%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM529+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:26 PM UTC 2026
% Result : ContradictoryAxioms 1.95s 0.67s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 87 ( 33 unt; 0 def)
% Number of atoms : 415 ( 182 equ)
% Maximal formula atoms : 69 ( 4 avg)
% Number of connectives : 508 ( 180 ~; 197 |; 96 &)
% ( 3 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 111 ( 0 sgn 60 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__3046,hypothesis,
( doDivides0(xp,xn)
& ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(m__3059,hypothesis,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(m__3124,hypothesis,
( sdtlseqdt0(xm,xn)
& ? [X1] :
( sdtpldt0(xm,X1) = xn
& aNaturalNumber0(X1) )
& xm != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3124) ).
fof(m__2963,hypothesis,
! [X1,X2,X3] :
( ( X3 != sz00
& X2 != sz00
& X1 != sz00
& aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X3,sdtasdt0(X2,X2)) = sdtasdt0(X1,X1)
=> ( iLess0(X1,xn)
=> ~ ( isPrime0(X3)
| ( ! [X4] :
( ( doDivides0(X4,X3)
& ? [X5] :
( X3 = sdtasdt0(X4,X5)
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
=> ( X4 = X3
| X4 = sz10 ) )
& X3 != sz10 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2963) ).
fof(m__3025,hypothesis,
( isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(c_0_17,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
fof(c_0_18,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[mMulCanc]) ).
fof(c_0_19,plain,
! [X9,X10] :
( aNaturalNumber0(sdtasdt0(X9,X10))
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_20,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X30,X31,X32] :
( ( ~ aNaturalNumber0(X30)
| X30 = sz00
| ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| X31 = X32
| sdtasdt0(X31,X30) != sdtasdt0(X32,X30) )
& ( ~ aNaturalNumber0(X30)
| X30 = sz00
| ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| X31 = X32
| sdtasdt0(X30,X31) != sdtasdt0(X30,X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).
fof(c_0_22,hypothesis,
( doDivides0(xp,xn)
& xn = sdtasdt0(xp,esk8_0)
& aNaturalNumber0(esk8_0)
& doDivides0(xp,sdtasdt0(xn,xn))
& sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0)
& aNaturalNumber0(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__3046])]) ).
cnf(c_0_23,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X65,X66,X68] :
( ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| doDivides0(X65,X66)
| X66 != sdtasdt0(X65,X68)
| ~ aNaturalNumber0(X68) )
& ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| ~ doDivides0(X65,X66)
| X66 = sdtasdt0(X65,esk2_2(X65,X66)) )
& ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| ~ doDivides0(X65,X66)
| aNaturalNumber0(esk2_2(X65,X66)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])])]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,hypothesis,
sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
fof(c_0_33,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
cnf(c_0_34,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_35,plain,
! [X19,X20,X21] :
( sdtasdt0(sdtasdt0(X19,X20),X21) = sdtasdt0(X19,sdtasdt0(X20,X21))
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ aNaturalNumber0(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_36,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,X1) != sdtasdt0(xn,xn)
| X1 = esk7_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_25])]),c_0_30]) ).
cnf(c_0_37,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_23]),c_0_32])]) ).
fof(c_0_39,plain,
! [X69,X70,X71] :
( ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 = sdtsldt0(X70,X69)
| X70 != sdtasdt0(X69,X71)
| ~ aNaturalNumber0(X71) )
& ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 != sdtsldt0(X70,X69)
| X70 = sdtasdt0(X69,X71) )
& ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 != sdtsldt0(X70,X69)
| aNaturalNumber0(X71) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])])]) ).
cnf(c_0_40,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_23]) ).
cnf(c_0_41,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,hypothesis,
sdtasdt0(xm,xm) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_43,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| X3 = sz00
| X1 = sdtsldt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_44,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mIH_03]) ).
fof(c_0_45,hypothesis,
( sdtlseqdt0(xm,xn)
& ? [X1] :
( sdtpldt0(xm,X1) = xn
& aNaturalNumber0(X1) )
& xm != xn ),
inference(fof_simplification,[status(thm)],[m__3124]) ).
cnf(c_0_46,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| doDivides0(sdtasdt0(X1,X2),sdtasdt0(X1,sdtasdt0(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_23]) ).
cnf(c_0_47,hypothesis,
sdtasdt0(xp,sdtasdt0(xq,xq)) = esk7_0,
inference(rw,[status(thm)],[c_0_24,c_0_42]) ).
cnf(c_0_48,hypothesis,
xn = sdtasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_49,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_43]),c_0_23]),c_0_40]) ).
fof(c_0_50,hypothesis,
! [X1,X2,X3] :
( ( X3 != sz00
& X2 != sz00
& X1 != sz00
& aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X3,sdtasdt0(X2,X2)) = sdtasdt0(X1,X1)
=> ( iLess0(X1,xn)
=> ~ ( isPrime0(X3)
| ( ! [X4] :
( ( doDivides0(X4,X3)
& ? [X5] :
( X3 = sdtasdt0(X4,X5)
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
=> ( X4 = X3
| X4 = sz10 ) )
& X3 != sz10 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[m__2963]) ).
fof(c_0_51,plain,
! [X63,X64] :
( iLess0(X63,X64)
| ~ sdtlseqdt0(X63,X64)
| X63 = X64
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])]) ).
fof(c_0_52,hypothesis,
( sdtlseqdt0(xm,xn)
& sdtpldt0(xm,esk9_0) = xn
& aNaturalNumber0(esk9_0)
& xm != xn ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_45])])]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 = sdtasdt0(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_54,hypothesis,
doDivides0(xn,esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_32]),c_0_25])]) ).
cnf(c_0_55,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_56,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,X2) = sz00
| sdtsldt0(sdtasdt0(X1,sdtasdt0(X2,X3)),sdtasdt0(X1,X2)) = X3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_23]) ).
cnf(c_0_57,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_58,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_59,hypothesis,
! [X94,X95,X96] :
( ( X96 = sz00
| X95 = sz00
| X94 = sz00
| ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X94)
| sdtasdt0(X96,sdtasdt0(X95,X95)) != sdtasdt0(X94,X94)
| ~ iLess0(X94,xn)
| ~ isPrime0(X96) )
& ( X96 = sz00
| X95 = sz00
| X94 = sz00
| ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X94)
| sdtasdt0(X96,sdtasdt0(X95,X95)) != sdtasdt0(X94,X94)
| ~ iLess0(X94,xn)
| X96 = sz10
| esk5_3(X94,X95,X96) != X96 )
& ( X96 = sz00
| X95 = sz00
| X94 = sz00
| ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X94)
| sdtasdt0(X96,sdtasdt0(X95,X95)) != sdtasdt0(X94,X94)
| ~ iLess0(X94,xn)
| X96 = sz10
| esk5_3(X94,X95,X96) != sz10 )
& ( X96 = sz00
| X95 = sz00
| X94 = sz00
| ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X94)
| sdtasdt0(X96,sdtasdt0(X95,X95)) != sdtasdt0(X94,X94)
| ~ iLess0(X94,xn)
| X96 = sz10
| doDivides0(esk5_3(X94,X95,X96),X96) )
& ( X96 = sz00
| X95 = sz00
| X94 = sz00
| ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X94)
| sdtasdt0(X96,sdtasdt0(X95,X95)) != sdtasdt0(X94,X94)
| ~ iLess0(X94,xn)
| X96 = sz10
| X96 = sdtasdt0(esk5_3(X94,X95,X96),esk6_3(X94,X95,X96)) )
& ( X96 = sz00
| X95 = sz00
| X94 = sz00
| ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X94)
| sdtasdt0(X96,sdtasdt0(X95,X95)) != sdtasdt0(X94,X94)
| ~ iLess0(X94,xn)
| X96 = sz10
| aNaturalNumber0(esk6_3(X94,X95,X96)) )
& ( X96 = sz00
| X95 = sz00
| X94 = sz00
| ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X94)
| sdtasdt0(X96,sdtasdt0(X95,X95)) != sdtasdt0(X94,X94)
| ~ iLess0(X94,xn)
| X96 = sz10
| aNaturalNumber0(esk5_3(X94,X95,X96)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])])]) ).
cnf(c_0_60,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| iLess0(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,hypothesis,
sdtlseqdt0(xm,xn),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_63,hypothesis,
xm != xn,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_64,hypothesis,
( isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10 ),
inference(fof_simplification,[status(thm)],[m__3025]) ).
fof(c_0_65,plain,
! [X23] :
( ( ~ aNaturalNumber0(X23)
| sz00 = sdtasdt0(sz00,X23) )
& ( ~ aNaturalNumber0(X23)
| sdtasdt0(X23,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_66,hypothesis,
sdtasdt0(xn,esk2_2(xn,esk7_0)) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_29])]) ).
cnf(c_0_67,hypothesis,
sdtsldt0(esk7_0,xn) = xq,
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_56,c_0_47]),c_0_48]),c_0_48]),c_0_32]),c_0_25])]),c_0_57]) ).
cnf(c_0_68,hypothesis,
aNaturalNumber0(esk2_2(xn,esk7_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_54]),c_0_29]),c_0_55])]) ).
cnf(c_0_69,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,sdtasdt0(X3,X3)) != sdtasdt0(X2,X2)
| ~ iLess0(X2,xn)
| ~ isPrime0(X1)
| X1 = sz00
| X3 = sz00
| X2 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_70,hypothesis,
iLess0(xm,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_55]),c_0_62])]),c_0_63]) ).
cnf(c_0_71,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_72,hypothesis,
! [X99,X100] :
( isPrime0(xp)
& ( X99 = xp
| X99 = sz10
| ~ aNaturalNumber0(X99)
| ~ doDivides0(X99,xp) )
& ( X99 = xp
| X99 = sz10
| ~ aNaturalNumber0(X99)
| xp != sdtasdt0(X99,X100)
| ~ aNaturalNumber0(X100) )
& xp != sz10 ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])])]) ).
cnf(c_0_73,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_75,plain,
! [X35,X36] :
( X36 = sz00
| X35 = sz00
| sdtasdt0(X35,X36) != sz00
| ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
cnf(c_0_76,hypothesis,
esk2_2(xn,esk7_0) = xq,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_66]),c_0_67]),c_0_55]),c_0_68])]),c_0_57]) ).
cnf(c_0_77,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ isPrime0(X1)
| sdtasdt0(X1,sdtasdt0(X2,X2)) != esk7_0
| X2 = sz00
| X1 = sz00 ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_62])]),c_0_71]),c_0_42]) ).
cnf(c_0_78,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_41]),c_0_74])]),c_0_23]) ).
cnf(c_0_80,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_32]),c_0_25])]) ).
cnf(c_0_81,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,hypothesis,
sdtasdt0(xn,xq) = esk7_0,
inference(rw,[status(thm)],[c_0_66,c_0_76]) ).
cnf(c_0_83,hypothesis,
xq = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_47]),c_0_78]),c_0_32]),c_0_25])]),c_0_30]) ).
cnf(c_0_84,hypothesis,
sdtasdt0(xn,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_32]),c_0_25]),c_0_74])]) ).
cnf(c_0_85,hypothesis,
esk7_0 != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_42]),c_0_62])]),c_0_71]) ).
cnf(c_0_86,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM529+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 02:37:37 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.95/0.67 % Version: 3.5.1
% 1.95/0.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.95/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.95/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.95/0.67 % Starting new_bool_3 with 300s (1) cores
% 1.95/0.67 % Starting new_bool_1 with 300s (1) cores
% 1.95/0.67 % Starting sh5l with 300s (1) cores
% 1.95/0.67 % sh5l with pid 1390112 completed with status 9
% 1.95/0.67 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1390109 completed with status 0
% 1.95/0.67 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.95/0.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.95/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.95/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.95/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.95/0.67 % No SInE strategy applied
% 1.95/0.67 % Search class: FGHSF-FSMM32-SFFFFFNN
% 1.95/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.95/0.67 % Starting SubtermCWHack with 136s (1) cores
% 1.95/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.95/0.67 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 1.95/0.67 % Starting new_bool_3 with 136s (1) cores
% 1.95/0.67 % Starting new_bool_1 with 136s (1) cores
% 1.95/0.67 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1390120 completed with status 0
% 1.95/0.67 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.95/0.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.95/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.95/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.95/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.95/0.67 % No SInE strategy applied
% 1.95/0.67 % Search class: FGHSF-FSMM32-SFFFFFNN
% 1.95/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.95/0.67 % Starting SubtermCWHack with 136s (1) cores
% 1.95/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.95/0.67 % Preprocessing time : 0.001 s
% 1.95/0.67 % Presaturation interreduction done
% 1.95/0.67
% 1.95/0.67 % Proof found!
% 1.95/0.67 % SZS status ContradictoryAxioms
% 1.95/0.67 % SZS output start CNFRefutation
% See solution above
% 1.95/0.67 % Parsed axioms : 48
% 1.95/0.67 % Removed by relevancy pruning/SinE : 0
% 1.95/0.67 % Initial clauses : 104
% 1.95/0.67 % Removed in clause preprocessing : 4
% 1.95/0.67 % Initial clauses in saturation : 100
% 1.95/0.67 % Processed clauses : 3615
% 1.95/0.67 % ...of these trivial : 249
% 1.95/0.67 % ...subsumed : 1758
% 1.95/0.67 % ...remaining for further processing : 1608
% 1.95/0.67 % Other redundant clauses eliminated : 132
% 1.95/0.67 % Clauses deleted for lack of memory : 0
% 1.95/0.67 % Backward-subsumed : 37
% 1.95/0.67 % Backward-rewritten : 377
% 1.95/0.67 % Generated clauses : 28922
% 1.95/0.67 % ...of the previous two non-redundant : 24877
% 1.95/0.67 % ...aggressively subsumed : 0
% 1.95/0.67 % Contextual simplify-reflections : 126
% 1.95/0.67 % Paramodulations : 28778
% 1.95/0.67 % Factorizations : 6
% 1.95/0.67 % NegExts : 0
% 1.95/0.67 % Equation resolutions : 138
% 1.95/0.67 % Disequality decompositions : 0
% 1.95/0.67 % Total rewrite steps : 38975
% 1.95/0.67 % ...of those cached : 38489
% 1.95/0.67 % Propositional unsat checks : 0
% 1.95/0.67 % Propositional check models : 0
% 1.95/0.67 % Propositional check unsatisfiable : 0
% 1.95/0.67 % Propositional clauses : 0
% 1.95/0.67 % Propositional clauses after purity: 0
% 1.95/0.67 % Propositional unsat core size : 0
% 1.95/0.67 % Propositional preprocessing time : 0.000
% 1.95/0.67 % Propositional encoding time : 0.000
% 1.95/0.67 % Propositional solver time : 0.000
% 1.95/0.67 % Success case prop preproc time : 0.000
% 1.95/0.67 % Success case prop encoding time : 0.000
% 1.95/0.67 % Success case prop solver time : 0.000
% 1.95/0.67 % Current number of processed clauses : 1088
% 1.95/0.67 % Positive orientable unit clauses : 382
% 1.95/0.67 % Positive unorientable unit clauses: 0
% 1.95/0.67 % Negative unit clauses : 114
% 1.95/0.67 % Non-unit-clauses : 592
% 1.95/0.67 % Current number of unprocessed clauses: 20962
% 1.95/0.67 % ...number of literals in the above : 93520
% 1.95/0.67 % Current number of archived formulas : 0
% 1.95/0.67 % Current number of archived clauses : 509
% 1.95/0.67 % Clause-clause subsumption calls (NU) : 69410
% 1.95/0.67 % Rec. Clause-clause subsumption calls : 25490
% 1.95/0.67 % Non-unit clause-clause subsumptions : 1245
% 1.95/0.67 % Unit Clause-clause subsumption calls : 12202
% 1.95/0.67 % Rewrite failures with RHS unbound : 0
% 1.95/0.67 % BW rewrite match attempts : 134
% 1.95/0.67 % BW rewrite match successes : 121
% 1.95/0.67 % Condensation attempts : 0
% 1.95/0.67 % Condensation successes : 0
% 1.95/0.67 % Termbank termtop insertions : 533249
% 1.95/0.67 % Search garbage collected termcells : 1654
% 1.95/0.67
% 1.95/0.67 % -------------------------------------------------
% 1.95/0.67 % User time : 0.311 s
% 1.95/0.67 % System time : 0.023 s
% 1.95/0.67 % Total time : 0.334 s
% 1.95/0.67 % Maximum resident set size: 3948 pages
% 1.95/0.67
% 1.95/0.67 % -------------------------------------------------
% 1.95/0.67 % User time : 1.526 s
% 1.95/0.67 % System time : 0.098 s
% 1.95/0.67 % Total time : 1.624 s
% 1.95/0.67 % Maximum resident set size: 4608 pages
% 1.95/0.67 % E exiting
%------------------------------------------------------------------------------