%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : RNG101+2 : 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 : n022.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 14:01:05 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 % 0.03/0.12 % Problem : RNG101+2 : TPTP v8.2.0. Released v4.0.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n022.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 : Tue Jun 18 13:32:53 EDT 2024 % 0.12/0.33 % CPUTime : % 0.50/0.56 start to proof:theBenchmark % 0.52/0.62 %------------------------------------------- % 0.52/0.62 % File :CSE---1.7 % 0.52/0.62 % Problem :theBenchmark % 0.52/0.62 % Transform :cnf % 0.52/0.62 % Format :tptp:raw % 0.52/0.62 % Command :java -jar mcs_scs.jar %d %s % 0.52/0.62 % 0.52/0.62 % Result :Theorem 0.010000s % 0.52/0.62 % Output :CNFRefutation 0.010000s % 0.52/0.62 %------------------------------------------- % 0.52/0.63 %------------------------------------------------------------------------------ % 0.52/0.63 % File : RNG101+2 : TPTP v8.2.0. Released v4.0.0. % 0.52/0.63 % Domain : Ring Theory % 0.52/0.63 % Problem : Chinese remainder theorem in a ring 06_01, 01 expansion % 0.52/0.63 % Version : Especial. % 0.52/0.63 % English : % 0.52/0.63 % 0.52/0.63 % Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction % 0.52/0.63 % : [Pas08] Paskevich (2008), Email to G. Sutcliffe % 0.52/0.63 % Source : [Pas08] % 0.52/0.63 % Names : chines_06_01.01 [Pas08] % 0.52/0.63 % 0.52/0.63 % Status : Theorem % 0.52/0.63 % Rating : 0.06 v8.1.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.19 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.10 v5.1.0, 0.19 v5.0.0, 0.25 v4.1.0, 0.35 v4.0.1, 0.70 v4.0.0 % 0.52/0.63 % Syntax : Number of formulae : 40 ( 4 unt; 9 def) % 0.52/0.63 % Number of atoms : 160 ( 34 equ) % 0.52/0.63 % Maximal formula atoms : 9 ( 4 avg) % 0.52/0.63 % Number of connectives : 124 ( 4 ~; 1 |; 60 &) % 0.52/0.63 % ( 12 <=>; 47 =>; 0 <=; 0 <~>) % 0.52/0.63 % Maximal formula depth : 13 ( 6 avg) % 0.52/0.63 % Maximal term depth : 3 ( 1 avg) % 0.52/0.63 % Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty) % 0.52/0.63 % Number of functors : 13 ( 13 usr; 6 con; 0-2 aty) % 0.52/0.63 % Number of variables : 86 ( 76 !; 10 ?) % 0.52/0.63 % SPC : FOF_THM_RFO_SEQ % 0.52/0.63 % 0.52/0.63 % Comments : Problem generated by the SAD system [VLP07] % 0.52/0.63 %------------------------------------------------------------------------------ % 0.52/0.63 fof(mElmSort,axiom, % 0.52/0.63 ! [W0] : % 0.52/0.63 ( aElement0(W0) % 0.52/0.63 => $true ) ). % 0.52/0.63 % 0.52/0.63 fof(mSortsC,axiom, % 0.52/0.63 aElement0(sz00) ). % 0.52/0.63 % 0.52/0.63 fof(mSortsC_01,axiom, % 0.52/0.63 aElement0(sz10) ). % 0.52/0.63 % 0.52/0.63 fof(mSortsU,axiom, % 0.52/0.63 ! [W0] : % 0.52/0.63 ( aElement0(W0) % 0.52/0.63 => aElement0(smndt0(W0)) ) ). % 0.52/0.63 % 0.52/0.63 fof(mSortsB,axiom, % 0.52/0.63 ! [W0,W1] : % 0.52/0.63 ( ( aElement0(W0) % 0.52/0.63 & aElement0(W1) ) % 0.52/0.63 => aElement0(sdtpldt0(W0,W1)) ) ). % 0.52/0.63 % 0.52/0.63 fof(mSortsB_02,axiom, % 0.52/0.63 ! [W0,W1] : % 0.52/0.63 ( ( aElement0(W0) % 0.52/0.63 & aElement0(W1) ) % 0.52/0.63 => aElement0(sdtasdt0(W0,W1)) ) ). % 0.52/0.63 % 0.52/0.63 fof(mAddComm,axiom, % 0.52/0.63 ! [W0,W1] : % 0.52/0.63 ( ( aElement0(W0) % 0.52/0.63 & aElement0(W1) ) % 0.52/0.63 => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ). % 0.52/0.63 % 0.52/0.63 fof(mAddAsso,axiom, % 0.52/0.63 ! [W0,W1,W2] : % 0.52/0.63 ( ( aElement0(W0) % 0.52/0.63 & aElement0(W1) % 0.52/0.63 & aElement0(W2) ) % 0.52/0.63 => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ). % 0.52/0.63 % 0.52/0.63 fof(mAddZero,axiom, % 0.52/0.63 ! [W0] : % 0.52/0.63 ( aElement0(W0) % 0.52/0.63 => ( sdtpldt0(W0,sz00) = W0 % 0.52/0.63 & W0 = sdtpldt0(sz00,W0) ) ) ). % 0.52/0.63 % 0.52/0.63 fof(mAddInvr,axiom, % 0.52/0.63 ! [W0] : % 0.52/0.63 ( aElement0(W0) % 0.52/0.63 => ( sdtpldt0(W0,smndt0(W0)) = sz00 % 0.52/0.63 & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ). % 0.52/0.63 % 0.52/0.63 fof(mMulComm,axiom, % 0.52/0.63 ! [W0,W1] : % 0.52/0.63 ( ( aElement0(W0) % 0.52/0.63 & aElement0(W1) ) % 0.52/0.63 => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ). % 0.52/0.63 % 0.52/0.63 fof(mMulAsso,axiom, % 0.52/0.63 ! [W0,W1,W2] : % 0.52/0.63 ( ( aElement0(W0) % 0.52/0.63 & aElement0(W1) % 0.52/0.63 & aElement0(W2) ) % 0.52/0.63 => sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ). % 0.52/0.63 % 0.52/0.63 fof(mMulUnit,axiom, % 0.52/0.63 ! [W0] : % 0.52/0.63 ( aElement0(W0) % 0.52/0.63 => ( sdtasdt0(W0,sz10) = W0 % 0.52/0.63 & W0 = sdtasdt0(sz10,W0) ) ) ). % 0.52/0.63 % 0.52/0.63 fof(mAMDistr,axiom, % 0.52/0.63 ! [W0,W1,W2] : % 0.52/0.63 ( ( aElement0(W0) % 0.52/0.63 & aElement0(W1) % 0.52/0.63 & aElement0(W2) ) % 0.52/0.63 => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) % 0.52/0.63 & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ). % 0.52/0.63 % 0.52/0.63 fof(mMulMnOne,axiom, % 0.52/0.63 ! [W0] : % 0.52/0.63 ( aElement0(W0) % 0.52/0.63 => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) % 0.52/0.63 & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ). % 0.52/0.63 % 0.52/0.63 fof(mMulZero,axiom, % 0.52/0.63 ! [W0] : % 0.52/0.63 ( aElement0(W0) % 0.52/0.63 => ( sdtasdt0(W0,sz00) = sz00 % 0.52/0.63 & sz00 = sdtasdt0(sz00,W0) ) ) ). % 0.52/0.63 % 0.52/0.63 fof(mCancel,axiom, % 0.52/0.63 ! [W0,W1] : % 0.52/0.63 ( ( aElement0(W0) % 0.52/0.63 & aElement0(W1) ) % 0.52/0.63 => ( sdtasdt0(W0,W1) = sz00 % 0.52/0.63 => ( W0 = sz00 % 0.52/0.63 | W1 = sz00 ) ) ) ). % 0.52/0.63 % 0.52/0.63 fof(mUnNeZr,axiom, % 0.52/0.63 sz10 != sz00 ). % 0.52/0.63 % 0.52/0.63 fof(mSetSort,axiom, % 0.52/0.63 ! [W0] : % 0.52/0.63 ( aSet0(W0) % 0.52/0.63 => $true ) ). % 0.52/0.63 % 0.52/0.63 fof(mEOfElem,axiom, % 0.52/0.63 ! [W0] : % 0.52/0.63 ( aSet0(W0) % 0.52/0.63 => ! [W1] : % 0.52/0.63 ( aElementOf0(W1,W0) % 0.52/0.63 => aElement0(W1) ) ) ). % 0.52/0.63 % 0.52/0.63 fof(mSetEq,axiom, % 0.52/0.63 ! [W0,W1] : % 0.52/0.63 ( ( aSet0(W0) % 0.52/0.63 & aSet0(W1) ) % 0.52/0.63 => ( ( ! [W2] : % 0.52/0.63 ( aElementOf0(W2,W0) % 0.52/0.63 => aElementOf0(W2,W1) ) % 0.54/0.63 & ! [W2] : % 0.54/0.63 ( aElementOf0(W2,W1) % 0.54/0.63 => aElementOf0(W2,W0) ) ) % 0.54/0.63 => W0 = W1 ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefSSum,definition, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aSet0(W0) % 0.54/0.63 & aSet0(W1) ) % 0.54/0.63 => ! [W2] : % 0.54/0.63 ( W2 = sdtpldt1(W0,W1) % 0.54/0.63 <=> ( aSet0(W2) % 0.54/0.63 & ! [W3] : % 0.54/0.63 ( aElementOf0(W3,W2) % 0.54/0.63 <=> ? [W4,W5] : % 0.54/0.63 ( aElementOf0(W4,W0) % 0.54/0.63 & aElementOf0(W5,W1) % 0.54/0.63 & sdtpldt0(W4,W5) = W3 ) ) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefSInt,definition, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aSet0(W0) % 0.54/0.63 & aSet0(W1) ) % 0.54/0.63 => ! [W2] : % 0.54/0.63 ( W2 = sdtasasdt0(W0,W1) % 0.54/0.63 <=> ( aSet0(W2) % 0.54/0.63 & ! [W3] : % 0.54/0.63 ( aElementOf0(W3,W2) % 0.54/0.63 <=> ( aElementOf0(W3,W0) % 0.54/0.63 & aElementOf0(W3,W1) ) ) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefIdeal,definition, % 0.54/0.63 ! [W0] : % 0.54/0.63 ( aIdeal0(W0) % 0.54/0.63 <=> ( aSet0(W0) % 0.54/0.63 & ! [W1] : % 0.54/0.63 ( aElementOf0(W1,W0) % 0.54/0.63 => ( ! [W2] : % 0.54/0.63 ( aElementOf0(W2,W0) % 0.54/0.63 => aElementOf0(sdtpldt0(W1,W2),W0) ) % 0.54/0.63 & ! [W2] : % 0.54/0.63 ( aElement0(W2) % 0.54/0.63 => aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mIdeSum,axiom, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aIdeal0(W0) % 0.54/0.63 & aIdeal0(W1) ) % 0.54/0.63 => aIdeal0(sdtpldt1(W0,W1)) ) ). % 0.54/0.63 % 0.54/0.63 fof(mIdeInt,axiom, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aIdeal0(W0) % 0.54/0.63 & aIdeal0(W1) ) % 0.54/0.63 => aIdeal0(sdtasasdt0(W0,W1)) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefMod,definition, % 0.54/0.63 ! [W0,W1,W2] : % 0.54/0.63 ( ( aElement0(W0) % 0.54/0.63 & aElement0(W1) % 0.54/0.63 & aIdeal0(W2) ) % 0.54/0.63 => ( sdteqdtlpzmzozddtrp0(W0,W1,W2) % 0.54/0.63 <=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mChineseRemainder,axiom, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aIdeal0(W0) % 0.54/0.63 & aIdeal0(W1) ) % 0.54/0.63 => ( ! [W2] : % 0.54/0.63 ( aElement0(W2) % 0.54/0.63 => aElementOf0(W2,sdtpldt1(W0,W1)) ) % 0.54/0.63 => ! [W2,W3] : % 0.54/0.63 ( ( aElement0(W2) % 0.54/0.63 & aElement0(W3) ) % 0.54/0.63 => ? [W4] : % 0.54/0.63 ( aElement0(W4) % 0.54/0.63 & sdteqdtlpzmzozddtrp0(W4,W2,W0) % 0.54/0.63 & sdteqdtlpzmzozddtrp0(W4,W3,W1) ) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mNatSort,axiom, % 0.54/0.63 ! [W0] : % 0.54/0.63 ( aNaturalNumber0(W0) % 0.54/0.63 => $true ) ). % 0.54/0.63 % 0.54/0.63 fof(mEucSort,axiom, % 0.54/0.63 ! [W0] : % 0.54/0.63 ( ( aElement0(W0) % 0.54/0.63 & W0 != sz00 ) % 0.54/0.63 => aNaturalNumber0(sbrdtbr0(W0)) ) ). % 0.54/0.63 % 0.54/0.63 fof(mNatLess,axiom, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aNaturalNumber0(W0) % 0.54/0.63 & aNaturalNumber0(W1) ) % 0.54/0.63 => ( iLess0(W0,W1) % 0.54/0.63 => $true ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDivision,axiom, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aElement0(W0) % 0.54/0.63 & aElement0(W1) % 0.54/0.63 & W1 != sz00 ) % 0.54/0.63 => ? [W2,W3] : % 0.54/0.63 ( aElement0(W2) % 0.54/0.63 & aElement0(W3) % 0.54/0.63 & W0 = sdtpldt0(sdtasdt0(W2,W1),W3) % 0.54/0.63 & ( W3 != sz00 % 0.54/0.63 => iLess0(sbrdtbr0(W3),sbrdtbr0(W1)) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefDiv,definition, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aElement0(W0) % 0.54/0.63 & aElement0(W1) ) % 0.54/0.63 => ( doDivides0(W0,W1) % 0.54/0.63 <=> ? [W2] : % 0.54/0.63 ( aElement0(W2) % 0.54/0.63 & sdtasdt0(W0,W2) = W1 ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefDvs,definition, % 0.54/0.63 ! [W0] : % 0.54/0.63 ( aElement0(W0) % 0.54/0.63 => ! [W1] : % 0.54/0.63 ( aDivisorOf0(W1,W0) % 0.54/0.63 <=> ( aElement0(W1) % 0.54/0.63 & doDivides0(W1,W0) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefGCD,definition, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aElement0(W0) % 0.54/0.63 & aElement0(W1) ) % 0.54/0.63 => ! [W2] : % 0.54/0.63 ( aGcdOfAnd0(W2,W0,W1) % 0.54/0.63 <=> ( aDivisorOf0(W2,W0) % 0.54/0.63 & aDivisorOf0(W2,W1) % 0.54/0.63 & ! [W3] : % 0.54/0.63 ( ( aDivisorOf0(W3,W0) % 0.54/0.63 & aDivisorOf0(W3,W1) ) % 0.54/0.63 => doDivides0(W3,W2) ) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefRel,definition, % 0.54/0.63 ! [W0,W1] : % 0.54/0.63 ( ( aElement0(W0) % 0.54/0.63 & aElement0(W1) ) % 0.54/0.63 => ( misRelativelyPrime0(W0,W1) % 0.54/0.63 <=> aGcdOfAnd0(sz10,W0,W1) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(mDefPrIdeal,definition, % 0.54/0.63 ! [W0] : % 0.54/0.63 ( aElement0(W0) % 0.54/0.63 => ! [W1] : % 0.54/0.63 ( W1 = slsdtgt0(W0) % 0.54/0.63 <=> ( aSet0(W1) % 0.54/0.63 & ! [W2] : % 0.54/0.63 ( aElementOf0(W2,W1) % 0.54/0.63 <=> ? [W3] : % 0.54/0.63 ( aElement0(W3) % 0.54/0.63 & sdtasdt0(W0,W3) = W2 ) ) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(m__1905,hypothesis, % 0.54/0.64 aElement0(xc) ). % 0.54/0.64 % 0.54/0.64 fof(m__1933,hypothesis, % 0.54/0.64 ( ? [W0] : % 0.54/0.64 ( aElement0(W0) % 0.54/0.64 & sdtasdt0(xc,W0) = xx ) % 0.54/0.64 & aElementOf0(xx,slsdtgt0(xc)) % 0.54/0.64 & ? [W0] : % 0.54/0.64 ( aElement0(W0) % 0.54/0.64 & sdtasdt0(xc,W0) = xy ) % 0.54/0.64 & aElementOf0(xy,slsdtgt0(xc)) % 0.54/0.64 & aElement0(xz) ) ). % 0.54/0.64 % 0.54/0.64 fof(m__,conjecture, % 0.54/0.64 ? [W0] : % 0.54/0.64 ( aElement0(W0) % 0.54/0.64 & sdtasdt0(xc,W0) = xx ) ). % 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:180(EqnAxiom:83) % 0.54/0.64 %VarNum:701(SingletonVarNum:213) % 0.54/0.64 %MaxLitNum:8 % 0.54/0.64 %MaxfuncDepth:2 % 0.54/0.64 %SharedTerms:23 % 0.54/0.64 %goalClause: 105 % 0.54/0.64 [84]P1(a1) % 0.54/0.64 [85]P1(a31) % 0.54/0.64 [86]P1(a32) % 0.54/0.64 [87]P1(a33) % 0.54/0.64 [88]P1(a2) % 0.54/0.64 [89]P1(a15) % 0.54/0.64 [94]~E(a1,a31) % 0.54/0.64 [90]E(f16(a32,a2),a34) % 0.54/0.64 [91]E(f16(a32,a15),a35) % 0.54/0.64 [92]P3(a34,f27(a32)) % 0.54/0.64 [93]P3(a35,f27(a32)) % 0.54/0.64 [95]~P5(x951)+P4(x951) % 0.54/0.64 [96]~P1(x961)+P1(f30(x961)) % 0.54/0.64 [98]~P1(x981)+E(f16(a1,x981),a1) % 0.54/0.64 [99]~P1(x991)+E(f16(x991,a1),a1) % 0.54/0.64 [101]~P1(x1011)+E(f28(a1,x1011),x1011) % 0.54/0.64 [102]~P1(x1021)+E(f16(a31,x1021),x1021) % 0.54/0.64 [103]~P1(x1031)+E(f28(x1031,a1),x1031) % 0.54/0.64 [104]~P1(x1041)+E(f16(x1041,a31),x1041) % 0.54/0.64 [105]~P1(x1051)+~E(f16(a32,x1051),a34) % 0.54/0.64 [106]~P1(x1061)+E(f28(f30(x1061),x1061),a1) % 0.54/0.64 [107]~P1(x1071)+E(f28(x1071,f30(x1071)),a1) % 0.54/0.64 [108]~P1(x1081)+E(f16(x1081,f30(a31)),f30(x1081)) % 0.54/0.64 [109]~P1(x1091)+E(f16(f30(a31),x1091),f30(x1091)) % 0.54/0.64 [97]~P1(x971)+E(x971,a1)+P7(f17(x971)) % 0.54/0.64 [110]~P4(x1101)+P5(x1101)+P3(f18(x1101),x1101) % 0.54/0.64 [111]~P3(x1111,x1112)+P1(x1111)+~P4(x1112) % 0.54/0.64 [112]~P2(x1121,x1122)+P1(x1121)+~P1(x1122) % 0.54/0.64 [119]~P1(x1192)+~P2(x1191,x1192)+P8(x1191,x1192) % 0.54/0.64 [100]~P1(x1002)+P4(x1001)+~E(x1001,f27(x1002)) % 0.54/0.64 [114]~P1(x1142)+~P1(x1141)+E(f28(x1141,x1142),f28(x1142,x1141)) % 0.54/0.64 [115]~P1(x1152)+~P1(x1151)+E(f16(x1151,x1152),f16(x1152,x1151)) % 0.54/0.64 [120]~P1(x1202)+~P1(x1201)+P1(f28(x1201,x1202)) % 0.54/0.64 [121]~P1(x1212)+~P1(x1211)+P1(f16(x1211,x1212)) % 0.54/0.64 [122]~P5(x1222)+~P5(x1221)+P5(f29(x1221,x1222)) % 0.54/0.64 [123]~P5(x1232)+~P5(x1231)+P5(f26(x1231,x1232)) % 0.54/0.64 [118]~P4(x1181)+P5(x1181)+P3(f4(x1181),x1181)+P1(f3(x1181)) % 0.54/0.64 [149]~P4(x1491)+P5(x1491)+P1(f3(x1491))+~P3(f28(f18(x1491),f4(x1491)),x1491) % 0.54/0.64 [152]~P4(x1521)+P5(x1521)+P3(f4(x1521),x1521)+~P3(f16(f3(x1521),f18(x1521)),x1521) % 0.54/0.64 [161]~P4(x1611)+P5(x1611)+~P3(f28(f18(x1611),f4(x1611)),x1611)+~P3(f16(f3(x1611),f18(x1611)),x1611) % 0.54/0.64 [126]~P1(x1262)+~P1(x1261)+~P8(x1261,x1262)+P2(x1261,x1262) % 0.54/0.64 [134]~P1(x1342)+~P1(x1341)+~P9(x1341,x1342)+P6(a31,x1341,x1342) % 0.54/0.64 [142]~P1(x1422)+~P1(x1421)+P9(x1421,x1422)+~P6(a31,x1421,x1422) % 0.54/0.64 [124]~P1(x1241)+~P1(x1242)+E(x1241,a1)+P1(f5(x1242,x1241)) % 0.54/0.64 [125]~P1(x1251)+~P1(x1252)+E(x1251,a1)+P1(f8(x1252,x1251)) % 0.54/0.64 [129]~P1(x1292)+~P1(x1291)+~P8(x1291,x1292)+P1(f9(x1291,x1292)) % 0.54/0.64 [133]~P1(x1332)+~P1(x1331)+~P8(x1331,x1332)+E(f16(x1331,f9(x1331,x1332)),x1332) % 0.54/0.64 [154]~P1(x1541)+~P1(x1542)+E(x1541,a1)+E(f28(f16(f5(x1542,x1541),x1541),f8(x1542,x1541)),x1542) % 0.54/0.64 [144]~P1(x1442)+~P6(x1441,x1443,x1442)+P2(x1441,x1442)+~P1(x1443) % 0.54/0.64 [145]~P1(x1452)+~P6(x1451,x1452,x1453)+P2(x1451,x1452)+~P1(x1453) % 0.54/0.64 [116]~P4(x1163)+~P4(x1162)+P4(x1161)+~E(x1161,f29(x1162,x1163)) % 0.54/0.64 [117]~P4(x1173)+~P4(x1172)+P4(x1171)+~E(x1171,f26(x1172,x1173)) % 0.54/0.64 [132]~P1(x1321)+~P5(x1323)+~P3(x1322,x1323)+P3(f16(x1321,x1322),x1323) % 0.54/0.64 [136]~P5(x1363)+~P3(x1361,x1363)+~P3(x1362,x1363)+P3(f28(x1361,x1362),x1363) % 0.54/0.64 [156]~P1(x1561)+~P3(x1563,x1562)+~E(x1562,f27(x1561))+P1(f12(x1561,x1562,x1563)) % 0.54/0.64 [139]~P1(x1393)+~P1(x1392)+~P1(x1391)+E(f28(f28(x1391,x1392),x1393),f28(x1391,f28(x1392,x1393))) % 0.54/0.64 [140]~P1(x1403)+~P1(x1402)+~P1(x1401)+E(f16(f16(x1401,x1402),x1403),f16(x1401,f16(x1402,x1403))) % 0.54/0.64 [150]~P1(x1503)+~P1(x1502)+~P1(x1501)+E(f28(f16(x1501,x1502),f16(x1501,x1503)),f16(x1501,f28(x1502,x1503))) % 0.54/0.64 [151]~P1(x1512)+~P1(x1513)+~P1(x1511)+E(f28(f16(x1511,x1512),f16(x1513,x1512)),f16(f28(x1511,x1513),x1512)) % 0.54/0.64 [158]~P1(x1581)+~P3(x1583,x1582)+~E(x1582,f27(x1581))+E(f16(x1581,f12(x1581,x1582,x1583)),x1583) % 0.54/0.64 [113]~P1(x1131)+~P1(x1132)+E(x1131,a1)+E(x1132,a1)+~E(f16(x1132,x1131),a1) % 0.54/0.64 [135]~P1(x1352)+~P4(x1351)+P3(f11(x1352,x1351),x1351)+E(x1351,f27(x1352))+P1(f10(x1352,x1351)) % 0.54/0.64 [137]~P4(x1372)+~P4(x1371)+E(x1371,x1372)+P3(f14(x1371,x1372),x1371)+P3(f19(x1371,x1372),x1372) % 0.54/0.64 [146]~P4(x1462)+~P4(x1461)+E(x1461,x1462)+P3(f14(x1461,x1462),x1461)+~P3(f19(x1461,x1462),x1461) % 0.54/0.64 [147]~P4(x1472)+~P4(x1471)+E(x1471,x1472)+P3(f19(x1471,x1472),x1472)+~P3(f14(x1471,x1472),x1472) % 0.54/0.64 [155]~P4(x1552)+~P4(x1551)+E(x1551,x1552)+~P3(f14(x1551,x1552),x1552)+~P3(f19(x1551,x1552),x1551) % 0.54/0.64 [141]~P1(x1411)+~P1(x1412)+E(x1411,a1)+P10(f17(f8(x1412,x1411)),f17(x1411))+E(f8(x1412,x1411),a1) % 0.54/0.64 [143]~P1(x1432)+~P4(x1431)+P3(f11(x1432,x1431),x1431)+E(x1431,f27(x1432))+E(f16(x1432,f10(x1432,x1431)),f11(x1432,x1431)) % 0.54/0.64 [127]~P1(x1272)+~P1(x1271)+~P1(x1273)+P8(x1271,x1272)+~E(f16(x1271,x1273),x1272) % 0.54/0.64 [157]~P1(x1572)+~P1(x1571)+~P5(x1573)+P11(x1571,x1572,x1573)+~P3(f28(x1571,f30(x1572)),x1573) % 0.54/0.64 [159]~P1(x1592)+~P1(x1591)+~P5(x1593)+~P11(x1591,x1592,x1593)+P3(f28(x1591,f30(x1592)),x1593) % 0.54/0.64 [128]~P1(x1283)+~P1(x1284)+P3(x1281,x1282)+~E(f16(x1283,x1284),x1281)+~E(x1282,f27(x1283)) % 0.54/0.64 [130]~P4(x1304)+~P4(x1302)+~P3(x1301,x1303)+P3(x1301,x1302)+~E(x1303,f26(x1304,x1302)) % 0.54/0.64 [131]~P4(x1314)+~P4(x1312)+~P3(x1311,x1313)+P3(x1311,x1312)+~E(x1313,f26(x1312,x1314)) % 0.54/0.64 [172]~P4(x1722)+~P4(x1721)+~P3(x1724,x1723)+~E(x1723,f29(x1721,x1722))+P3(f21(x1721,x1722,x1723,x1724),x1721) % 0.54/0.64 [173]~P4(x1732)+~P4(x1731)+~P3(x1734,x1733)+~E(x1733,f29(x1731,x1732))+P3(f22(x1731,x1732,x1733,x1734),x1732) % 0.54/0.64 [180]~P4(x1802)+~P4(x1801)+~P3(x1804,x1803)+~E(x1803,f29(x1801,x1802))+E(f28(f21(x1801,x1802,x1803,x1804),f22(x1801,x1802,x1803,x1804)),x1804) % 0.54/0.64 [153]~P1(x1533)+~P1(x1532)+~P4(x1531)+~P3(f11(x1532,x1531),x1531)+~E(f11(x1532,x1531),f16(x1532,x1533))+E(x1531,f27(x1532)) % 0.54/0.64 [162]~P1(x1623)+~P1(x1622)+~P2(x1621,x1623)+~P2(x1621,x1622)+P6(x1621,x1622,x1623)+P2(f13(x1622,x1623,x1621),x1623) % 0.54/0.64 [163]~P1(x1633)+~P1(x1632)+~P2(x1631,x1633)+~P2(x1631,x1632)+P6(x1631,x1632,x1633)+P2(f13(x1632,x1633,x1631),x1632) % 0.54/0.64 [164]~P4(x1641)+~P4(x1643)+~P4(x1642)+P3(f20(x1642,x1643,x1641),x1641)+P3(f23(x1642,x1643,x1641),x1642)+E(x1641,f29(x1642,x1643)) % 0.54/0.64 [165]~P4(x1651)+~P4(x1653)+~P4(x1652)+P3(f20(x1652,x1653,x1651),x1651)+P3(f24(x1652,x1653,x1651),x1653)+E(x1651,f29(x1652,x1653)) % 0.54/0.64 [166]~P4(x1661)+~P4(x1663)+~P4(x1662)+P3(f25(x1662,x1663,x1661),x1661)+P3(f25(x1662,x1663,x1661),x1663)+E(x1661,f26(x1662,x1663)) % 0.54/0.64 [167]~P4(x1671)+~P4(x1673)+~P4(x1672)+P3(f25(x1672,x1673,x1671),x1671)+P3(f25(x1672,x1673,x1671),x1672)+E(x1671,f26(x1672,x1673)) % 0.54/0.64 [168]~P1(x1683)+~P1(x1682)+~P2(x1681,x1683)+~P2(x1681,x1682)+P6(x1681,x1682,x1683)+~P8(f13(x1682,x1683,x1681),x1681) % 0.54/0.64 [170]~P4(x1701)+~P4(x1703)+~P4(x1702)+P3(f20(x1702,x1703,x1701),x1701)+E(x1701,f29(x1702,x1703))+E(f28(f23(x1702,x1703,x1701),f24(x1702,x1703,x1701)),f20(x1702,x1703,x1701)) % 0.54/0.64 [160]~P2(x1601,x1603)+~P2(x1601,x1604)+~P6(x1602,x1604,x1603)+P8(x1601,x1602)+~P1(x1603)+~P1(x1604) % 0.54/0.64 [138]~P4(x1384)+~P4(x1383)+~P3(x1381,x1384)+~P3(x1381,x1383)+P3(x1381,x1382)+~E(x1382,f26(x1383,x1384)) % 0.54/0.64 [171]~P1(x1714)+~P1(x1713)+~P5(x1712)+~P5(x1711)+P1(f6(x1711,x1712))+P1(f7(x1711,x1712,x1713,x1714)) % 0.54/0.64 [174]~P1(x1744)+~P1(x1743)+~P5(x1742)+~P5(x1741)+P11(f7(x1741,x1742,x1743,x1744),x1744,x1742)+P1(f6(x1741,x1742)) % 0.54/0.64 [175]~P1(x1754)+~P1(x1753)+~P5(x1752)+~P5(x1751)+P11(f7(x1751,x1752,x1753,x1754),x1753,x1751)+P1(f6(x1751,x1752)) % 0.54/0.64 [177]~P1(x1774)+~P1(x1773)+~P5(x1772)+~P5(x1771)+~P3(f6(x1771,x1772),f29(x1771,x1772))+P1(f7(x1771,x1772,x1773,x1774)) % 0.54/0.64 [178]~P1(x1784)+~P1(x1783)+~P5(x1782)+~P5(x1781)+P11(f7(x1781,x1782,x1783,x1784),x1784,x1782)+~P3(f6(x1781,x1782),f29(x1781,x1782)) % 0.54/0.64 [179]~P1(x1794)+~P1(x1793)+~P5(x1792)+~P5(x1791)+P11(f7(x1791,x1792,x1793,x1794),x1793,x1791)+~P3(f6(x1791,x1792),f29(x1791,x1792)) % 0.54/0.64 [176]~P4(x1761)+~P4(x1763)+~P4(x1762)+~P3(f25(x1762,x1763,x1761),x1761)+~P3(f25(x1762,x1763,x1761),x1763)+~P3(f25(x1762,x1763,x1761),x1762)+E(x1761,f26(x1762,x1763)) % 0.54/0.64 [148]~P4(x1484)+~P4(x1483)+~P3(x1486,x1484)+~P3(x1485,x1483)+P3(x1481,x1482)+~E(x1482,f29(x1483,x1484))+~E(f28(x1485,x1486),x1481) % 0.54/0.64 [169]~P4(x1691)+~P4(x1693)+~P4(x1692)+~P3(x1695,x1693)+~P3(x1694,x1692)+~P3(f20(x1692,x1693,x1691),x1691)+E(x1691,f29(x1692,x1693))+~E(f28(x1694,x1695),f20(x1692,x1693,x1691)) % 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(f16(x41,x43),f16(x42,x43)) % 0.54/0.64 [5]~E(x51,x52)+E(f16(x53,x51),f16(x53,x52)) % 0.54/0.64 [6]~E(x61,x62)+E(f29(x61,x63),f29(x62,x63)) % 0.54/0.64 [7]~E(x71,x72)+E(f29(x73,x71),f29(x73,x72)) % 0.54/0.64 [8]~E(x81,x82)+E(f27(x81),f27(x82)) % 0.54/0.64 [9]~E(x91,x92)+E(f24(x91,x93,x94),f24(x92,x93,x94)) % 0.54/0.64 [10]~E(x101,x102)+E(f24(x103,x101,x104),f24(x103,x102,x104)) % 0.54/0.64 [11]~E(x111,x112)+E(f24(x113,x114,x111),f24(x113,x114,x112)) % 0.54/0.64 [12]~E(x121,x122)+E(f30(x121),f30(x122)) % 0.54/0.64 [13]~E(x131,x132)+E(f17(x131),f17(x132)) % 0.54/0.64 [14]~E(x141,x142)+E(f28(x141,x143),f28(x142,x143)) % 0.54/0.64 [15]~E(x151,x152)+E(f28(x153,x151),f28(x153,x152)) % 0.54/0.64 [16]~E(x161,x162)+E(f22(x161,x163,x164,x165),f22(x162,x163,x164,x165)) % 0.54/0.64 [17]~E(x171,x172)+E(f22(x173,x171,x174,x175),f22(x173,x172,x174,x175)) % 0.54/0.64 [18]~E(x181,x182)+E(f22(x183,x184,x181,x185),f22(x183,x184,x182,x185)) % 0.54/0.64 [19]~E(x191,x192)+E(f22(x193,x194,x195,x191),f22(x193,x194,x195,x192)) % 0.54/0.64 [20]~E(x201,x202)+E(f20(x201,x203,x204),f20(x202,x203,x204)) % 0.54/0.64 [21]~E(x211,x212)+E(f20(x213,x211,x214),f20(x213,x212,x214)) % 0.54/0.64 [22]~E(x221,x222)+E(f20(x223,x224,x221),f20(x223,x224,x222)) % 0.54/0.64 [23]~E(x231,x232)+E(f13(x231,x233,x234),f13(x232,x233,x234)) % 0.54/0.64 [24]~E(x241,x242)+E(f13(x243,x241,x244),f13(x243,x242,x244)) % 0.54/0.64 [25]~E(x251,x252)+E(f13(x253,x254,x251),f13(x253,x254,x252)) % 0.54/0.64 [26]~E(x261,x262)+E(f21(x261,x263,x264,x265),f21(x262,x263,x264,x265)) % 0.54/0.64 [27]~E(x271,x272)+E(f21(x273,x271,x274,x275),f21(x273,x272,x274,x275)) % 0.54/0.64 [28]~E(x281,x282)+E(f21(x283,x284,x281,x285),f21(x283,x284,x282,x285)) % 0.54/0.64 [29]~E(x291,x292)+E(f21(x293,x294,x295,x291),f21(x293,x294,x295,x292)) % 0.54/0.64 [30]~E(x301,x302)+E(f18(x301),f18(x302)) % 0.54/0.64 [31]~E(x311,x312)+E(f6(x311,x313),f6(x312,x313)) % 0.54/0.64 [32]~E(x321,x322)+E(f6(x323,x321),f6(x323,x322)) % 0.54/0.64 [33]~E(x331,x332)+E(f14(x331,x333),f14(x332,x333)) % 0.54/0.64 [34]~E(x341,x342)+E(f14(x343,x341),f14(x343,x342)) % 0.54/0.64 [35]~E(x351,x352)+E(f25(x351,x353,x354),f25(x352,x353,x354)) % 0.54/0.64 [36]~E(x361,x362)+E(f25(x363,x361,x364),f25(x363,x362,x364)) % 0.54/0.64 [37]~E(x371,x372)+E(f25(x373,x374,x371),f25(x373,x374,x372)) % 0.54/0.64 [38]~E(x381,x382)+E(f12(x381,x383,x384),f12(x382,x383,x384)) % 0.54/0.64 [39]~E(x391,x392)+E(f12(x393,x391,x394),f12(x393,x392,x394)) % 0.54/0.64 [40]~E(x401,x402)+E(f12(x403,x404,x401),f12(x403,x404,x402)) % 0.54/0.64 [41]~E(x411,x412)+E(f3(x411),f3(x412)) % 0.54/0.64 [42]~E(x421,x422)+E(f19(x421,x423),f19(x422,x423)) % 0.54/0.64 [43]~E(x431,x432)+E(f19(x433,x431),f19(x433,x432)) % 0.54/0.64 [44]~E(x441,x442)+E(f4(x441),f4(x442)) % 0.54/0.64 [45]~E(x451,x452)+E(f7(x451,x453,x454,x455),f7(x452,x453,x454,x455)) % 0.54/0.64 [46]~E(x461,x462)+E(f7(x463,x461,x464,x465),f7(x463,x462,x464,x465)) % 0.54/0.64 [47]~E(x471,x472)+E(f7(x473,x474,x471,x475),f7(x473,x474,x472,x475)) % 0.54/0.64 [48]~E(x481,x482)+E(f7(x483,x484,x485,x481),f7(x483,x484,x485,x482)) % 0.54/0.64 [49]~E(x491,x492)+E(f26(x491,x493),f26(x492,x493)) % 0.54/0.64 [50]~E(x501,x502)+E(f26(x503,x501),f26(x503,x502)) % 0.54/0.64 [51]~E(x511,x512)+E(f11(x511,x513),f11(x512,x513)) % 0.54/0.64 [52]~E(x521,x522)+E(f11(x523,x521),f11(x523,x522)) % 0.54/0.64 [53]~E(x531,x532)+E(f8(x531,x533),f8(x532,x533)) % 0.54/0.64 [54]~E(x541,x542)+E(f8(x543,x541),f8(x543,x542)) % 0.54/0.64 [55]~E(x551,x552)+E(f10(x551,x553),f10(x552,x553)) % 0.54/0.64 [56]~E(x561,x562)+E(f10(x563,x561),f10(x563,x562)) % 0.54/0.64 [57]~E(x571,x572)+E(f9(x571,x573),f9(x572,x573)) % 0.54/0.64 [58]~E(x581,x582)+E(f9(x583,x581),f9(x583,x582)) % 0.54/0.64 [59]~E(x591,x592)+E(f5(x591,x593),f5(x592,x593)) % 0.54/0.64 [60]~E(x601,x602)+E(f5(x603,x601),f5(x603,x602)) % 0.54/0.64 [61]~E(x611,x612)+E(f23(x611,x613,x614),f23(x612,x613,x614)) % 0.54/0.64 [62]~E(x621,x622)+E(f23(x623,x621,x624),f23(x623,x622,x624)) % 0.54/0.64 [63]~E(x631,x632)+E(f23(x633,x634,x631),f23(x633,x634,x632)) % 0.54/0.64 [64]~P1(x641)+P1(x642)+~E(x641,x642) % 0.54/0.64 [65]P3(x652,x653)+~E(x651,x652)+~P3(x651,x653) % 0.54/0.64 [66]P3(x663,x662)+~E(x661,x662)+~P3(x663,x661) % 0.54/0.64 [67]~P4(x671)+P4(x672)+~E(x671,x672) % 0.54/0.64 [68]P10(x682,x683)+~E(x681,x682)+~P10(x681,x683) % 0.54/0.64 [69]P10(x693,x692)+~E(x691,x692)+~P10(x693,x691) % 0.54/0.64 [70]~P5(x701)+P5(x702)+~E(x701,x702) % 0.54/0.64 [71]P2(x712,x713)+~E(x711,x712)+~P2(x711,x713) % 0.54/0.64 [72]P2(x723,x722)+~E(x721,x722)+~P2(x723,x721) % 0.54/0.64 [73]P11(x732,x733,x734)+~E(x731,x732)+~P11(x731,x733,x734) % 0.54/0.64 [74]P11(x743,x742,x744)+~E(x741,x742)+~P11(x743,x741,x744) % 0.54/0.64 [75]P11(x753,x754,x752)+~E(x751,x752)+~P11(x753,x754,x751) % 0.54/0.64 [76]P6(x762,x763,x764)+~E(x761,x762)+~P6(x761,x763,x764) % 0.54/0.64 [77]P6(x773,x772,x774)+~E(x771,x772)+~P6(x773,x771,x774) % 0.54/0.64 [78]P6(x783,x784,x782)+~E(x781,x782)+~P6(x783,x784,x781) % 0.54/0.64 [79]P9(x792,x793)+~E(x791,x792)+~P9(x791,x793) % 0.54/0.64 [80]P9(x803,x802)+~E(x801,x802)+~P9(x803,x801) % 0.54/0.64 [81]P8(x812,x813)+~E(x811,x812)+~P8(x811,x813) % 0.54/0.64 [82]P8(x823,x822)+~E(x821,x822)+~P8(x823,x821) % 0.54/0.64 [83]~P7(x831)+P7(x832)+~E(x831,x832) % 0.54/0.64 % 0.54/0.64 %------------------------------------------- % 0.54/0.64 cnf(193,plain, % 0.54/0.64 ($false), % 0.54/0.64 inference(scs_inference,[],[88,90,105]), % 0.54/0.64 ['proof']). % 0.54/0.64 % SZS output end Proof % 0.54/0.64 % Total time :0.010000s %------------------------------------------------------------------------------