%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COM012+3 : TPTP v8.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 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 : Mon Jun 24 04:52:44 EDT 2024 % Result : Theorem 0.55s 0.65s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.11 % Problem : COM012+3 : TPTP v8.2.0. Released v4.0.0. % 0.02/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n020.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 Jun 21 00:07:08 EDT 2024 % 0.12/0.33 % CPUTime : % 0.51/0.58 start to proof:theBenchmark % 0.55/0.64 %------------------------------------------- % 0.55/0.64 % File :CSE---1.7 % 0.55/0.64 % Problem :theBenchmark % 0.55/0.64 % Transform :cnf % 0.55/0.64 % Format :tptp:raw % 0.55/0.64 % Command :java -jar mcs_scs.jar %d %s % 0.55/0.64 % 0.55/0.64 % Result :Theorem 0.020000s % 0.55/0.64 % Output :CNFRefutation 0.020000s % 0.55/0.64 %------------------------------------------- % 0.55/0.64 %------------------------------------------------------------------------------ % 0.55/0.64 % File : COM012+3 : TPTP v8.2.0. Released v4.0.0. % 0.55/0.64 % Domain : Computing Theory % 0.55/0.64 % Problem : Newman's lemma on rewriting systems 01, 02 expansion % 0.55/0.64 % Version : Especial. % 0.55/0.64 % English : % 0.55/0.64 % 0.55/0.64 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.55/0.64 % : [PV+07] Paskevich et al. (2007), Reasoning Inside a Formula an % 0.55/0.64 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.55/0.64 % Source : [Pas08] % 0.55/0.64 % Names : newman_01.02 [Pas08] % 0.55/0.64 % 0.55/0.64 % Status : Theorem % 0.55/0.64 % 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 % 0.55/0.64 % Syntax : Number of formulae : 10 ( 0 unt; 2 def) % 0.55/0.64 % Number of atoms : 63 ( 4 equ) % 0.55/0.64 % Maximal formula atoms : 21 ( 6 avg) % 0.55/0.64 % Number of connectives : 53 ( 0 ~; 10 |; 28 &) % 0.55/0.64 % ( 2 <=>; 13 =>; 0 <=; 0 <~>) % 0.55/0.64 % Maximal formula depth : 11 ( 7 avg) % 0.55/0.64 % Maximal term depth : 1 ( 1 avg) % 0.55/0.64 % Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty) % 0.55/0.64 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty) % 0.55/0.64 % Number of variables : 24 ( 20 !; 4 ?) % 0.55/0.64 % SPC : FOF_THM_RFO_SEQ % 0.55/0.64 % 0.55/0.64 % Comments : Problem generated by the SAD system [VLP07] % 0.55/0.64 %------------------------------------------------------------------------------ % 0.55/0.64 fof(mElmSort,axiom, % 0.55/0.64 ! [W0] : % 0.55/0.64 ( aElement0(W0) % 0.55/0.64 => $true ) ). % 0.55/0.64 % 0.55/0.64 fof(mRelSort,axiom, % 0.55/0.64 ! [W0] : % 0.55/0.64 ( aRewritingSystem0(W0) % 0.55/0.64 => $true ) ). % 0.55/0.64 % 0.55/0.64 fof(mReduct,axiom, % 0.55/0.64 ! [W0,W1] : % 0.55/0.64 ( ( aElement0(W0) % 0.55/0.64 & aRewritingSystem0(W1) ) % 0.55/0.64 => ! [W2] : % 0.55/0.64 ( aReductOfIn0(W2,W0,W1) % 0.55/0.64 => aElement0(W2) ) ) ). % 0.55/0.64 % 0.55/0.64 fof(mWFOrd,axiom, % 0.55/0.64 ! [W0,W1] : % 0.55/0.64 ( ( aElement0(W0) % 0.55/0.64 & aElement0(W1) ) % 0.55/0.64 => ( iLess0(W0,W1) % 0.55/0.64 => $true ) ) ). % 0.55/0.64 % 0.55/0.64 fof(mTCbr,axiom, % 0.55/0.64 ! [W0,W1,W2] : % 0.55/0.65 ( ( aElement0(W0) % 0.55/0.65 & aRewritingSystem0(W1) % 0.55/0.65 & aElement0(W2) ) % 0.55/0.65 => ( sdtmndtplgtdt0(W0,W1,W2) % 0.55/0.65 => $true ) ) ). % 0.55/0.65 % 0.55/0.65 fof(mTCDef,definition, % 0.55/0.65 ! [W0,W1,W2] : % 0.55/0.65 ( ( aElement0(W0) % 0.55/0.65 & aRewritingSystem0(W1) % 0.55/0.65 & aElement0(W2) ) % 0.55/0.65 => ( sdtmndtplgtdt0(W0,W1,W2) % 0.55/0.65 <=> ( aReductOfIn0(W2,W0,W1) % 0.55/0.65 | ? [W3] : % 0.55/0.65 ( aElement0(W3) % 0.55/0.65 & aReductOfIn0(W3,W0,W1) % 0.55/0.65 & sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(mTCTrans,axiom, % 0.55/0.65 ! [W0,W1,W2,W3] : % 0.55/0.65 ( ( aElement0(W0) % 0.55/0.65 & aRewritingSystem0(W1) % 0.55/0.65 & aElement0(W2) % 0.55/0.65 & aElement0(W3) ) % 0.55/0.65 => ( ( sdtmndtplgtdt0(W0,W1,W2) % 0.55/0.65 & sdtmndtplgtdt0(W2,W1,W3) ) % 0.55/0.65 => sdtmndtplgtdt0(W0,W1,W3) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(mTCRDef,definition, % 0.55/0.65 ! [W0,W1,W2] : % 0.55/0.65 ( ( aElement0(W0) % 0.55/0.65 & aRewritingSystem0(W1) % 0.55/0.65 & aElement0(W2) ) % 0.55/0.65 => ( sdtmndtasgtdt0(W0,W1,W2) % 0.55/0.65 <=> ( W0 = W2 % 0.55/0.65 | sdtmndtplgtdt0(W0,W1,W2) ) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(m__349,hypothesis, % 0.55/0.65 ( aElement0(xx) % 0.55/0.65 & aRewritingSystem0(xR) % 0.55/0.65 & aElement0(xy) % 0.55/0.65 & aElement0(xz) ) ). % 0.55/0.65 % 0.55/0.65 fof(m__,conjecture, % 0.55/0.65 ( ( ( xx = xy % 0.55/0.65 | ( ( aReductOfIn0(xy,xx,xR) % 0.55/0.65 | ? [W0] : % 0.55/0.65 ( aElement0(W0) % 0.55/0.65 & aReductOfIn0(W0,xx,xR) % 0.55/0.65 & sdtmndtplgtdt0(W0,xR,xy) ) ) % 0.55/0.65 & sdtmndtplgtdt0(xx,xR,xy) ) ) % 0.55/0.65 & sdtmndtasgtdt0(xx,xR,xy) % 0.55/0.65 & ( xy = xz % 0.55/0.65 | ( ( aReductOfIn0(xz,xy,xR) % 0.55/0.65 | ? [W0] : % 0.55/0.65 ( aElement0(W0) % 0.55/0.65 & aReductOfIn0(W0,xy,xR) % 0.55/0.65 & sdtmndtplgtdt0(W0,xR,xz) ) ) % 0.55/0.65 & sdtmndtplgtdt0(xy,xR,xz) ) ) % 0.55/0.65 & sdtmndtasgtdt0(xy,xR,xz) ) % 0.55/0.65 => ( xx = xz % 0.55/0.65 | aReductOfIn0(xz,xx,xR) % 0.55/0.65 | ? [W0] : % 0.55/0.65 ( aElement0(W0) % 0.55/0.65 & aReductOfIn0(W0,xx,xR) % 0.55/0.65 & sdtmndtplgtdt0(W0,xR,xz) ) % 0.55/0.65 | sdtmndtplgtdt0(xx,xR,xz) % 0.55/0.65 | sdtmndtasgtdt0(xx,xR,xz) ) ) ). % 0.55/0.65 % 0.55/0.65 %------------------------------------------------------------------------------ % 0.55/0.65 %------------------------------------------- % 0.55/0.65 % Proof found % 0.55/0.65 % SZS status Theorem for theBenchmark % 0.55/0.65 % SZS output start Proof % 0.55/0.65 %ClaNum:46(EqnAxiom:17) % 0.55/0.65 %VarNum:112(SingletonVarNum:33) % 0.55/0.65 %MaxLitNum:7 % 0.55/0.65 %MaxfuncDepth:1 % 0.55/0.65 %SharedTerms:28 % 0.55/0.65 %goalClause: 22 23 24 25 26 27 28 29 30 31 33 34 35 36 41 % 0.55/0.65 %singleGoalClaCount:6 % 0.55/0.65 [18]P1(a1) % 0.55/0.65 [19]P1(a6) % 0.55/0.65 [20]P1(a7) % 0.55/0.65 [21]P2(a2) % 0.55/0.65 [22]P4(a1,a2,a6) % 0.55/0.65 [23]P4(a6,a2,a7) % 0.55/0.65 [24]~E(a1,a7) % 0.55/0.65 [25]~P3(a7,a1,a2) % 0.55/0.65 [26]~P5(a1,a2,a7) % 0.55/0.65 [27]~P4(a1,a2,a7) % 0.55/0.65 [28]E(a1,a6)+P5(a1,a2,a6) % 0.55/0.65 [29]E(a7,a6)+P5(a6,a2,a7) % 0.55/0.65 [30]E(a1,a6)+P1(a3)+P3(a6,a1,a2) % 0.55/0.65 [31]E(a7,a6)+P1(a5)+P3(a7,a6,a2) % 0.55/0.65 [33]E(a1,a6)+P3(a6,a1,a2)+P3(a3,a1,a2) % 0.55/0.65 [34]P3(a6,a1,a2)+E(a1,a6)+P5(a3,a2,a6) % 0.55/0.65 [35]E(a7,a6)+P3(a7,a6,a2)+P3(a5,a6,a2) % 0.55/0.65 [36]P3(a7,a6,a2)+E(a7,a6)+P5(a5,a2,a7) % 0.55/0.65 [41]~P1(x411)+~P3(x411,a1,a2)+~P5(x411,a2,a7) % 0.55/0.65 [37]~P3(x371,x372,x373)+P1(x371)+~P1(x372)+~P2(x373) % 0.55/0.65 [32]~E(x321,x323)+~P1(x323)+~P1(x321)+~P2(x322)+P4(x321,x322,x323) % 0.55/0.65 [38]~P1(x381)+~P1(x383)+~P2(x382)+~P3(x383,x381,x382)+P5(x381,x382,x383) % 0.55/0.65 [39]~P1(x393)+~P1(x391)+~P2(x392)+~P5(x391,x392,x393)+P4(x391,x392,x393) % 0.55/0.65 [40]~P1(x402)+~P1(x401)+~P2(x403)+~P4(x401,x403,x402)+E(x401,x402)+P5(x401,x403,x402) % 0.55/0.65 [44]~P1(x441)+~P1(x442)+~P2(x443)+~P5(x442,x443,x441)+P3(x441,x442,x443)+P1(f4(x442,x443,x441)) % 0.55/0.65 [45]~P1(x451)+~P1(x452)+~P2(x453)+~P5(x452,x453,x451)+P3(x451,x452,x453)+P3(f4(x452,x453,x451),x452,x453) % 0.55/0.65 [46]~P1(x461)+~P1(x462)+~P2(x463)+~P5(x462,x463,x461)+P3(x461,x462,x463)+P5(f4(x462,x463,x461),x463,x461) % 0.55/0.65 [42]~P1(x423)+~P1(x421)+~P2(x422)+~P3(x424,x421,x422)+~P5(x424,x422,x423)+P5(x421,x422,x423)+~P1(x424) % 0.55/0.65 [43]~P1(x433)+~P1(x431)+~P2(x432)+~P5(x434,x432,x433)+~P5(x431,x432,x434)+P5(x431,x432,x433)+~P1(x434) % 0.55/0.65 %EqnAxiom % 0.55/0.65 [1]E(x11,x11) % 0.55/0.65 [2]E(x22,x21)+~E(x21,x22) % 0.55/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.55/0.65 [4]~E(x41,x42)+E(f4(x41,x43,x44),f4(x42,x43,x44)) % 0.55/0.65 [5]~E(x51,x52)+E(f4(x53,x51,x54),f4(x53,x52,x54)) % 0.55/0.65 [6]~E(x61,x62)+E(f4(x63,x64,x61),f4(x63,x64,x62)) % 0.55/0.65 [7]~P1(x71)+P1(x72)+~E(x71,x72) % 0.55/0.65 [8]P5(x82,x83,x84)+~E(x81,x82)+~P5(x81,x83,x84) % 0.55/0.65 [9]P5(x93,x92,x94)+~E(x91,x92)+~P5(x93,x91,x94) % 0.55/0.65 [10]P5(x103,x104,x102)+~E(x101,x102)+~P5(x103,x104,x101) % 0.55/0.65 [11]~P2(x111)+P2(x112)+~E(x111,x112) % 0.55/0.65 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124) % 0.55/0.65 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134) % 0.55/0.65 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141) % 0.55/0.65 [15]P4(x152,x153,x154)+~E(x151,x152)+~P4(x151,x153,x154) % 0.55/0.65 [16]P4(x163,x162,x164)+~E(x161,x162)+~P4(x163,x161,x164) % 0.55/0.65 [17]P4(x173,x174,x172)+~E(x171,x172)+~P4(x173,x174,x171) % 0.55/0.65 % 0.55/0.65 %------------------------------------------- % 0.55/0.65 cnf(47,plain, % 0.55/0.65 (~P1(x471)+~P1(x471)+P4(x471,x472,x471)+~P2(x472)), % 0.55/0.65 inference(equality_inference,[],[32])). % 0.55/0.65 cnf(48,plain, % 0.55/0.65 (~E(a6,a1)), % 0.55/0.65 inference(scs_inference,[],[23,27,15])). % 0.55/0.65 cnf(52,plain, % 0.55/0.65 (P5(a6,a2,a7)), % 0.55/0.65 inference(scs_inference,[],[22,23,27,18,19,20,21,15,17,47,40])). % 0.55/0.65 cnf(116,plain, % 0.55/0.65 (E(a1,a6)), % 0.55/0.65 inference(scs_inference,[],[26,19,20,52,18,21,28,43])). % 0.55/0.65 cnf(118,plain, % 0.55/0.65 ($false), % 0.55/0.65 inference(scs_inference,[],[116,48,2]), % 0.55/0.65 ['proof']). % 0.55/0.65 % SZS output end Proof % 0.55/0.65 % Total time :0.020000s %------------------------------------------------------------------------------