0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : java -jar mcs_epr.jar %d %s 0.02/0.23 % Computer : n014.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 05:09:25 CDT 2018 0.02/0.23 % CPUTime : 0.02/0.30 openjdk version "1.8.0_144" 0.02/0.30 OpenJDK Runtime Environment (build 1.8.0_144-b01) 0.02/0.30 OpenJDK 64-Bit Server VM (build 25.144-b01, mixed mode) 0.14/0.42 start to proof:theBenchmark.p 84.04/84.19 % Version : CSE_E---1.0 84.04/84.19 % Problem : theBenchmark.p 84.04/84.19 % Proof found! 84.04/84.19 % SZS status Theorem for theBenchmark.p 84.04/84.19 % SZS output start Proof 84.04/84.19 fof(mDimNat, axiom, (![X1]:(aNaturalNumber0(aDimensionOf0(X1))<=aVector0(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mDimNat)). 84.04/84.19 fof(mNatExtr, axiom, (![X1]:(?[X2]:(X1=szszuzczcdt0(X2)&aNaturalNumber0(X2))<=(aNaturalNumber0(X1)&sz00!=X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mNatExtr)). 84.04/84.19 fof(m__1542, hypothesis, (aVector0(xs)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', m__1542)). 84.04/84.19 fof(mElmSc, axiom, (![X1]:![X2]:((aNaturalNumber0(X2)&aVector0(X1))=>aScalar0(sdtlbdtrb0(X1,X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mElmSc)). 84.04/84.19 fof(m__1542_01, hypothesis, (aDimensionOf0(xs)!=sz00), file('/export/starexec/sandbox/benchmark/theBenchmark.p', m__1542_01)). 84.04/84.19 fof(mSuccEqu, axiom, (![X1]:![X2]:((aNaturalNumber0(X2)&aNaturalNumber0(X1))=>(X1=X2<=szszuzczcdt0(X1)=szszuzczcdt0(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mSuccEqu)). 84.04/84.19 fof(m__1568, hypothesis, ((((((szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))=aDimensionOf0(xs)&aVector0(sziznziztdt0(xs)))&![X1]:(aNaturalNumber0(X1)=>sdtlbdtrb0(sziznziztdt0(xs),X1)=sdtlbdtrb0(xs,X1)))&szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))=aDimensionOf0(xs))&![X1]:(aNaturalNumber0(X1)=>sdtlbdtrb0(sziznziztdt0(xs),X1)=sdtlbdtrb0(xs,X1)))&aVector0(sziznziztdt0(xs)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', m__1568)). 84.04/84.19 fof(m__1590, hypothesis, (((((((aVector0(sziznziztdt0(xs))&aDimensionOf0(xs)=szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))))&![X1]:(sdtlbdtrb0(xs,X1)=sdtlbdtrb0(sziznziztdt0(xs),X1)<=aNaturalNumber0(X1)))&aVector0(sziznziztdt0(xs)))&aDimensionOf0(xs)=szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))))&![X1]:(sdtlbdtrb0(sziznziztdt0(xs),X1)=sdtlbdtrb0(xs,X1)<=aNaturalNumber0(X1)))&sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', m__1590)). 84.04/84.19 fof(mSumSc, axiom, (![X1]:![X2]:((aScalar0(X1)&aScalar0(X2))=>aScalar0(sdtpldt0(X1,X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mSumSc)). 84.04/84.19 fof(mNegSc, axiom, (![X1]:(aScalar0(smndt0(X1))<=aScalar0(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mNegSc)). 84.04/84.19 fof(mArith, axiom, (![X1]:![X2]:![X3]:(((aScalar0(X1)&aScalar0(X3))&aScalar0(X2))=>(((sdtpldt0(sdtpldt0(X1,X2),X3)=sdtpldt0(X1,sdtpldt0(X2,X3))&sdtpldt0(X2,X1)=sdtpldt0(X1,X2))&sdtasdt0(sdtasdt0(X1,X2),X3)=sdtasdt0(X1,sdtasdt0(X2,X3)))&sdtasdt0(X2,X1)=sdtasdt0(X1,X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mArith)). 84.04/84.19 fof(mSZeroSc, axiom, (aScalar0(sz0z00)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mSZeroSc)). 84.04/84.19 fof(mMulSc, axiom, (![X1]:![X2]:((aScalar0(X2)&aScalar0(X1))=>aScalar0(sdtasdt0(X1,X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mMulSc)). 84.04/84.19 fof(mScZero, axiom, (![X1]:((((((((X1=sdtpldt0(X1,sz0z00)&sz0z00=sdtasdt0(sz0z00,X1))&sz0z00=smndt0(sz0z00))&smndt0(smndt0(X1))=X1)&sdtpldt0(smndt0(X1),X1)=sz0z00)&sdtpldt0(X1,smndt0(X1))=sz0z00)&sz0z00=sdtasdt0(X1,sz0z00))&sdtpldt0(sz0z00,X1)=X1)<=aScalar0(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mScZero)). 84.04/84.19 fof(mLEMon, axiom, (![X1]:![X2]:![X3]:![X4]:(((sdtlseqdt0(X3,X4)&sdtlseqdt0(X1,X2))=>sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4)))<=(((aScalar0(X2)&aScalar0(X3))&aScalar0(X4))&aScalar0(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mLEMon)). 84.04/84.19 fof(mIH, axiom, (![X1]:(aNaturalNumber0(X1)=>iLess0(X1,szszuzczcdt0(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mIH)). 84.04/84.19 fof(mDefSPN, axiom, (![X1]:![X2]:((sdtasasdt0(X1,X2)=sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2))))<=(sz00!=aDimensionOf0(X2)&aDimensionOf0(X2)=aDimensionOf0(X1)))<=(aVector0(X1)&aVector0(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mDefSPN)). 84.04/84.19 fof(mScPr, axiom, (![X1]:![X2]:((aScalar0(sdtasasdt0(X1,X2))<=aDimensionOf0(X2)=aDimensionOf0(X1))<=(aVector0(X1)&aVector0(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mScPr)). 84.04/84.19 fof(m__1516, hypothesis, (![X1]:((iLess0(aDimensionOf0(X1),aDimensionOf0(xs))=>sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)))<=aVector0(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', m__1516)). 84.04/84.19 fof(m__, conjecture, (sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', m__)). 84.04/84.19 fof(c_0_20, plain, (![X2]:(~aVector0(X2)|aNaturalNumber0(aDimensionOf0(X2)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mDimNat])])])). 84.04/84.19 fof(c_0_21, plain, (![X3]:((X3=szszuzczcdt0(esk2_1(X3))|(~aNaturalNumber0(X3)|sz00=X3))&(aNaturalNumber0(esk2_1(X3))|(~aNaturalNumber0(X3)|sz00=X3)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mNatExtr])])])])])])])). 84.04/84.19 cnf(c_0_22,plain,(aNaturalNumber0(aDimensionOf0(X1))|~aVector0(X1)), inference(split_conjunct,[status(thm)],[c_0_20])). 84.04/84.19 cnf(c_0_23,hypothesis,(aVector0(xs)), inference(split_conjunct,[status(thm)],[m__1542])). 84.04/84.19 fof(c_0_24, plain, (![X3]:![X4]:((~aNaturalNumber0(X4)|~aVector0(X3))|aScalar0(sdtlbdtrb0(X3,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mElmSc])])). 84.04/84.19 cnf(c_0_25,plain,(sz00=X1|aNaturalNumber0(esk2_1(X1))|~aNaturalNumber0(X1)), inference(split_conjunct,[status(thm)],[c_0_21])). 84.04/84.19 cnf(c_0_26,hypothesis,(aNaturalNumber0(aDimensionOf0(xs))), inference(spm,[status(thm)],[c_0_22, c_0_23])). 84.04/84.19 cnf(c_0_27,hypothesis,(aDimensionOf0(xs)!=sz00), inference(split_conjunct,[status(thm)],[m__1542_01])). 84.04/84.19 fof(c_0_28, plain, (![X3]:![X4]:((~aNaturalNumber0(X4)|~aNaturalNumber0(X3))|(szszuzczcdt0(X3)!=szszuzczcdt0(X4)|X3=X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mSuccEqu])])])). 84.04/84.19 cnf(c_0_29,plain,(sz00=X1|X1=szszuzczcdt0(esk2_1(X1))|~aNaturalNumber0(X1)), inference(split_conjunct,[status(thm)],[c_0_21])). 84.04/84.19 fof(c_0_30, hypothesis, (![X2]:![X3]:(((((szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))=aDimensionOf0(xs)&aVector0(sziznziztdt0(xs)))&(~aNaturalNumber0(X2)|sdtlbdtrb0(sziznziztdt0(xs),X2)=sdtlbdtrb0(xs,X2)))&szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))=aDimensionOf0(xs))&(~aNaturalNumber0(X3)|sdtlbdtrb0(sziznziztdt0(xs),X3)=sdtlbdtrb0(xs,X3)))&aVector0(sziznziztdt0(xs)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1568])])])])])). 84.04/84.19 cnf(c_0_31,plain,(aScalar0(sdtlbdtrb0(X1,X2))|~aVector0(X1)|~aNaturalNumber0(X2)), inference(split_conjunct,[status(thm)],[c_0_24])). 84.04/84.19 cnf(c_0_32,hypothesis,(aNaturalNumber0(esk2_1(aDimensionOf0(xs)))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_27])). 84.04/84.19 cnf(c_0_33,plain,(X1=X2|szszuzczcdt0(X1)!=szszuzczcdt0(X2)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)), inference(split_conjunct,[status(thm)],[c_0_28])). 84.04/84.19 cnf(c_0_34,hypothesis,(szszuzczcdt0(esk2_1(aDimensionOf0(xs)))=aDimensionOf0(xs)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_26]), c_0_27])). 84.04/84.19 fof(c_0_35, hypothesis, (![X2]:![X3]:((((((aVector0(sziznziztdt0(xs))&aDimensionOf0(xs)=szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))))&(~aNaturalNumber0(X2)|sdtlbdtrb0(xs,X2)=sdtlbdtrb0(sziznziztdt0(xs),X2)))&aVector0(sziznziztdt0(xs)))&aDimensionOf0(xs)=szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))))&(~aNaturalNumber0(X3)|sdtlbdtrb0(sziznziztdt0(xs),X3)=sdtlbdtrb0(xs,X3)))&sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[m__1590])])])])])])). 84.04/84.19 cnf(c_0_36,hypothesis,(aVector0(sziznziztdt0(xs))), inference(split_conjunct,[status(thm)],[c_0_30])). 84.04/84.19 cnf(c_0_37,hypothesis,(aScalar0(sdtlbdtrb0(X1,esk2_1(aDimensionOf0(xs))))|~aVector0(X1)), inference(spm,[status(thm)],[c_0_31, c_0_32])). 84.04/84.19 cnf(c_0_38,hypothesis,(X1=esk2_1(aDimensionOf0(xs))|szszuzczcdt0(X1)!=aDimensionOf0(xs)|~aNaturalNumber0(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_32]), c_0_34])). 84.04/84.19 cnf(c_0_39,hypothesis,(aDimensionOf0(xs)=szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))), inference(split_conjunct,[status(thm)],[c_0_35])). 84.04/84.19 cnf(c_0_40,hypothesis,(aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))), inference(spm,[status(thm)],[c_0_22, c_0_36])). 84.04/84.19 fof(c_0_41, plain, (![X3]:![X4]:((~aScalar0(X3)|~aScalar0(X4))|aScalar0(sdtpldt0(X3,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])])). 84.04/84.19 fof(c_0_42, plain, (![X2]:(~aScalar0(X2)|aScalar0(smndt0(X2)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mNegSc])])])). 84.04/84.19 cnf(c_0_43,hypothesis,(aScalar0(sdtlbdtrb0(xs,esk2_1(aDimensionOf0(xs))))), inference(spm,[status(thm)],[c_0_37, c_0_23])). 84.04/84.19 cnf(c_0_44,hypothesis,(esk2_1(aDimensionOf0(xs))=aDimensionOf0(sziznziztdt0(xs))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_40])])). 84.04/84.19 fof(c_0_45, plain, (![X4]:![X5]:![X6]:((((sdtpldt0(sdtpldt0(X4,X5),X6)=sdtpldt0(X4,sdtpldt0(X5,X6))|((~aScalar0(X4)|~aScalar0(X6))|~aScalar0(X5)))&(sdtpldt0(X5,X4)=sdtpldt0(X4,X5)|((~aScalar0(X4)|~aScalar0(X6))|~aScalar0(X5))))&(sdtasdt0(sdtasdt0(X4,X5),X6)=sdtasdt0(X4,sdtasdt0(X5,X6))|((~aScalar0(X4)|~aScalar0(X6))|~aScalar0(X5))))&(sdtasdt0(X5,X4)=sdtasdt0(X4,X5)|((~aScalar0(X4)|~aScalar0(X6))|~aScalar0(X5))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])])). 84.04/84.19 cnf(c_0_46,plain,(aScalar0(sdtpldt0(X1,X2))|~aScalar0(X2)|~aScalar0(X1)), inference(split_conjunct,[status(thm)],[c_0_41])). 84.04/84.19 cnf(c_0_47,plain,(aScalar0(sz0z00)), inference(split_conjunct,[status(thm)],[mSZeroSc])). 84.04/84.19 cnf(c_0_48,plain,(aScalar0(smndt0(X1))|~aScalar0(X1)), inference(split_conjunct,[status(thm)],[c_0_42])). 84.04/84.19 cnf(c_0_49,hypothesis,(aScalar0(sdtlbdtrb0(xs,aDimensionOf0(sziznziztdt0(xs))))), inference(rw,[status(thm)],[c_0_43, c_0_44])). 84.04/84.19 cnf(c_0_50,plain,(sdtpldt0(X1,X3)=sdtpldt0(X3,X1)|~aScalar0(X1)|~aScalar0(X2)|~aScalar0(X3)), inference(split_conjunct,[status(thm)],[c_0_45])). 84.04/84.19 cnf(c_0_51,plain,(aScalar0(sdtpldt0(X1,sz0z00))|~aScalar0(X1)), inference(spm,[status(thm)],[c_0_46, c_0_47])). 84.04/84.19 cnf(c_0_52,hypothesis,(aScalar0(smndt0(sdtlbdtrb0(xs,aDimensionOf0(sziznziztdt0(xs)))))), inference(spm,[status(thm)],[c_0_48, c_0_49])). 84.04/84.19 cnf(c_0_53,hypothesis,(aScalar0(sdtlbdtrb0(X1,aDimensionOf0(xs)))|~aVector0(X1)), inference(spm,[status(thm)],[c_0_31, c_0_26])). 84.04/84.19 cnf(c_0_54,plain,(sdtpldt0(X1,sz0z00)=sdtpldt0(sz0z00,X1)|~aScalar0(X2)|~aScalar0(X1)), inference(spm,[status(thm)],[c_0_50, c_0_47])). 84.04/84.19 cnf(c_0_55,hypothesis,(aScalar0(sdtpldt0(smndt0(sdtlbdtrb0(xs,aDimensionOf0(sziznziztdt0(xs)))),sz0z00))), inference(spm,[status(thm)],[c_0_51, c_0_52])). 84.04/84.19 cnf(c_0_56,hypothesis,(aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))), inference(spm,[status(thm)],[c_0_53, c_0_23])). 84.04/84.19 cnf(c_0_57,hypothesis,(sdtpldt0(X1,sz0z00)=sdtpldt0(sz0z00,X1)|~aScalar0(X1)), inference(spm,[status(thm)],[c_0_54, c_0_55])). 84.04/84.19 cnf(c_0_58,hypothesis,(aScalar0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sz0z00))), inference(spm,[status(thm)],[c_0_51, c_0_56])). 84.04/84.19 cnf(c_0_59,hypothesis,(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sz0z00)=sdtpldt0(sz0z00,sdtlbdtrb0(xs,aDimensionOf0(xs)))), inference(spm,[status(thm)],[c_0_57, c_0_56])). 84.04/84.19 cnf(c_0_60,hypothesis,(aScalar0(sdtpldt0(sz0z00,sdtlbdtrb0(xs,aDimensionOf0(xs))))), inference(rw,[status(thm)],[c_0_58, c_0_59])). 84.04/84.19 fof(c_0_61, plain, (![X3]:![X4]:((~aScalar0(X4)|~aScalar0(X3))|aScalar0(sdtasdt0(X3,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])])). 84.04/84.19 cnf(c_0_62,hypothesis,(aScalar0(sdtpldt0(X1,sdtpldt0(sz0z00,sdtlbdtrb0(xs,aDimensionOf0(xs)))))|~aScalar0(X1)), inference(spm,[status(thm)],[c_0_46, c_0_60])). 84.04/84.19 fof(c_0_63, plain, (![X2]:((((((((X2=sdtpldt0(X2,sz0z00)|~aScalar0(X2))&(sz0z00=sdtasdt0(sz0z00,X2)|~aScalar0(X2)))&(sz0z00=smndt0(sz0z00)|~aScalar0(X2)))&(smndt0(smndt0(X2))=X2|~aScalar0(X2)))&(sdtpldt0(smndt0(X2),X2)=sz0z00|~aScalar0(X2)))&(sdtpldt0(X2,smndt0(X2))=sz0z00|~aScalar0(X2)))&(sz0z00=sdtasdt0(X2,sz0z00)|~aScalar0(X2)))&(sdtpldt0(sz0z00,X2)=X2|~aScalar0(X2)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mScZero])])])])). 84.04/84.19 cnf(c_0_64,plain,(aScalar0(sdtasdt0(X1,X2))|~aScalar0(X1)|~aScalar0(X2)), inference(split_conjunct,[status(thm)],[c_0_61])). 84.04/84.19 cnf(c_0_65,hypothesis,(aScalar0(sdtpldt0(sz0z00,sdtpldt0(sz0z00,sdtlbdtrb0(xs,aDimensionOf0(xs)))))), inference(spm,[status(thm)],[c_0_62, c_0_47])). 84.04/84.19 cnf(c_0_66,plain,(X1=sdtpldt0(X1,sz0z00)|~aScalar0(X1)), inference(split_conjunct,[status(thm)],[c_0_63])). 84.04/84.19 fof(c_0_67, plain, (![X5]:![X6]:![X7]:![X8]:((((~aScalar0(X6)|~aScalar0(X7))|~aScalar0(X8))|~aScalar0(X5))|((~sdtlseqdt0(X7,X8)|~sdtlseqdt0(X5,X6))|sdtlseqdt0(sdtpldt0(X5,X7),sdtpldt0(X6,X8))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mLEMon])])])). 84.04/84.19 cnf(c_0_68,hypothesis,(aScalar0(sdtasdt0(X1,sdtpldt0(sz0z00,sdtpldt0(sz0z00,sdtlbdtrb0(xs,aDimensionOf0(xs))))))|~aScalar0(X1)), inference(spm,[status(thm)],[c_0_64, c_0_65])). 84.04/84.19 cnf(c_0_69,hypothesis,(sdtpldt0(sz0z00,sdtlbdtrb0(xs,aDimensionOf0(xs)))=sdtlbdtrb0(xs,aDimensionOf0(xs))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_56]), c_0_59])). 84.04/84.19 fof(c_0_70, plain, (![X2]:(~aNaturalNumber0(X2)|iLess0(X2,szszuzczcdt0(X2)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH])])). 84.04/84.19 fof(c_0_71, plain, (![X3]:![X4]:((~aVector0(X3)|~aVector0(X4))|((sz00=aDimensionOf0(X4)|aDimensionOf0(X4)!=aDimensionOf0(X3))|sdtasasdt0(X3,X4)=sdtpldt0(sdtasasdt0(sziznziztdt0(X3),sziznziztdt0(X4)),sdtasdt0(sdtlbdtrb0(X3,aDimensionOf0(X3)),sdtlbdtrb0(X4,aDimensionOf0(X4))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mDefSPN])])])). 84.04/84.19 fof(c_0_72, plain, (![X3]:![X4]:((~aVector0(X3)|~aVector0(X4))|(aDimensionOf0(X4)!=aDimensionOf0(X3)|aScalar0(sdtasasdt0(X3,X4))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mScPr])])])). 84.04/84.19 cnf(c_0_73,plain,(sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4))|~sdtlseqdt0(X1,X3)|~sdtlseqdt0(X2,X4)|~aScalar0(X1)|~aScalar0(X4)|~aScalar0(X2)|~aScalar0(X3)), inference(split_conjunct,[status(thm)],[c_0_67])). 84.04/84.19 cnf(c_0_74,hypothesis,(sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))), inference(split_conjunct,[status(thm)],[c_0_35])). 84.04/84.19 cnf(c_0_75,hypothesis,(aScalar0(sdtasdt0(X1,sdtlbdtrb0(xs,aDimensionOf0(xs))))|~aScalar0(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68, c_0_69]), c_0_69])). 84.04/84.19 fof(c_0_76, hypothesis, (![X2]:(~aVector0(X2)|(~iLess0(aDimensionOf0(X2),aDimensionOf0(xs))|sdtlseqdt0(sz0z00,sdtasasdt0(X2,X2))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[m__1516])])])). 84.04/84.19 cnf(c_0_77,plain,(iLess0(X1,szszuzczcdt0(X1))|~aNaturalNumber0(X1)), inference(split_conjunct,[status(thm)],[c_0_70])). 84.04/84.19 cnf(c_0_78,plain,(sdtasasdt0(X1,X2)=sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2))))|sz00=aDimensionOf0(X2)|aDimensionOf0(X2)!=aDimensionOf0(X1)|~aVector0(X2)|~aVector0(X1)), inference(split_conjunct,[status(thm)],[c_0_71])). 84.04/84.19 cnf(c_0_79,plain,(aScalar0(sdtasasdt0(X1,X2))|aDimensionOf0(X2)!=aDimensionOf0(X1)|~aVector0(X2)|~aVector0(X1)), inference(split_conjunct,[status(thm)],[c_0_72])). 84.04/84.19 fof(c_0_80, negated_conjecture, (~(sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)))), inference(assume_negation,[status(cth)],[m__])). 84.04/84.19 cnf(c_0_81,hypothesis,(sdtlseqdt0(sdtpldt0(X1,sz0z00),sdtpldt0(X2,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))|~sdtlseqdt0(X1,X2)|~aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))|~aScalar0(X2)|~aScalar0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_74]), c_0_47])])). 84.04/84.19 cnf(c_0_82,hypothesis,(aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))), inference(spm,[status(thm)],[c_0_75, c_0_56])). 84.04/84.19 cnf(c_0_83,hypothesis,(sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))|~iLess0(aDimensionOf0(X1),aDimensionOf0(xs))|~aVector0(X1)), inference(split_conjunct,[status(thm)],[c_0_76])). 84.04/84.19 cnf(c_0_84,hypothesis,(iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_40]), c_0_39])). 84.04/84.19 cnf(c_0_85,hypothesis,(sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(xs,aDimensionOf0(xs))))=sdtasasdt0(X1,xs)|aDimensionOf0(X1)!=aDimensionOf0(xs)|~aVector0(X1)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_23]), c_0_27])). 84.04/84.19 cnf(c_0_86,hypothesis,(aScalar0(sdtasasdt0(X1,sziznziztdt0(xs)))|aDimensionOf0(X1)!=aDimensionOf0(sziznziztdt0(xs))|~aVector0(X1)), inference(spm,[status(thm)],[c_0_79, c_0_36])). 84.04/84.19 fof(c_0_87, negated_conjecture, (~sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))), inference(fof_simplification,[status(thm)],[c_0_80])). 84.04/84.19 cnf(c_0_88,hypothesis,(sdtlseqdt0(sdtpldt0(X1,sz0z00),sdtpldt0(X2,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))|~sdtlseqdt0(X1,X2)|~aScalar0(X2)|~aScalar0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81, c_0_82])])). 84.04/84.19 cnf(c_0_89,hypothesis,(sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84]), c_0_36])])). 84.04/84.19 cnf(c_0_90,plain,(sdtpldt0(sz0z00,sz0z00)=sz0z00), inference(spm,[status(thm)],[c_0_66, c_0_47])). 84.04/84.19 cnf(c_0_91,hypothesis,(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))=sdtasasdt0(xs,xs)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_85]), c_0_23])])). 84.04/84.19 cnf(c_0_92,hypothesis,(aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_86]), c_0_36])])). 84.04/84.19 cnf(c_0_93,negated_conjecture,(~sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))), inference(split_conjunct,[status(thm)],[c_0_87])). 84.04/84.19 cnf(c_0_94,hypothesis,($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_90]), c_0_91]), c_0_92]), c_0_47])]), c_0_93]), ['proof']). 84.04/84.19 % SZS output end Proof 84.04/84.19 % User time : 82.124 s 84.04/84.19 % System time : 1.557 s 84.04/84.19 % Total time : 83.681 s 84.04/84.19 84.15/84.20 EOF