%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COM018+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 : n024.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 04:52:46 EDT 2024 % Result : Theorem 0.56s 0.62s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : COM018+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 : n024.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 : Thu Jun 20 23:37:38 EDT 2024 % 0.12/0.33 % CPUTime : % 0.20/0.56 start to proof:theBenchmark % 0.56/0.61 %------------------------------------------- % 0.56/0.61 % File :CSE---1.7 % 0.56/0.61 % Problem :theBenchmark % 0.56/0.61 % Transform :cnf % 0.56/0.61 % Format :tptp:raw % 0.56/0.61 % Command :java -jar mcs_scs.jar %d %s % 0.56/0.61 % 0.56/0.61 % Result :Theorem 0.000000s % 0.56/0.61 % Output :CNFRefutation 0.000000s % 0.56/0.61 %------------------------------------------- % 0.56/0.61 %------------------------------------------------------------------------------ % 0.56/0.61 % File : COM018+1 : TPTP v8.2.0. Released v4.0.0. % 0.56/0.61 % Domain : Computing Theory % 0.56/0.61 % Problem : Newman's lemma on rewriting systems 03_01_04, 00 expansion % 0.56/0.61 % Version : Especial. % 0.56/0.61 % English : % 0.56/0.61 % 0.56/0.61 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.56/0.61 % : [PV+07] Paskevich et al. (2007), Reasoning Inside a Formula an % 0.56/0.61 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.56/0.61 % Source : [Pas08] % 0.56/0.61 % Names : newman_03_01_04.00 [Pas08] % 0.56/0.61 % 0.56/0.61 % Status : Theorem % 0.56/0.61 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.05 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.1, 0.57 v4.0.0 % 0.56/0.61 % Syntax : Number of formulae : 23 ( 2 unt; 6 def) % 0.56/0.61 % Number of atoms : 108 ( 1 equ) % 0.56/0.61 % Maximal formula atoms : 10 ( 4 avg) % 0.56/0.61 % Number of connectives : 86 ( 1 ~; 2 |; 51 &) % 0.56/0.61 % ( 6 <=>; 26 =>; 0 <=; 0 <~>) % 0.56/0.61 % Maximal formula depth : 12 ( 6 avg) % 0.56/0.61 % Maximal term depth : 1 ( 1 avg) % 0.56/0.61 % Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty) % 0.56/0.61 % Number of functors : 7 ( 7 usr; 7 con; 0-0 aty) % 0.56/0.61 % Number of variables : 50 ( 43 !; 7 ?) % 0.56/0.61 % SPC : FOF_THM_RFO_SEQ % 0.56/0.61 % 0.56/0.61 % Comments : Problem generated by the SAD system [VLP07] % 0.56/0.61 %------------------------------------------------------------------------------ % 0.56/0.61 fof(mElmSort,axiom, % 0.56/0.61 ! [W0] : % 0.56/0.61 ( aElement0(W0) % 0.56/0.61 => $true ) ). % 0.56/0.61 % 0.56/0.61 fof(mRelSort,axiom, % 0.56/0.61 ! [W0] : % 0.56/0.61 ( aRewritingSystem0(W0) % 0.56/0.61 => $true ) ). % 0.56/0.61 % 0.56/0.61 fof(mReduct,axiom, % 0.56/0.61 ! [W0,W1] : % 0.56/0.61 ( ( aElement0(W0) % 0.56/0.61 & aRewritingSystem0(W1) ) % 0.56/0.61 => ! [W2] : % 0.56/0.61 ( aReductOfIn0(W2,W0,W1) % 0.56/0.61 => aElement0(W2) ) ) ). % 0.56/0.61 % 0.56/0.61 fof(mWFOrd,axiom, % 0.56/0.61 ! [W0,W1] : % 0.56/0.61 ( ( aElement0(W0) % 0.56/0.61 & aElement0(W1) ) % 0.56/0.61 => ( iLess0(W0,W1) % 0.56/0.61 => $true ) ) ). % 0.56/0.61 % 0.56/0.61 fof(mTCbr,axiom, % 0.56/0.61 ! [W0,W1,W2] : % 0.56/0.61 ( ( aElement0(W0) % 0.56/0.61 & aRewritingSystem0(W1) % 0.56/0.61 & aElement0(W2) ) % 0.56/0.61 => ( sdtmndtplgtdt0(W0,W1,W2) % 0.56/0.61 => $true ) ) ). % 0.56/0.61 % 0.56/0.61 fof(mTCDef,definition, % 0.56/0.61 ! [W0,W1,W2] : % 0.56/0.61 ( ( aElement0(W0) % 0.56/0.61 & aRewritingSystem0(W1) % 0.56/0.61 & aElement0(W2) ) % 0.56/0.61 => ( sdtmndtplgtdt0(W0,W1,W2) % 0.56/0.61 <=> ( aReductOfIn0(W2,W0,W1) % 0.56/0.61 | ? [W3] : % 0.56/0.61 ( aElement0(W3) % 0.56/0.61 & aReductOfIn0(W3,W0,W1) % 0.56/0.61 & sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ). % 0.56/0.61 % 0.56/0.61 fof(mTCTrans,axiom, % 0.56/0.61 ! [W0,W1,W2,W3] : % 0.56/0.61 ( ( aElement0(W0) % 0.56/0.61 & aRewritingSystem0(W1) % 0.56/0.61 & aElement0(W2) % 0.56/0.61 & aElement0(W3) ) % 0.56/0.61 => ( ( sdtmndtplgtdt0(W0,W1,W2) % 0.56/0.61 & sdtmndtplgtdt0(W2,W1,W3) ) % 0.56/0.61 => sdtmndtplgtdt0(W0,W1,W3) ) ) ). % 0.56/0.61 % 0.56/0.61 fof(mTCRDef,definition, % 0.56/0.61 ! [W0,W1,W2] : % 0.56/0.61 ( ( aElement0(W0) % 0.56/0.61 & aRewritingSystem0(W1) % 0.56/0.61 & aElement0(W2) ) % 0.56/0.61 => ( sdtmndtasgtdt0(W0,W1,W2) % 0.56/0.61 <=> ( W0 = W2 % 0.56/0.61 | sdtmndtplgtdt0(W0,W1,W2) ) ) ) ). % 0.56/0.61 % 0.56/0.61 fof(mTCRTrans,axiom, % 0.56/0.61 ! [W0,W1,W2,W3] : % 0.56/0.61 ( ( aElement0(W0) % 0.56/0.61 & aRewritingSystem0(W1) % 0.56/0.61 & aElement0(W2) % 0.56/0.61 & aElement0(W3) ) % 0.56/0.61 => ( ( sdtmndtasgtdt0(W0,W1,W2) % 0.56/0.61 & sdtmndtasgtdt0(W2,W1,W3) ) % 0.56/0.61 => sdtmndtasgtdt0(W0,W1,W3) ) ) ). % 0.56/0.61 % 0.56/0.61 fof(mCRDef,definition, % 0.56/0.61 ! [W0] : % 0.56/0.61 ( aRewritingSystem0(W0) % 0.56/0.61 => ( isConfluent0(W0) % 0.56/0.61 <=> ! [W1,W2,W3] : % 0.56/0.61 ( ( aElement0(W1) % 0.56/0.61 & aElement0(W2) % 0.56/0.61 & aElement0(W3) % 0.56/0.61 & sdtmndtasgtdt0(W1,W0,W2) % 0.56/0.61 & sdtmndtasgtdt0(W1,W0,W3) ) % 0.56/0.61 => ? [W4] : % 0.56/0.61 ( aElement0(W4) % 0.56/0.61 & sdtmndtasgtdt0(W2,W0,W4) % 0.56/0.61 & sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) ). % 0.56/0.61 % 0.56/0.61 fof(mWCRDef,definition, % 0.56/0.61 ! [W0] : % 0.56/0.61 ( aRewritingSystem0(W0) % 0.56/0.61 => ( isLocallyConfluent0(W0) % 0.56/0.61 <=> ! [W1,W2,W3] : % 0.56/0.61 ( ( aElement0(W1) % 0.56/0.61 & aElement0(W2) % 0.56/0.61 & aElement0(W3) % 0.56/0.61 & aReductOfIn0(W2,W1,W0) % 0.56/0.61 & aReductOfIn0(W3,W1,W0) ) % 0.56/0.62 => ? [W4] : % 0.56/0.62 ( aElement0(W4) % 0.56/0.62 & sdtmndtasgtdt0(W2,W0,W4) % 0.56/0.62 & sdtmndtasgtdt0(W3,W0,W4) ) ) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mTermin,definition, % 0.56/0.62 ! [W0] : % 0.56/0.62 ( aRewritingSystem0(W0) % 0.56/0.62 => ( isTerminating0(W0) % 0.56/0.62 <=> ! [W1,W2] : % 0.56/0.62 ( ( aElement0(W1) % 0.56/0.62 & aElement0(W2) ) % 0.56/0.62 => ( sdtmndtplgtdt0(W1,W0,W2) % 0.56/0.62 => iLess0(W2,W1) ) ) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mNFRDef,definition, % 0.56/0.62 ! [W0,W1] : % 0.56/0.62 ( ( aElement0(W0) % 0.56/0.62 & aRewritingSystem0(W1) ) % 0.56/0.62 => ! [W2] : % 0.56/0.62 ( aNormalFormOfIn0(W2,W0,W1) % 0.56/0.62 <=> ( aElement0(W2) % 0.56/0.62 & sdtmndtasgtdt0(W0,W1,W2) % 0.56/0.62 & ~ ? [W3] : aReductOfIn0(W3,W2,W1) ) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(mTermNF,axiom, % 0.56/0.62 ! [W0] : % 0.56/0.62 ( ( aRewritingSystem0(W0) % 0.56/0.62 & isTerminating0(W0) ) % 0.56/0.62 => ! [W1] : % 0.56/0.62 ( aElement0(W1) % 0.56/0.62 => ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(m__656,hypothesis, % 0.56/0.62 aRewritingSystem0(xR) ). % 0.56/0.62 % 0.56/0.62 fof(m__656_01,hypothesis, % 0.56/0.62 ( isLocallyConfluent0(xR) % 0.56/0.62 & isTerminating0(xR) ) ). % 0.56/0.62 % 0.56/0.62 fof(m__731,hypothesis, % 0.56/0.62 ( aElement0(xa) % 0.56/0.62 & aElement0(xb) % 0.56/0.62 & aElement0(xc) ) ). % 0.56/0.62 % 0.56/0.62 fof(m__715,hypothesis, % 0.56/0.62 ! [W0,W1,W2] : % 0.56/0.62 ( ( aElement0(W0) % 0.56/0.62 & aElement0(W1) % 0.56/0.62 & aElement0(W2) % 0.56/0.62 & sdtmndtasgtdt0(W0,xR,W1) % 0.56/0.62 & sdtmndtasgtdt0(W0,xR,W2) ) % 0.56/0.62 => ( iLess0(W0,xa) % 0.56/0.62 => ? [W3] : % 0.56/0.62 ( aElement0(W3) % 0.56/0.62 & sdtmndtasgtdt0(W1,xR,W3) % 0.56/0.62 & sdtmndtasgtdt0(W2,xR,W3) ) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(m__731_02,hypothesis, % 0.56/0.62 ( sdtmndtplgtdt0(xa,xR,xb) % 0.56/0.62 & sdtmndtplgtdt0(xa,xR,xc) ) ). % 0.56/0.62 % 0.56/0.62 fof(m__755,hypothesis, % 0.56/0.62 ( aElement0(xu) % 0.56/0.62 & aReductOfIn0(xu,xa,xR) % 0.56/0.62 & sdtmndtasgtdt0(xu,xR,xb) ) ). % 0.56/0.62 % 0.56/0.62 fof(m__779,hypothesis, % 0.56/0.62 ( aElement0(xv) % 0.56/0.62 & aReductOfIn0(xv,xa,xR) % 0.56/0.62 & sdtmndtasgtdt0(xv,xR,xc) ) ). % 0.56/0.62 % 0.56/0.62 fof(m__799,hypothesis, % 0.56/0.62 ( aElement0(xw) % 0.56/0.62 & sdtmndtasgtdt0(xu,xR,xw) % 0.56/0.62 & sdtmndtasgtdt0(xv,xR,xw) ) ). % 0.56/0.62 % 0.56/0.62 fof(m__,conjecture, % 0.56/0.62 ? [W0] : aNormalFormOfIn0(W0,xw,xR) ). % 0.56/0.62 % 0.56/0.62 %------------------------------------------------------------------------------ % 0.56/0.62 %------------------------------------------- % 0.56/0.62 % Proof found % 0.56/0.62 % SZS status Theorem for theBenchmark % 0.56/0.62 % SZS output start Proof % 0.56/0.62 %ClaNum:109(EqnAxiom:49) % 0.56/0.62 %VarNum:379(SingletonVarNum:106) % 0.56/0.62 %MaxLitNum:8 % 0.56/0.62 %MaxfuncDepth:1 % 0.56/0.62 %SharedTerms:24 % 0.56/0.62 %goalClause: 67 % 0.56/0.62 %singleGoalClaCount:1 % 0.56/0.62 [50]P1(a1) % 0.56/0.62 [51]P1(a17) % 0.56/0.62 [52]P1(a18) % 0.56/0.62 [53]P1(a19) % 0.56/0.62 [54]P1(a20) % 0.56/0.62 [55]P1(a21) % 0.56/0.62 [56]P2(a2) % 0.56/0.62 [57]P5(a2) % 0.56/0.62 [58]P8(a2) % 0.56/0.62 [59]P3(a19,a1,a2) % 0.56/0.62 [60]P3(a20,a1,a2) % 0.56/0.62 [61]P9(a1,a2,a17) % 0.56/0.62 [62]P9(a1,a2,a18) % 0.56/0.62 [63]P10(a19,a2,a17) % 0.56/0.62 [64]P10(a19,a2,a21) % 0.56/0.62 [65]P10(a20,a2,a18) % 0.56/0.62 [66]P10(a20,a2,a21) % 0.56/0.62 [67]~P4(x671,a21,a2) % 0.56/0.62 [68]~P2(x681)+P6(x681)+P1(f3(x681)) % 0.56/0.62 [69]~P2(x691)+P6(x691)+P1(f11(x691)) % 0.56/0.62 [70]~P2(x701)+P6(x701)+P1(f12(x701)) % 0.56/0.62 [71]~P2(x711)+P5(x711)+P1(f13(x711)) % 0.56/0.62 [72]~P2(x721)+P5(x721)+P1(f15(x721)) % 0.56/0.62 [73]~P2(x731)+P5(x731)+P1(f16(x731)) % 0.56/0.62 [74]~P2(x741)+P8(x741)+P1(f4(x741)) % 0.56/0.62 [75]~P2(x751)+P8(x751)+P1(f5(x751)) % 0.56/0.62 [76]~P2(x761)+P8(x761)+~P7(f5(x761),f4(x761)) % 0.56/0.62 [77]~P2(x771)+P6(x771)+P10(f3(x771),x771,f11(x771)) % 0.56/0.62 [78]~P2(x781)+P6(x781)+P10(f3(x781),x781,f12(x781)) % 0.56/0.62 [79]~P2(x791)+P8(x791)+P9(f4(x791),x791,f5(x791)) % 0.56/0.62 [80]~P2(x801)+P5(x801)+P3(f15(x801),f13(x801),x801) % 0.56/0.62 [81]~P2(x811)+P5(x811)+P3(f16(x811),f13(x811),x811) % 0.56/0.62 [83]~P1(x832)+~P2(x831)+~P8(x831)+P4(f6(x831,x832),x832,x831) % 0.56/0.62 [84]~P3(x841,x842,x843)+P1(x841)+~P1(x842)+~P2(x843) % 0.56/0.62 [85]~P4(x851,x852,x853)+P1(x851)+~P1(x852)+~P2(x853) % 0.56/0.62 [87]~P1(x871)+~P2(x872)+~P4(x873,x871,x872)+P10(x871,x872,x873) % 0.56/0.62 [91]~P4(x914,x911,x912)+~P1(x911)+~P3(x913,x914,x912)+~P2(x912) % 0.56/0.62 [92]~P2(x921)+P6(x921)+~P1(x922)+~P10(f11(x921),x921,x922)+~P10(f12(x921),x921,x922) % 0.56/0.62 [93]~P2(x931)+P5(x931)+~P1(x932)+~P10(f15(x931),x931,x932)+~P10(f16(x931),x931,x932) % 0.56/0.62 [82]~E(x821,x823)+~P1(x823)+~P1(x821)+~P2(x822)+P10(x821,x822,x823) % 0.56/0.62 [88]~P1(x881)+~P1(x883)+~P2(x882)+~P3(x883,x881,x882)+P9(x881,x882,x883) % 0.56/0.62 [89]~P1(x893)+~P1(x891)+~P2(x892)+~P9(x891,x892,x893)+P10(x891,x892,x893) % 0.56/0.62 [86]~P1(x861)+~P1(x862)+~P8(x863)+~P9(x862,x863,x861)+P7(x861,x862)+~P2(x863) % 0.56/0.62 [90]~P1(x902)+~P1(x901)+~P2(x903)+~P10(x901,x903,x902)+E(x901,x902)+P9(x901,x903,x902) % 0.56/0.62 [97]~P1(x971)+~P1(x972)+~P2(x973)+~P9(x972,x973,x971)+P3(x971,x972,x973)+P1(f8(x972,x973,x971)) % 0.56/0.62 [99]~P1(x991)+~P1(x992)+~P2(x993)+~P9(x992,x993,x991)+P3(x991,x992,x993)+P3(f8(x992,x993,x991),x992,x993) % 0.56/0.62 [100]~P1(x1001)+~P1(x1002)+~P2(x1003)+~P9(x1002,x1003,x1001)+P3(x1001,x1002,x1003)+P9(f8(x1002,x1003,x1001),x1003,x1001) % 0.56/0.62 [101]~P1(x1012)+~P1(x1011)+~P2(x1013)+~P10(x1012,x1013,x1011)+P4(x1011,x1012,x1013)+P3(f7(x1012,x1013,x1011),x1011,x1013) % 0.56/0.62 [98]~P1(x983)+~P1(x982)+~P1(x981)+~P10(x981,a2,x983)+~P10(x981,a2,x982)+~P7(x981,a1)+P1(f9(x981,x982,x983)) % 0.56/0.62 [102]~P1(x1023)+~P1(x1022)+~P1(x1021)+~P10(x1022,a2,x1023)+~P10(x1022,a2,x1021)+~P7(x1022,a1)+P10(x1021,a2,f9(x1022,x1023,x1021)) % 0.56/0.62 [103]~P1(x1033)+~P1(x1032)+~P1(x1031)+~P10(x1032,a2,x1033)+~P10(x1032,a2,x1031)+~P7(x1032,a1)+P10(x1031,a2,f9(x1032,x1031,x1033)) % 0.56/0.62 [94]~P1(x943)+~P1(x941)+~P2(x942)+~P3(x944,x941,x942)+~P9(x944,x942,x943)+P9(x941,x942,x943)+~P1(x944) % 0.56/0.62 [95]~P1(x953)+~P1(x951)+~P2(x952)+~P9(x954,x952,x953)+~P9(x951,x952,x954)+P9(x951,x952,x953)+~P1(x954) % 0.56/0.62 [96]~P1(x963)+~P1(x961)+~P2(x962)+~P10(x964,x962,x963)+~P10(x961,x962,x964)+P10(x961,x962,x963)+~P1(x964) % 0.56/0.62 [104]~P1(x1044)+~P1(x1043)+~P1(x1042)+~P2(x1041)+~P6(x1041)+~P10(x1042,x1041,x1044)+~P10(x1042,x1041,x1043)+P1(f10(x1041,x1042,x1043,x1044)) % 0.56/0.62 [105]~P1(x1054)+~P1(x1053)+~P1(x1052)+~P2(x1051)+~P5(x1051)+~P3(x1054,x1052,x1051)+~P3(x1053,x1052,x1051)+P1(f14(x1051,x1052,x1053,x1054)) % 0.56/0.62 [106]~P1(x1064)+~P1(x1063)+~P1(x1061)+~P2(x1062)+~P6(x1062)+~P10(x1063,x1062,x1064)+~P10(x1063,x1062,x1061)+P10(x1061,x1062,f10(x1062,x1063,x1064,x1061)) % 0.56/0.62 [107]~P1(x1074)+~P1(x1073)+~P1(x1071)+~P2(x1072)+~P6(x1072)+~P10(x1073,x1072,x1074)+~P10(x1073,x1072,x1071)+P10(x1071,x1072,f10(x1072,x1073,x1071,x1074)) % 0.56/0.62 [108]~P1(x1084)+~P1(x1083)+~P1(x1081)+~P2(x1082)+~P5(x1082)+~P3(x1084,x1083,x1082)+~P3(x1081,x1083,x1082)+P10(x1081,x1082,f14(x1082,x1083,x1084,x1081)) % 0.56/0.62 [109]~P1(x1094)+~P1(x1093)+~P1(x1091)+~P2(x1092)+~P5(x1092)+~P3(x1094,x1093,x1092)+~P3(x1091,x1093,x1092)+P10(x1091,x1092,f14(x1092,x1093,x1091,x1094)) % 0.56/0.62 %EqnAxiom % 0.56/0.62 [1]E(x11,x11) % 0.56/0.62 [2]E(x22,x21)+~E(x21,x22) % 0.56/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.56/0.62 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 0.56/0.62 [5]~E(x51,x52)+E(f11(x51),f11(x52)) % 0.56/0.62 [6]~E(x61,x62)+E(f12(x61),f12(x62)) % 0.56/0.62 [7]~E(x71,x72)+E(f13(x71),f13(x72)) % 0.56/0.62 [8]~E(x81,x82)+E(f15(x81),f15(x82)) % 0.56/0.62 [9]~E(x91,x92)+E(f16(x91),f16(x92)) % 0.56/0.62 [10]~E(x101,x102)+E(f4(x101),f4(x102)) % 0.56/0.62 [11]~E(x111,x112)+E(f5(x111),f5(x112)) % 0.56/0.62 [12]~E(x121,x122)+E(f8(x121,x123,x124),f8(x122,x123,x124)) % 0.56/0.62 [13]~E(x131,x132)+E(f8(x133,x131,x134),f8(x133,x132,x134)) % 0.56/0.62 [14]~E(x141,x142)+E(f8(x143,x144,x141),f8(x143,x144,x142)) % 0.56/0.62 [15]~E(x151,x152)+E(f10(x151,x153,x154,x155),f10(x152,x153,x154,x155)) % 0.56/0.62 [16]~E(x161,x162)+E(f10(x163,x161,x164,x165),f10(x163,x162,x164,x165)) % 0.56/0.62 [17]~E(x171,x172)+E(f10(x173,x174,x171,x175),f10(x173,x174,x172,x175)) % 0.56/0.62 [18]~E(x181,x182)+E(f10(x183,x184,x185,x181),f10(x183,x184,x185,x182)) % 0.56/0.62 [19]~E(x191,x192)+E(f14(x191,x193,x194,x195),f14(x192,x193,x194,x195)) % 0.56/0.62 [20]~E(x201,x202)+E(f14(x203,x201,x204,x205),f14(x203,x202,x204,x205)) % 0.56/0.62 [21]~E(x211,x212)+E(f14(x213,x214,x211,x215),f14(x213,x214,x212,x215)) % 0.56/0.62 [22]~E(x221,x222)+E(f14(x223,x224,x225,x221),f14(x223,x224,x225,x222)) % 0.56/0.62 [23]~E(x231,x232)+E(f9(x231,x233,x234),f9(x232,x233,x234)) % 0.56/0.62 [24]~E(x241,x242)+E(f9(x243,x241,x244),f9(x243,x242,x244)) % 0.56/0.62 [25]~E(x251,x252)+E(f9(x253,x254,x251),f9(x253,x254,x252)) % 0.56/0.62 [26]~E(x261,x262)+E(f6(x261,x263),f6(x262,x263)) % 0.56/0.62 [27]~E(x271,x272)+E(f6(x273,x271),f6(x273,x272)) % 0.56/0.62 [28]~E(x281,x282)+E(f7(x281,x283,x284),f7(x282,x283,x284)) % 0.56/0.62 [29]~E(x291,x292)+E(f7(x293,x291,x294),f7(x293,x292,x294)) % 0.56/0.62 [30]~E(x301,x302)+E(f7(x303,x304,x301),f7(x303,x304,x302)) % 0.56/0.62 [31]~P1(x311)+P1(x312)+~E(x311,x312) % 0.56/0.62 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324) % 0.56/0.62 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334) % 0.56/0.62 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341) % 0.56/0.62 [35]P10(x352,x353,x354)+~E(x351,x352)+~P10(x351,x353,x354) % 0.56/0.62 [36]P10(x363,x362,x364)+~E(x361,x362)+~P10(x363,x361,x364) % 0.56/0.62 [37]P10(x373,x374,x372)+~E(x371,x372)+~P10(x373,x374,x371) % 0.56/0.62 [38]~P5(x381)+P5(x382)+~E(x381,x382) % 0.56/0.62 [39]~P2(x391)+P2(x392)+~E(x391,x392) % 0.56/0.62 [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404) % 0.56/0.62 [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414) % 0.56/0.62 [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421) % 0.56/0.62 [43]P9(x432,x433,x434)+~E(x431,x432)+~P9(x431,x433,x434) % 0.56/0.62 [44]P9(x443,x442,x444)+~E(x441,x442)+~P9(x443,x441,x444) % 0.56/0.62 [45]P9(x453,x454,x452)+~E(x451,x452)+~P9(x453,x454,x451) % 0.56/0.62 [46]~P8(x461)+P8(x462)+~E(x461,x462) % 0.56/0.62 [47]~P6(x471)+P6(x472)+~E(x471,x472) % 0.56/0.62 [48]P7(x482,x483)+~E(x481,x482)+~P7(x481,x483) % 0.56/0.62 [49]P7(x493,x492)+~E(x491,x492)+~P7(x493,x491) % 0.56/0.62 % 0.56/0.62 %------------------------------------------- % 0.56/0.62 cnf(111,plain, % 0.56/0.62 ($false), % 0.56/0.62 inference(scs_inference,[],[67,55,56,58,83]), % 0.56/0.62 ['proof']). % 0.56/0.62 % SZS output end Proof % 0.56/0.62 % Total time :0.000000s %------------------------------------------------------------------------------