TSTP Solution File: COM012+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n020.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 0.57s 0.68s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 13:28:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.57/0.67 %-------------------------------------------
% 0.57/0.67 % File :CSE---1.6
% 0.57/0.67 % Problem :theBenchmark
% 0.57/0.67 % Transform :cnf
% 0.57/0.67 % Format :tptp:raw
% 0.57/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.57/0.67
% 0.57/0.67 % Result :Theorem 0.040000s
% 0.57/0.67 % Output :CNFRefutation 0.040000s
% 0.57/0.67 %-------------------------------------------
% 0.57/0.68 %------------------------------------------------------------------------------
% 0.57/0.68 % File : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% 0.57/0.68 % Domain : Computing Theory
% 0.57/0.68 % Problem : Newman's lemma on rewriting systems 01, 02 expansion
% 0.57/0.68 % Version : Especial.
% 0.57/0.68 % English :
% 0.57/0.68
% 0.57/0.68 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% 0.57/0.68 % : [PV+07] Paskevich et al. (2007), Reasoning Inside a Formula an
% 0.57/0.68 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% 0.57/0.68 % Source : [Pas08]
% 0.57/0.68 % Names : newman_01.02 [Pas08]
% 0.57/0.68
% 0.57/0.68 % Status : Theorem
% 0.57/0.68 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.04 v6.3.0, 0.00 v6.2.0, 0.04 v6.1.0, 0.07 v6.0.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.00 v5.1.0, 0.10 v5.0.0, 0.17 v4.1.0, 0.22 v4.0.1, 0.48 v4.0.0
% 0.57/0.68 % Syntax : Number of formulae : 10 ( 0 unt; 2 def)
% 0.57/0.68 % Number of atoms : 63 ( 4 equ)
% 0.57/0.68 % Maximal formula atoms : 21 ( 6 avg)
% 0.57/0.68 % Number of connectives : 53 ( 0 ~; 10 |; 28 &)
% 0.57/0.68 % ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% 0.57/0.68 % Maximal formula depth : 11 ( 7 avg)
% 0.57/0.68 % Maximal term depth : 1 ( 1 avg)
% 0.57/0.68 % Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% 0.57/0.68 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 0.57/0.68 % Number of variables : 24 ( 20 !; 4 ?)
% 0.57/0.68 % SPC : FOF_THM_RFO_SEQ
% 0.57/0.68
% 0.57/0.68 % Comments : Problem generated by the SAD system [VLP07]
% 0.57/0.68 %------------------------------------------------------------------------------
% 0.57/0.68 fof(mElmSort,axiom,
% 0.57/0.68 ! [W0] :
% 0.57/0.68 ( aElement0(W0)
% 0.57/0.68 => $true ) ).
% 0.57/0.68
% 0.57/0.68 fof(mRelSort,axiom,
% 0.57/0.68 ! [W0] :
% 0.57/0.68 ( aRewritingSystem0(W0)
% 0.57/0.68 => $true ) ).
% 0.57/0.68
% 0.57/0.68 fof(mReduct,axiom,
% 0.57/0.68 ! [W0,W1] :
% 0.57/0.68 ( ( aElement0(W0)
% 0.57/0.68 & aRewritingSystem0(W1) )
% 0.57/0.68 => ! [W2] :
% 0.57/0.68 ( aReductOfIn0(W2,W0,W1)
% 0.57/0.68 => aElement0(W2) ) ) ).
% 0.57/0.68
% 0.57/0.68 fof(mWFOrd,axiom,
% 0.57/0.68 ! [W0,W1] :
% 0.57/0.68 ( ( aElement0(W0)
% 0.57/0.68 & aElement0(W1) )
% 0.57/0.68 => ( iLess0(W0,W1)
% 0.57/0.68 => $true ) ) ).
% 0.57/0.68
% 0.57/0.68 fof(mTCbr,axiom,
% 0.57/0.68 ! [W0,W1,W2] :
% 0.57/0.68 ( ( aElement0(W0)
% 0.57/0.68 & aRewritingSystem0(W1)
% 0.57/0.68 & aElement0(W2) )
% 0.57/0.68 => ( sdtmndtplgtdt0(W0,W1,W2)
% 0.57/0.68 => $true ) ) ).
% 0.57/0.68
% 0.57/0.68 fof(mTCDef,definition,
% 0.57/0.68 ! [W0,W1,W2] :
% 0.57/0.68 ( ( aElement0(W0)
% 0.57/0.68 & aRewritingSystem0(W1)
% 0.57/0.68 & aElement0(W2) )
% 0.57/0.68 => ( sdtmndtplgtdt0(W0,W1,W2)
% 0.57/0.68 <=> ( aReductOfIn0(W2,W0,W1)
% 0.57/0.68 | ? [W3] :
% 0.57/0.68 ( aElement0(W3)
% 0.57/0.68 & aReductOfIn0(W3,W0,W1)
% 0.57/0.68 & sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ).
% 0.57/0.68
% 0.57/0.68 fof(mTCTrans,axiom,
% 0.57/0.68 ! [W0,W1,W2,W3] :
% 0.57/0.68 ( ( aElement0(W0)
% 0.57/0.68 & aRewritingSystem0(W1)
% 0.57/0.68 & aElement0(W2)
% 0.57/0.68 & aElement0(W3) )
% 0.57/0.68 => ( ( sdtmndtplgtdt0(W0,W1,W2)
% 0.57/0.68 & sdtmndtplgtdt0(W2,W1,W3) )
% 0.57/0.68 => sdtmndtplgtdt0(W0,W1,W3) ) ) ).
% 0.57/0.68
% 0.57/0.68 fof(mTCRDef,definition,
% 0.57/0.68 ! [W0,W1,W2] :
% 0.57/0.68 ( ( aElement0(W0)
% 0.57/0.68 & aRewritingSystem0(W1)
% 0.57/0.68 & aElement0(W2) )
% 0.57/0.68 => ( sdtmndtasgtdt0(W0,W1,W2)
% 0.57/0.68 <=> ( W0 = W2
% 0.57/0.68 | sdtmndtplgtdt0(W0,W1,W2) ) ) ) ).
% 0.57/0.68
% 0.57/0.68 fof(m__349,hypothesis,
% 0.57/0.68 ( aElement0(xx)
% 0.57/0.68 & aRewritingSystem0(xR)
% 0.57/0.68 & aElement0(xy)
% 0.57/0.68 & aElement0(xz) ) ).
% 0.57/0.68
% 0.57/0.68 fof(m__,conjecture,
% 0.57/0.68 ( ( ( xx = xy
% 0.57/0.68 | ( ( aReductOfIn0(xy,xx,xR)
% 0.57/0.68 | ? [W0] :
% 0.57/0.68 ( aElement0(W0)
% 0.57/0.68 & aReductOfIn0(W0,xx,xR)
% 0.57/0.68 & sdtmndtplgtdt0(W0,xR,xy) ) )
% 0.57/0.68 & sdtmndtplgtdt0(xx,xR,xy) ) )
% 0.57/0.68 & sdtmndtasgtdt0(xx,xR,xy)
% 0.57/0.68 & ( xy = xz
% 0.57/0.68 | ( ( aReductOfIn0(xz,xy,xR)
% 0.57/0.68 | ? [W0] :
% 0.57/0.68 ( aElement0(W0)
% 0.57/0.68 & aReductOfIn0(W0,xy,xR)
% 0.57/0.68 & sdtmndtplgtdt0(W0,xR,xz) ) )
% 0.57/0.68 & sdtmndtplgtdt0(xy,xR,xz) ) )
% 0.57/0.68 & sdtmndtasgtdt0(xy,xR,xz) )
% 0.57/0.68 => ( xx = xz
% 0.57/0.68 | aReductOfIn0(xz,xx,xR)
% 0.57/0.68 | ? [W0] :
% 0.57/0.68 ( aElement0(W0)
% 0.57/0.68 & aReductOfIn0(W0,xx,xR)
% 0.57/0.68 & sdtmndtplgtdt0(W0,xR,xz) )
% 0.57/0.68 | sdtmndtplgtdt0(xx,xR,xz)
% 0.57/0.68 | sdtmndtasgtdt0(xx,xR,xz) ) ) ).
% 0.57/0.68
% 0.57/0.68 %------------------------------------------------------------------------------
% 0.57/0.68 %-------------------------------------------
% 0.57/0.68 % Proof found
% 0.57/0.68 % SZS status Theorem for theBenchmark
% 0.57/0.68 % SZS output start Proof
% 0.57/0.68 %ClaNum:46(EqnAxiom:17)
% 0.57/0.68 %VarNum:112(SingletonVarNum:33)
% 0.57/0.68 %MaxLitNum:7
% 0.57/0.68 %MaxfuncDepth:1
% 0.57/0.68 %SharedTerms:28
% 0.57/0.68 %goalClause: 22 23 24 25 26 27 28 29 30 31 33 34 35 36 41
% 0.57/0.68 %singleGoalClaCount:6
% 0.57/0.68 [18]P1(a1)
% 0.57/0.68 [19]P1(a6)
% 0.57/0.68 [20]P1(a7)
% 0.57/0.68 [21]P2(a2)
% 0.57/0.68 [22]P4(a1,a2,a6)
% 0.57/0.68 [23]P4(a6,a2,a7)
% 0.57/0.68 [24]~E(a1,a7)
% 0.57/0.68 [25]~P3(a7,a1,a2)
% 0.57/0.68 [26]~P5(a1,a2,a7)
% 0.57/0.68 [27]~P4(a1,a2,a7)
% 0.57/0.68 [28]E(a1,a6)+P5(a1,a2,a6)
% 0.57/0.68 [29]E(a7,a6)+P5(a6,a2,a7)
% 0.57/0.68 [30]E(a1,a6)+P1(a3)+P3(a6,a1,a2)
% 0.57/0.68 [31]E(a7,a6)+P1(a5)+P3(a7,a6,a2)
% 0.57/0.68 [33]E(a1,a6)+P3(a6,a1,a2)+P3(a3,a1,a2)
% 0.57/0.68 [34]P3(a6,a1,a2)+E(a1,a6)+P5(a3,a2,a6)
% 0.57/0.68 [35]E(a7,a6)+P3(a7,a6,a2)+P3(a5,a6,a2)
% 0.57/0.68 [36]P3(a7,a6,a2)+E(a7,a6)+P5(a5,a2,a7)
% 0.57/0.68 [41]~P1(x411)+~P3(x411,a1,a2)+~P5(x411,a2,a7)
% 0.57/0.68 [37]~P3(x371,x372,x373)+P1(x371)+~P1(x372)+~P2(x373)
% 0.57/0.68 [32]~E(x321,x323)+~P1(x323)+~P1(x321)+~P2(x322)+P4(x321,x322,x323)
% 0.57/0.68 [38]~P1(x381)+~P1(x383)+~P2(x382)+~P3(x383,x381,x382)+P5(x381,x382,x383)
% 0.57/0.68 [39]~P1(x393)+~P1(x391)+~P2(x392)+~P5(x391,x392,x393)+P4(x391,x392,x393)
% 0.57/0.68 [40]~P1(x402)+~P1(x401)+~P2(x403)+~P4(x401,x403,x402)+E(x401,x402)+P5(x401,x403,x402)
% 0.57/0.68 [44]~P1(x441)+~P1(x442)+~P2(x443)+~P5(x442,x443,x441)+P3(x441,x442,x443)+P1(f4(x442,x443,x441))
% 0.57/0.68 [45]~P1(x451)+~P1(x452)+~P2(x453)+~P5(x452,x453,x451)+P3(x451,x452,x453)+P3(f4(x452,x453,x451),x452,x453)
% 0.57/0.68 [46]~P1(x461)+~P1(x462)+~P2(x463)+~P5(x462,x463,x461)+P3(x461,x462,x463)+P5(f4(x462,x463,x461),x463,x461)
% 0.57/0.68 [42]~P1(x423)+~P1(x421)+~P2(x422)+~P3(x424,x421,x422)+~P5(x424,x422,x423)+P5(x421,x422,x423)+~P1(x424)
% 0.57/0.68 [43]~P1(x433)+~P1(x431)+~P2(x432)+~P5(x434,x432,x433)+~P5(x431,x432,x434)+P5(x431,x432,x433)+~P1(x434)
% 0.57/0.68 %EqnAxiom
% 0.57/0.68 [1]E(x11,x11)
% 0.57/0.68 [2]E(x22,x21)+~E(x21,x22)
% 0.57/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.57/0.68 [4]~E(x41,x42)+E(f4(x41,x43,x44),f4(x42,x43,x44))
% 0.57/0.68 [5]~E(x51,x52)+E(f4(x53,x51,x54),f4(x53,x52,x54))
% 0.57/0.68 [6]~E(x61,x62)+E(f4(x63,x64,x61),f4(x63,x64,x62))
% 0.57/0.68 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.57/0.68 [8]P5(x82,x83,x84)+~E(x81,x82)+~P5(x81,x83,x84)
% 0.57/0.68 [9]P5(x93,x92,x94)+~E(x91,x92)+~P5(x93,x91,x94)
% 0.57/0.68 [10]P5(x103,x104,x102)+~E(x101,x102)+~P5(x103,x104,x101)
% 0.57/0.68 [11]~P2(x111)+P2(x112)+~E(x111,x112)
% 0.57/0.68 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124)
% 0.57/0.68 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134)
% 0.57/0.68 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141)
% 0.57/0.68 [15]P4(x152,x153,x154)+~E(x151,x152)+~P4(x151,x153,x154)
% 0.57/0.68 [16]P4(x163,x162,x164)+~E(x161,x162)+~P4(x163,x161,x164)
% 0.57/0.68 [17]P4(x173,x174,x172)+~E(x171,x172)+~P4(x173,x174,x171)
% 0.57/0.68
% 0.57/0.68 %-------------------------------------------
% 0.57/0.68 cnf(48,plain,
% 0.57/0.68 (~E(a6,a1)),
% 0.57/0.68 inference(scs_inference,[],[22,23,27,17,15])).
% 0.57/0.68 cnf(49,plain,
% 0.57/0.68 (P5(a6,a2,a7)),
% 0.57/0.68 inference(scs_inference,[],[22,23,27,19,20,21,17,15,40])).
% 0.57/0.68 cnf(87,plain,
% 0.57/0.68 (E(a1,a6)),
% 0.57/0.68 inference(scs_inference,[],[25,26,18,20,19,21,49,13,43,28])).
% 0.57/0.68 cnf(145,plain,
% 0.57/0.68 ($false),
% 0.57/0.68 inference(scs_inference,[],[48,87,2]),
% 0.57/0.68 ['proof']).
% 0.57/0.68 % SZS output end Proof
% 0.57/0.68 % Total time :0.040000s
%------------------------------------------------------------------------------