conjecture,
% 0.18/0.65 sdtlseqdt0(xm,xm) ).
% 0.18/0.65
% 0.18/0.65 %------------------------------------------------------------------------------
% 0.18/0.65 %-------------------------------------------
% 0.18/0.65 % Proof found
% 0.18/0.65 % SZS status Theorem for theBenchmark
% 0.18/0.65 % SZS output start Proof
% 0.18/0.65 %ClaNum:46(EqnAxiom:14)
% 0.18/0.65 %VarNum:179(SingletonVarNum:60)
% 0.18/0.65 %MaxLitNum:6
% 0.18/0.65 %MaxfuncDepth:2
% 0.18/0.65 %SharedTerms:8
% 0.18/0.65 %goalClause: 19
% 0.18/0.65 %singleGoalClaCount:1
% 0.18/0.65 [15]P1(a1)
% 0.18/0.65 [16]P1(a6)
% 0.18/0.65 [17]P1(a7)
% 0.18/0.65 [18]~E(a1,a6)
% 0.18/0.65 [19]~P2(a7,a7)
% 0.18/0.65 [20]~P1(x201)+E(f2(a1,x201),a1)
% 0.18/0.65 [21]~P1(x211)+E(f2(x211,a1),a1)
% 0.18/0.65 [22]~P1(x221)+E(f4(a1,x221),x221)
% 0.18/0.65 [23]~P1(x231)+E(f2(a6,x231),x231)
% 0.18/0.65 [24]~P1(x241)+E(f4(x241,a1),x241)
% 0.18/0.65 [25]~P1(x251)+E(f2(x251,a6),x251)
% 0.18/0.65 [29]~P1(x292)+~P1(x291)+E(f4(x291,x292),f4(x292,x291))
% 0.18/0.65 [30]~P1(x302)+~P1(x301)+E(f2(x301,x302),f2(x302,x301))
% 0.18/0.65 [31]~P1(x312)+~P1(x311)+P1(f4(x311,x312))
% 0.18/0.65 [32]~P1(x322)+~P1(x321)+P1(f2(x321,x322))
% 0.18/0.65 [26]~P1(x262)+~P1(x261)+E(x261,a1)+~E(f4(x262,x261),a1)
% 0.18/0.65 [27]~P1(x272)+~P1(x271)+E(x271,a1)+~E(f4(x271,x272),a1)
% 0.18/0.65 [35]~P1(x352)+~P1(x351)+~P2(x351,x352)+P1(f3(x351,x352))
% 0.18/0.65 [41]~P1(x412)+~P1(x411)+~P2(x411,x412)+E(f4(x411,f3(x411,x412)),x412)
% 0.18/0.65 [43]~P1(x433)+~P1(x432)+~P1(x431)+E(f4(f4(x431,x432),x433),f4(x431,f4(x432,x433)))
% 0.18/0.65 [44]~P1(x443)+~P1(x442)+~P1(x441)+E(f2(f2(x441,x442),x443),f2(x441,f2(x442,x443)))
% 0.18/0.65 [45]~P1(x453)+~P1(x452)+~P1(x451)+E(f4(f2(x451,x452),f2(x451,x453)),f2(x451,f4(x452,x453)))
% 0.18/0.65 [46]~P1(x462)+~P1(x463)+~P1(x461)+E(f4(f2(x461,x462),f2(x463,x462)),f2(f4(x461,x463),x462))
% 0.18/0.65 [28]~P1(x281)+~P1(x282)+E(x281,a1)+E(x282,a1)+~E(f2(x282,x281),a1)
% 0.18/0.65 [33]~P1(x332)+~P1(x331)+~P1(x333)+P2(x331,x332)+~E(f4(x331,x333),x332)
% 0.18/0.65 [34]~P1(x343)+~P1(x342)+~P2(x343,x342)+P1(x341)+~E(x341,f5(x342,x343))
% 0.18/0.65 [36]~P1(x362)+~P1(x361)+~P1(x363)+E(x361,x362)+~E(f4(x363,x361),f4(x363,x362))
% 0.18/0.65 [37]~P1(x372)+~P1(x373)+~P1(x371)+E(x371,x372)+~E(f4(x371,x373),f4(x372,x373))
% 0.18/0.65 [40]~P1(x403)+~P1(x401)+~P2(x401,x403)+~E(x402,f5(x403,x401))+E(f4(x401,x402),x403)
% 0.18/0.65 [38]~P1(x382)+~P1(x381)+~P1(x383)+E(x381,x382)+~E(f2(x383,x381),f2(x383,x382))+E(x383,a1)
% 0.18/0.65 [39]~P1(x392)+~P1(x393)+~P1(x391)+E(x391,x392)+~E(f2(x391,x393),f2(x392,x393))+E(x393,a1)
% 0.18/0.65 [42]~P1(x422)+~P1(x423)+~P1(x421)+~P2(x423,x422)+~E(f4(x423,x421),x422)+E(x421,f5(x422,x423))
% 0.18/0.65 %EqnAxiom
% 0.18/0.65 [1]E(x11,x11)
% 0.18/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.65 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.18/0.65 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.18/0.65 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.18/0.65 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.18/0.65 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83))
% 0.18/0.65 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92))
% 0.18/0.65 [10]~E(x101,x102)+E(f5(x101,x103),f5(x102,x103))
% 0.18/0.65 [11]~E(x111,x112)+E(f5(x113,x111),f5(x113,x112))
% 0.18/0.65 [12]~P1(x121)+P1(x122)+~E(x121,x122)
% 0.18/0.65 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133)
% 0.18/0.65 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141)
% 0.18/0.65
% 0.18/0.65 %-------------------------------------------
% 0.18/0.65 cnf(47,plain,
% 0.18/0.65 (~E(a6,a1)),
% 0.18/0.65 inference(scs_inference,[],[18,2])).
% 0.18/0.65 cnf(86,plain,
% 0.18/0.65 (~E(f4(a7,a1),a7)),
% 0.18/0.65 inference(scs_inference,[],[19,15,16,17,18,2,25,24,23,22,21,20,11,10,9,8,7,6,5,4,14,3,32,31,27,26,44,43,46,45,33])).
% 0.18/0.65 cnf(112,plain,
% 0.18/0.65 ($false),
% 0.18/0.65 inference(scs_inference,[],[17,16,86,47,32,31,27,24]),
% 0.18/0.65 ['proof']).
% 0.18/0.65 % SZS output end Proof
% 0.18/0.65 % Total time :0.020000s
%------------------------------------------------------------------------------