%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COM012+1 : 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 : 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 : Mon Jun 24 04:52:44 EDT 2024 % Result : Theorem 0.54s 0.64s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : COM012+1 : TPTP v8.2.0. Released v4.0.0. % 0.12/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 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 Jun 21 00:08:23 EDT 2024 % 0.12/0.33 % CPUTime : % 0.20/0.56 start to proof:theBenchmark % 0.54/0.63 %------------------------------------------- % 0.54/0.63 % File :CSE---1.7 % 0.54/0.63 % Problem :theBenchmark % 0.54/0.63 % Transform :cnf % 0.54/0.63 % Format :tptp:raw % 0.54/0.63 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.63 % 0.54/0.63 % Result :Theorem 0.030000s % 0.54/0.63 % Output :CNFRefutation 0.030000s % 0.54/0.63 %------------------------------------------- % 0.54/0.64 %------------------------------------------------------------------------------ % 0.54/0.64 % File : COM012+1 : TPTP v8.2.0. Released v4.0.0. % 0.54/0.64 % Domain : Computing Theory % 0.54/0.64 % Problem : Newman's lemma on rewriting systems 01, 00 expansion % 0.54/0.64 % Version : Especial. % 0.54/0.64 % English : % 0.54/0.64 % 0.54/0.64 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.54/0.64 % : [PV+07] Paskevich et al. (2007), Reasoning Inside a Formula an % 0.54/0.64 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.54/0.64 % Source : [Pas08] % 0.54/0.64 % Names : newman_01.00 [Pas08] % 0.54/0.64 % 0.54/0.64 % Status : Theorem % 0.54/0.64 % Rating : 0.11 v8.2.0, 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 % 0.54/0.64 % Syntax : Number of formulae : 10 ( 0 unt; 2 def) % 0.54/0.64 % Number of atoms : 45 ( 1 equ) % 0.54/0.64 % Maximal formula atoms : 8 ( 4 avg) % 0.54/0.64 % Number of connectives : 35 ( 0 ~; 2 |; 18 &) % 0.54/0.64 % ( 2 <=>; 13 =>; 0 <=; 0 <~>) % 0.54/0.64 % Maximal formula depth : 10 ( 6 avg) % 0.54/0.64 % Maximal term depth : 1 ( 1 avg) % 0.54/0.64 % Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty) % 0.54/0.64 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty) % 0.54/0.64 % Number of variables : 21 ( 20 !; 1 ?) % 0.54/0.64 % SPC : FOF_THM_RFO_SEQ % 0.54/0.64 % 0.54/0.64 % Comments : Problem generated by the SAD system [VLP07] % 0.54/0.64 %------------------------------------------------------------------------------ % 0.54/0.64 fof(mElmSort,axiom, % 0.54/0.64 ! [W0] : % 0.54/0.64 ( aElement0(W0) % 0.54/0.64 => $true ) ). % 0.54/0.64 % 0.54/0.64 fof(mRelSort,axiom, % 0.54/0.64 ! [W0] : % 0.54/0.64 ( aRewritingSystem0(W0) % 0.54/0.64 => $true ) ). % 0.54/0.64 % 0.54/0.64 fof(mReduct,axiom, % 0.54/0.64 ! [W0,W1] : % 0.54/0.64 ( ( aElement0(W0) % 0.54/0.64 & aRewritingSystem0(W1) ) % 0.54/0.64 => ! [W2] : % 0.54/0.64 ( aReductOfIn0(W2,W0,W1) % 0.54/0.64 => aElement0(W2) ) ) ). % 0.54/0.64 % 0.54/0.64 fof(mWFOrd,axiom, % 0.54/0.64 ! [W0,W1] : % 0.54/0.64 ( ( aElement0(W0) % 0.54/0.64 & aElement0(W1) ) % 0.54/0.64 => ( iLess0(W0,W1) % 0.54/0.64 => $true ) ) ). % 0.54/0.64 % 0.54/0.64 fof(mTCbr,axiom, % 0.54/0.64 ! [W0,W1,W2] : % 0.54/0.64 ( ( aElement0(W0) % 0.54/0.64 & aRewritingSystem0(W1) % 0.54/0.64 & aElement0(W2) ) % 0.54/0.64 => ( sdtmndtplgtdt0(W0,W1,W2) % 0.54/0.64 => $true ) ) ). % 0.54/0.64 % 0.54/0.64 fof(mTCDef,definition, % 0.54/0.64 ! [W0,W1,W2] : % 0.54/0.64 ( ( aElement0(W0) % 0.54/0.64 & aRewritingSystem0(W1) % 0.54/0.64 & aElement0(W2) ) % 0.54/0.64 => ( sdtmndtplgtdt0(W0,W1,W2) % 0.54/0.64 <=> ( aReductOfIn0(W2,W0,W1) % 0.54/0.64 | ? [W3] : % 0.54/0.64 ( aElement0(W3) % 0.54/0.64 & aReductOfIn0(W3,W0,W1) % 0.54/0.64 & sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ). % 0.54/0.64 % 0.54/0.64 fof(mTCTrans,axiom, % 0.54/0.64 ! [W0,W1,W2,W3] : % 0.54/0.64 ( ( aElement0(W0) % 0.54/0.64 & aRewritingSystem0(W1) % 0.54/0.64 & aElement0(W2) % 0.54/0.64 & aElement0(W3) ) % 0.54/0.64 => ( ( sdtmndtplgtdt0(W0,W1,W2) % 0.54/0.64 & sdtmndtplgtdt0(W2,W1,W3) ) % 0.54/0.64 => sdtmndtplgtdt0(W0,W1,W3) ) ) ). % 0.54/0.64 % 0.54/0.64 fof(mTCRDef,definition, % 0.54/0.64 ! [W0,W1,W2] : % 0.54/0.64 ( ( aElement0(W0) % 0.54/0.64 & aRewritingSystem0(W1) % 0.54/0.64 & aElement0(W2) ) % 0.54/0.64 => ( sdtmndtasgtdt0(W0,W1,W2) % 0.54/0.64 <=> ( W0 = W2 % 0.54/0.64 | sdtmndtplgtdt0(W0,W1,W2) ) ) ) ). % 0.54/0.64 % 0.54/0.64 fof(m__349,hypothesis, % 0.54/0.64 ( aElement0(xx) % 0.54/0.64 & aRewritingSystem0(xR) % 0.54/0.64 & aElement0(xy) % 0.54/0.64 & aElement0(xz) ) ). % 0.54/0.64 % 0.54/0.64 fof(m__,conjecture, % 0.54/0.64 ( ( sdtmndtasgtdt0(xx,xR,xy) % 0.54/0.64 & sdtmndtasgtdt0(xy,xR,xz) ) % 0.54/0.64 => sdtmndtasgtdt0(xx,xR,xz) ) ). % 0.54/0.64 % 0.54/0.64 %------------------------------------------------------------------------------ % 0.54/0.64 %------------------------------------------- % 0.54/0.64 % Proof found % 0.54/0.64 % SZS status Theorem for theBenchmark % 0.54/0.64 % SZS output start Proof % 0.54/0.64 %ClaNum:34(EqnAxiom:17) % 0.54/0.64 %VarNum:109(SingletonVarNum:32) % 0.54/0.64 %MaxLitNum:7 % 0.54/0.64 %MaxfuncDepth:1 % 0.54/0.64 %SharedTerms:11 % 0.54/0.64 %goalClause: 22 23 24 % 0.54/0.64 %singleGoalClaCount:3 % 0.54/0.64 [18]P1(a1) % 0.54/0.64 [19]P1(a4) % 0.54/0.64 [20]P1(a5) % 0.54/0.64 [21]P2(a2) % 0.54/0.64 [22]P4(a1,a2,a4) % 0.54/0.64 [23]P4(a4,a2,a5) % 0.54/0.64 [24]~P4(a1,a2,a5) % 0.54/0.64 [26]~P3(x261,x262,x263)+P1(x261)+~P1(x262)+~P2(x263) % 0.54/0.64 [25]~E(x251,x253)+~P1(x253)+~P1(x251)+~P2(x252)+P4(x251,x252,x253) % 0.54/0.64 [27]~P1(x271)+~P1(x273)+~P2(x272)+~P3(x273,x271,x272)+P5(x271,x272,x273) % 0.54/0.64 [28]~P1(x283)+~P1(x281)+~P2(x282)+~P5(x281,x282,x283)+P4(x281,x282,x283) % 0.54/0.64 [29]~P1(x292)+~P1(x291)+~P2(x293)+~P4(x291,x293,x292)+E(x291,x292)+P5(x291,x293,x292) % 0.54/0.64 [32]~P1(x321)+~P1(x322)+~P2(x323)+~P5(x322,x323,x321)+P3(x321,x322,x323)+P1(f3(x322,x323,x321)) % 0.54/0.64 [33]~P1(x331)+~P1(x332)+~P2(x333)+~P5(x332,x333,x331)+P3(x331,x332,x333)+P3(f3(x332,x333,x331),x332,x333) % 0.54/0.64 [34]~P1(x341)+~P1(x342)+~P2(x343)+~P5(x342,x343,x341)+P3(x341,x342,x343)+P5(f3(x342,x343,x341),x343,x341) % 0.54/0.64 [30]~P1(x303)+~P1(x301)+~P2(x302)+~P3(x304,x301,x302)+~P5(x304,x302,x303)+P5(x301,x302,x303)+~P1(x304) % 0.54/0.64 [31]~P1(x313)+~P1(x311)+~P2(x312)+~P5(x314,x312,x313)+~P5(x311,x312,x314)+P5(x311,x312,x313)+~P1(x314) % 0.54/0.64 %EqnAxiom % 0.54/0.64 [1]E(x11,x11) % 0.54/0.64 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.64 [4]~E(x41,x42)+E(f3(x41,x43,x44),f3(x42,x43,x44)) % 0.54/0.64 [5]~E(x51,x52)+E(f3(x53,x51,x54),f3(x53,x52,x54)) % 0.54/0.64 [6]~E(x61,x62)+E(f3(x63,x64,x61),f3(x63,x64,x62)) % 0.54/0.64 [7]~P1(x71)+P1(x72)+~E(x71,x72) % 0.54/0.64 [8]P5(x82,x83,x84)+~E(x81,x82)+~P5(x81,x83,x84) % 0.54/0.64 [9]P5(x93,x92,x94)+~E(x91,x92)+~P5(x93,x91,x94) % 0.54/0.64 [10]P5(x103,x104,x102)+~E(x101,x102)+~P5(x103,x104,x101) % 0.54/0.64 [11]~P2(x111)+P2(x112)+~E(x111,x112) % 0.54/0.64 [12]P3(x122,x123,x124)+~E(x121,x122)+~P3(x121,x123,x124) % 0.54/0.64 [13]P3(x133,x132,x134)+~E(x131,x132)+~P3(x133,x131,x134) % 0.54/0.64 [14]P3(x143,x144,x142)+~E(x141,x142)+~P3(x143,x144,x141) % 0.54/0.64 [15]P4(x152,x153,x154)+~E(x151,x152)+~P4(x151,x153,x154) % 0.54/0.64 [16]P4(x163,x162,x164)+~E(x161,x162)+~P4(x163,x161,x164) % 0.54/0.65 [17]P4(x173,x174,x172)+~E(x171,x172)+~P4(x173,x174,x171) % 0.54/0.65 % 0.54/0.65 %------------------------------------------- % 0.54/0.65 cnf(35,plain, % 0.54/0.65 (~P1(x351)+~P1(x351)+P4(x351,x352,x351)+~P2(x352)), % 0.54/0.65 inference(equality_inference,[],[25])). % 0.54/0.65 cnf(36,plain, % 0.54/0.65 (~E(a4,a1)), % 0.54/0.65 inference(scs_inference,[],[23,24,15])). % 0.54/0.65 cnf(38,plain, % 0.54/0.65 (P4(a1,a2,a1)), % 0.54/0.65 inference(scs_inference,[],[22,23,24,18,21,15,17,35])). % 0.54/0.65 cnf(40,plain, % 0.54/0.65 (P5(a4,a2,a5)), % 0.54/0.65 inference(scs_inference,[],[22,23,24,18,19,20,21,15,17,35,29])). % 0.54/0.65 cnf(58,plain, % 0.54/0.65 (E(a1,a4)+P5(a1,a2,a4)), % 0.54/0.65 inference(scs_inference,[],[22,23,24,38,18,20,19,21,17,15,16,25,29])). % 0.54/0.65 cnf(88,plain, % 0.54/0.65 (P5(a1,a2,a4)), % 0.54/0.65 inference(scs_inference,[],[36,2,58])). % 0.54/0.65 cnf(98,plain, % 0.54/0.65 (P5(a1,a2,a5)), % 0.54/0.65 inference(scs_inference,[],[40,88,21,18,20,19,31])). % 0.54/0.65 cnf(109,plain, % 0.54/0.65 ($false), % 0.54/0.65 inference(scs_inference,[],[24,21,18,20,98,28]), % 0.54/0.65 ['proof']). % 0.54/0.65 % SZS output end Proof % 0.54/0.65 % Total time :0.030000s %------------------------------------------------------------------------------