TSTP Solution File: COM012+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COM012+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 : n008.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 : Wed Aug 30 18:35:10 EDT 2023
% Result : Theorem 0.20s 0.66s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COM012+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
% 0.13/0.35 % Computer : n008.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 : Tue Aug 29 13:31:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % File :CSE---1.6
% 0.20/0.65 % Problem :theBenchmark
% 0.20/0.65 % Transform :cnf
% 0.20/0.65 % Format :tptp:raw
% 0.20/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.65
% 0.20/0.65 % Result :Theorem 0.020000s
% 0.20/0.65 % Output :CNFRefutation 0.020000s
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 % File : COM012+1 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.65 % Domain : Computing Theory
% 0.20/0.65 % Problem : Newman's lemma on rewriting systems 01, 00 expansion
% 0.20/0.65 % Version : Especial.
% 0.20/0.65 % English :
% 0.20/0.65
% 0.20/0.65 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.20/0.65 % : [PV+07] Paskevich et al. (2007), Reasoning Inside a Formula an
% 0.20/0.65 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.20/0.65 % Source : [Pas08]
% 0.20/0.65 % Names : newman_01.00 [Pas08]
% 0.20/0.65
% 0.20/0.65 % Status : Theorem
% 0.20/0.65 % Rating : 0.14 v8.1.0, 0.06 v7.5.0, 0.09 v7.4.0, 0.13 v7.3.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.08 v6.3.0, 0.00 v6.2.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.04 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.1.0, 0.05 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.1, 0.39 v4.0.0
% 0.20/0.65 % Syntax : Number of formulae : 10 ( 0 unt; 2 def)
% 0.20/0.65 % Number of atoms : 45 ( 1 equ)
% 0.20/0.65 % Maximal formula atoms : 8 ( 4 avg)
% 0.20/0.65 % Number of connectives : 35 ( 0 ~; 2 |; 18 &)
% 0.20/0.65 % ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% 0.20/0.65 % Maximal formula depth : 10 ( 6 avg)
% 0.20/0.65 % Maximal term depth : 1 ( 1 avg)
% 0.20/0.65 % Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% 0.20/0.65 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 0.20/0.65 % Number of variables : 21 ( 20 !; 1 ?)
% 0.20/0.65 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.65
% 0.20/0.65 % Comments : Problem generated by the SAD system [VLP07]
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 fof(mElmSort,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aElement0(W0)
% 0.20/0.65 => $true ) ).
% 0.20/0.65
% 0.20/0.65 fof(mRelSort,axiom,
% 0.20/0.65 ! [W0] :
% 0.20/0.65 ( aRewritingSystem0(W0)
% 0.20/0.65 => $true ) ).
% 0.20/0.65
% 0.20/0.65 fof(mReduct,axiom,
% 0.20/0.65 ! [W0,W1] :
% 0.20/0.65 ( ( aElement0(W0)
% 0.20/0.65 & aRewritingSystem0(W1) )
% 0.20/0.65 => ! [W2] :
% 0.20/0.65 ( aReductOfIn0(W2,W0,W1)
% 0.20/0.65 => aElement0(W2) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mWFOrd,axiom,
% 0.20/0.65 ! [W0,W1] :
% 0.20/0.65 ( ( aElement0(W0)
% 0.20/0.65 & aElement0(W1) )
% 0.20/0.65 => ( iLess0(W0,W1)
% 0.20/0.65 => $true ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mTCbr,axiom,
% 0.20/0.65 ! [W0,W1,W2] :
% 0.20/0.65 ( ( aElement0(W0)
% 0.20/0.65 & aRewritingSystem0(W1)
% 0.20/0.65 & aElement0(W2) )
% 0.20/0.65 => ( sdtmndtplgtdt0(W0,W1,W2)
% 0.20/0.65 => $true ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mTCDef,definition,
% 0.20/0.65 ! [W0,W1,W2] :
% 0.20/0.65 ( ( aElement0(W0)
% 0.20/0.65 & aRewritingSystem0(W1)
% 0.20/0.65 & aElement0(W2) )
% 0.20/0.65 => ( sdtmndtplgtdt0(W0,W1,W2)
% 0.20/0.65 <=> ( aReductOfIn0(W2,W0,W1)
% 0.20/0.65 | ? [W3] :
% 0.20/0.65 ( aElement0(W3)
% 0.20/0.65 & aReductOfIn0(W3,W0,W1)
% 0.20/0.65 & sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mTCTrans,axiom,
% 0.20/0.65 ! [W0,W1,W2,W3] :
% 0.20/0.65 ( ( aElement0(W0)
% 0.20/0.65 & aRewritingSystem0(W1)
% 0.20/0.65 & aElement0(W2)
% 0.20/0.65 & aElement0(W3) )
% 0.20/0.65 => ( ( sdtmndtplgtdt0(W0,W1,W2)
% 0.20/0.65 & sdtmndtplgtdt0(W2,W1,W3) )
% 0.20/0.65 => sdtmndtplgtdt0(W0,W1,W3) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(mTCRDef,definition,
% 0.20/0.65 ! [W0,W1,W2] :
% 0.20/0.65 ( ( aElement0(W0)
% 0.20/0.66 & aRewritingSystem0(W1)
% 0.20/0.66 & aElement0(W2) )
% 0.20/0.66 => ( sdtmndtasgtdt0(W0,W1,W2)
% 0.20/0.66 <=> ( W0 = W2
% 0.20/0.66 | sdtmndtplgtdt0(W0,W1,W2) ) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(m__349,hypothesis,
% 0.20/0.66 ( aElement0(xx)
% 0.20/0.66 & aRewritingSystem0(xR)
% 0.20/0.66 & aElement0(xy)
% 0.20/0.66 & aElement0(xz) ) ).
% 0.20/0.66
% 0.20/0.66 fof(m__,conjecture,
% 0.20/0.66 ( ( sdtmndtasgtdt0(xx,xR,xy)
% 0.20/0.66 & sdtmndtasgtdt0(xy,xR,xz) )
% 0.20/0.66 => sdtmndtasgtdt0(xx,xR,xz) ) ).
% 0.20/0.66
% 0.20/0.66 %------------------------------------------------------------------------------
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % Proof found
% 0.20/0.66 % SZS status Theorem for theBenchmark
% 0.20/0.66 % SZS output start Proof
% 0.20/0.66 %ClaNum:34(EqnAxiom:17)
% 0.20/0.66 %VarNum:109(SingletonVarNum:32)
% 0.20/0.66 %MaxLitNum:7
% 0.20/0.66 %MaxfuncDepth:1
% 0.20/0.66 %SharedTerms:11
% 0.20/0.66 %goalClause: 22 23 24
% 0.20/0.66 %singleGoalClaCount:3
% 0.20/0.66 [18]P1(a1)
% 0.20/0.66 [19]P1(a4)
% 0.20/0.66 [20]P1(a5)
% 0.20/0.66 [21]P2(a2)
% 0.20/0.66 [22]P4(a1,a2,a4)
% 0.20/0.66 [23]P4(a4,a2,a5)
% 0.20/0.66 [24]~P4(a1,a2,a5)
% 0.20/0.66 [26]~P3(x261,x262,x263)+P1(x261)+~P1(x262)+~P2(x263)
% 0.20/0.66 [25]~E(x251,x253)+~P1(x253)+~P1(x251)+~P2(x252)+P4(x251,x252,x253)
% 0.20/0.66 [27]~P1(x271)+~P1(x273)+~P2(x272)+~P3(x273,x271,x272)+P5(x271,x272,x273)
% 0.20/0.66 [28]~P1(x283)+~P1(x281)+~P2(x282)+~P5(x281,x282,x283)+P4(x281,x282,x283)
% 0.20/0.66 [29]~P1(x292)+~P1(x291)+~P2(x293)+~P4(x291,x293,x292)+E(x291,x292)+P5(x291,x293,x292)
% 0.20/0.66 [32]~P1(x321)+~P1(x322)+~P2(x323)+~P5(x322,x323,x321)+P3(x321,x322,x323)+P1(f3(x322,x323,x321))
% 0.20/0.66 [33]~P1(x331)+~P1(x332)+~P2(x333)+~P5(x332,x333,x331)+P3(x331,x332,x333)+P3(f3(x332,x333,x331),x332,x333)
% 0.20/0.66 [34]~P1(x341)+~P1(x342)+~P2(x343)+~P5(x342,x343,x341)+P3(x341,x342,x343)+P5(f3(x342,x343,x341),x343,x341)
% 0.20/0.66 [30]~P1(x303)+~P1(x301)+~P2(x302)+~P3(x304,x301,x302)+~P5(x304,x302,x303)+P5(x301,x302,x303)+~P1(x304)
% 0.20/0.66 [31]~P1(x313)+~P1(x311)+~P2(x312)+~P5(x314,x312,x313)+~P5(x311,x312,x314)+P5(x311,x312,x313)+~P1(x314)
% 0.20/0.66 %EqnAxiom
% 0.20/0.66 [1]E(x11,x11)
% 0.20/0.66 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.66 [4]~E(x41,x42)+E(f3(x41,x43,x44),f3(x42,x43,x44))
% 0.20/0.66 [5]~E(x51,x52)+E(f3(x53,x51,x54),f3(x53,x52,x54))
% 0.20/0.66 [6]~E(x61,x62)+E(f3(x63,x64,x61),f3(x63,x64,x62))
% 0.20/0.66 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.20/0.66 [8]P5(x82,x83,x84)+~E(x81,x82)+~P5(x81,x83,x84)
% 0.20/0.66 [9]P5(x93,x92,x94)+~E(x91,x92)+~P5(x93,x91,x94)
% 0.20/0.66 [10]P5(x103,x104,x102)+~E(x101,x102)+~P5(x103,x104,x101)
% 0.20/0.66 [11]~P2(x111)+P2(x112)+~E(x111,x112)
% 0.20/0.66 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124)
% 0.20/0.66 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134)
% 0.20/0.66 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141)
% 0.20/0.66 [15]P4(x152,x153,x154)+~E(x151,x152)+~P4(x151,x153,x154)
% 0.20/0.66 [16]P4(x163,x162,x164)+~E(x161,x162)+~P4(x163,x161,x164)
% 0.20/0.66 [17]P4(x173,x174,x172)+~E(x171,x172)+~P4(x173,x174,x171)
% 0.20/0.66
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 cnf(36,plain,
% 0.20/0.66 (~E(a4,a1)),
% 0.20/0.66 inference(scs_inference,[],[22,23,24,17,15])).
% 0.20/0.66 cnf(37,plain,
% 0.20/0.66 (P5(a4,a2,a5)),
% 0.20/0.66 inference(scs_inference,[],[22,23,24,19,20,21,17,15,29])).
% 0.20/0.66 cnf(38,plain,
% 0.20/0.66 (~E(a5,a4)),
% 0.20/0.66 inference(scs_inference,[],[22,23,24,19,20,21,17,15,29,2])).
% 0.20/0.66 cnf(40,plain,
% 0.20/0.66 (~P5(a1,a2,a5)),
% 0.20/0.66 inference(scs_inference,[],[22,23,24,18,19,20,21,17,15,29,2,16,28])).
% 0.20/0.66 cnf(42,plain,
% 0.20/0.66 (~P3(a5,a1,a2)),
% 0.20/0.66 inference(scs_inference,[],[22,23,24,18,19,20,21,17,15,29,2,16,28,27])).
% 0.20/0.66 cnf(71,plain,
% 0.20/0.66 (E(a1,a4)),
% 0.20/0.66 inference(scs_inference,[],[19,18,20,21,40,37,42,22,30,31,13,34,33,32,29])).
% 0.20/0.66 cnf(89,plain,
% 0.20/0.66 ($false),
% 0.20/0.66 inference(scs_inference,[],[38,71,36,6,5,4,3,2]),
% 0.20/0.66 ['proof']).
% 0.20/0.66 % SZS output end Proof
% 0.20/0.66 % Total time :0.020000s
%------------------------------------------------------------------------------