%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM459+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 01:55:06 PM UTC 2026
% Result : Theorem 0.14s 10.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 84 ( 32 unt; 0 def)
% Number of atoms : 258 ( 99 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 299 ( 125 ~; 122 |; 37 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 37 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( sdtlseqdt0(xn,xm)
& ? [X1] :
( sdtpldt0(xn,X1) = xm
& aNaturalNumber0(X1) )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( sdtpldt0(xm,X1) = xn
& aNaturalNumber0(X1) ) )
=> xm = xn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtpldt0(X2,X1) = sdtpldt0(X3,X1)
| sdtpldt0(X1,X2) = sdtpldt0(X1,X3) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(m__745,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__745) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X2 = sz00
& X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(c_0_11,negated_conjecture,
~ ( ( sdtlseqdt0(xn,xm)
& ? [X1] :
( sdtpldt0(xn,X1) = xm
& aNaturalNumber0(X1) )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( sdtpldt0(xm,X1) = xn
& aNaturalNumber0(X1) ) )
=> xm = xn ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,plain,
! [X35,X36,X38] :
( ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| sdtlseqdt0(X35,X36)
| sdtpldt0(X35,X38) != X36
| ~ aNaturalNumber0(X38) )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| sdtpldt0(X35,esk1_2(X35,X36)) = X36 )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| aNaturalNumber0(esk1_2(X35,X36)) ) ),
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)],[mDefLE])])])])])]) ).
fof(c_0_13,plain,
! [X5,X6] :
( aNaturalNumber0(sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
fof(c_0_14,plain,
! [X25,X26,X27] :
( ( ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X25)
| X26 = X27
| sdtpldt0(X26,X25) != sdtpldt0(X27,X25) )
& ( ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X25)
| X26 = X27
| sdtpldt0(X25,X26) != sdtpldt0(X25,X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])])]) ).
fof(c_0_15,negated_conjecture,
( xm != xn
& sdtlseqdt0(xn,xm)
& sdtpldt0(xn,esk3_0) = xm
& aNaturalNumber0(esk3_0)
& sdtlseqdt0(xm,xn)
& sdtpldt0(xm,esk2_0) = xn
& aNaturalNumber0(esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_16,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X9,X10] :
( sdtpldt0(X9,X10) = sdtpldt0(X10,X9)
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_19,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
sdtpldt0(xm,esk2_0) = xn,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__745]) ).
cnf(c_0_22,negated_conjecture,
aNaturalNumber0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]) ).
cnf(c_0_24,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
sdtpldt0(xn,esk3_0) = xm,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__745]) ).
cnf(c_0_27,negated_conjecture,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,esk2_0) != xn
| X1 = xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_29,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X2,X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,esk3_0) != xm
| X1 = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_25]),c_0_26]),c_0_27])]) ).
cnf(c_0_31,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(esk2_0,X1) != xn
| X1 = xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_22])]) ).
cnf(c_0_32,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_33,negated_conjecture,
sdtlseqdt0(esk2_0,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_20]),c_0_22]),c_0_21])]) ).
cnf(c_0_34,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(esk3_0,X1) != xm
| X1 = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24]),c_0_27])]) ).
cnf(c_0_35,negated_conjecture,
sdtlseqdt0(esk3_0,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_27]),c_0_26])]) ).
cnf(c_0_36,negated_conjecture,
( ~ aNaturalNumber0(esk1_2(esk2_0,xn))
| esk1_2(esk2_0,xn) = xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22])])]),c_0_33]),c_0_26])]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,negated_conjecture,
( ~ aNaturalNumber0(esk1_2(esk3_0,xm))
| esk1_2(esk3_0,xm) = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_27])])]),c_0_35]),c_0_21])]) ).
fof(c_0_39,plain,
! [X11,X12,X13] :
( sdtpldt0(sdtpldt0(X11,X12),X13) = sdtpldt0(X11,sdtpldt0(X12,X13))
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_40,negated_conjecture,
esk1_2(esk2_0,xn) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33]),c_0_26]),c_0_22])]) ).
cnf(c_0_41,negated_conjecture,
esk1_2(esk3_0,xm) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_35]),c_0_21]),c_0_27])]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,negated_conjecture,
sdtpldt0(esk2_0,xm) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_33]),c_0_26]),c_0_22])]) ).
fof(c_0_44,plain,
! [X14] :
( ( ~ aNaturalNumber0(X14)
| X14 = sdtpldt0(sz00,X14) )
& ( ~ aNaturalNumber0(X14)
| sdtpldt0(X14,sz00) = X14 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
cnf(c_0_45,negated_conjecture,
sdtpldt0(esk3_0,xn) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_35]),c_0_21]),c_0_27])]) ).
cnf(c_0_46,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(esk2_0,sdtpldt0(xm,X1)) = sdtpldt0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_21]),c_0_22])]) ).
cnf(c_0_47,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_48,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_49,plain,
! [X39,X40,X41] :
( ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 = sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) != X40
| ~ aNaturalNumber0(X41) )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) = X40 )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| aNaturalNumber0(X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])]) ).
cnf(c_0_50,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(esk3_0,sdtpldt0(xn,X1)) = sdtpldt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_45]),c_0_26]),c_0_27])]) ).
cnf(c_0_51,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_52,negated_conjecture,
sdtpldt0(xn,sz00) = xn,
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_43]),c_0_48]),c_0_21])]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X3)
| X2 != sdtmndt0(X3,X1)
| sdtpldt0(X1,X2) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(esk3_0,sdtpldt0(X1,xn)) = sdtpldt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_24]),c_0_26])]) ).
cnf(c_0_55,negated_conjecture,
sdtpldt0(esk2_0,xn) = sdtpldt0(xn,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_20]),c_0_22])]) ).
cnf(c_0_56,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xn,X1) != xn
| sz00 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_48]),c_0_26])]) ).
cnf(c_0_57,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_58,negated_conjecture,
sdtlseqdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_52]),c_0_26]),c_0_48])]) ).
cnf(c_0_59,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X3,X2)
| X1 != sdtmndt0(X2,X3)
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_60,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X3)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| X1 = sdtmndt0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,negated_conjecture,
sdtpldt0(esk3_0,sdtpldt0(xn,esk2_0)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_20]),c_0_22])]) ).
cnf(c_0_62,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_42]),c_0_17]) ).
cnf(c_0_63,negated_conjecture,
( ~ aNaturalNumber0(sdtmndt0(xn,xn))
| sdtmndt0(xn,xn) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_26])])]),c_0_58]),c_0_26])]) ).
cnf(c_0_64,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| aNaturalNumber0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_59]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtmndt0(sdtpldt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_60]),c_0_17]),c_0_23]) ).
cnf(c_0_66,negated_conjecture,
sdtpldt0(xn,sdtpldt0(esk2_0,esk3_0)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_27]),c_0_22]),c_0_26])]) ).
cnf(c_0_67,negated_conjecture,
sdtmndt0(xn,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_58]),c_0_26])]) ).
cnf(c_0_68,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(esk2_0,sdtpldt0(X1,xm)) = sdtpldt0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_24]),c_0_21])]) ).
cnf(c_0_69,negated_conjecture,
sdtpldt0(esk3_0,xm) = sdtpldt0(xm,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_25]),c_0_27])]) ).
fof(c_0_70,plain,
! [X31,X32] :
( ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X32 = sz00 )
& ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X31 = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])])]) ).
cnf(c_0_71,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(esk2_0,esk3_0))
| sdtpldt0(esk2_0,esk3_0) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_26])]) ).
cnf(c_0_72,negated_conjecture,
sdtpldt0(xm,sz00) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_47]),c_0_45]),c_0_48]),c_0_26])]) ).
cnf(c_0_73,negated_conjecture,
sdtpldt0(esk2_0,sdtpldt0(xm,esk3_0)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_25]),c_0_27])]) ).
cnf(c_0_74,negated_conjecture,
aNaturalNumber0(sdtpldt0(xm,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_69]),c_0_21]),c_0_27])]) ).
cnf(c_0_75,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_76,negated_conjecture,
sdtpldt0(esk2_0,esk3_0) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_17]),c_0_27]),c_0_22])]) ).
cnf(c_0_77,negated_conjecture,
sdtpldt0(sz00,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_72]),c_0_48]),c_0_21])]) ).
cnf(c_0_78,negated_conjecture,
xm != xn,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_79,negated_conjecture,
sdtmndt0(xm,esk2_0) = sdtpldt0(xm,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_73]),c_0_22]),c_0_74])]) ).
cnf(c_0_80,negated_conjecture,
esk2_0 = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_27]),c_0_22])]) ).
cnf(c_0_81,negated_conjecture,
sdtmndt0(xm,sz00) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_77]),c_0_48]),c_0_21])]) ).
cnf(c_0_82,negated_conjecture,
sdtpldt0(xm,esk3_0) != xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_69]),c_0_21])]),c_0_78]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM459+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/10.38 % Computer : n006.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Mon Sep 21 02:31:54 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/10.43 Running first-order theorem proving
% 0.14/10.43 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.14/10.58 % Version: 3.5.1
% 0.14/10.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/10.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/10.58 % Starting new_bool_3 with 300s (1) cores
% 0.14/10.58 % Starting new_bool_1 with 300s (1) cores
% 0.14/10.58 % Starting sh5l with 300s (1) cores
% 0.14/10.58 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1812914 completed with status 0
% 0.14/10.58 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/10.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/10.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/10.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/10.58 % No SInE strategy applied
% 0.14/10.58 % Search class: FGUSF-FFMM22-SFFFFFNN
% 0.14/10.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/10.58 % Starting SubtermCWHack with 136s (1) cores
% 0.14/10.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/10.58 % Starting G-E--_107_B42_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.14/10.58 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/10.58 % Starting new_bool_3 with 136s (1) cores
% 0.14/10.58 % SubtermCWHack with pid 1812922 completed with status 0
% 0.14/10.58 % Result found by SubtermCWHack
% 0.14/10.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/10.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/10.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/10.58 % No SInE strategy applied
% 0.14/10.58 % Search class: FGUSF-FFMM22-SFFFFFNN
% 0.14/10.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/10.58 % Starting SubtermCWHack with 136s (1) cores
% 0.14/10.58 % Preprocessing time : 0.001 s
% 0.14/10.58
% 0.14/10.58 % Proof found!
% 0.14/10.58 % SZS status Theorem
% 0.14/10.58 % SZS output start CNFRefutation
% See solution above
% 0.14/10.58 % Parsed axioms : 22
% 0.14/10.58 % Removed by relevancy pruning/SinE : 0
% 0.14/10.58 % Initial clauses : 41
% 0.14/10.58 % Removed in clause preprocessing : 1
% 0.14/10.58 % Initial clauses in saturation : 40
% 0.14/10.58 % Processed clauses : 1890
% 0.14/10.58 % ...of these trivial : 62
% 0.14/10.58 % ...subsumed : 1171
% 0.14/10.58 % ...remaining for further processing : 657
% 0.14/10.58 % Other redundant clauses eliminated : 96
% 0.14/10.58 % Clauses deleted for lack of memory : 0
% 0.14/10.58 % Backward-subsumed : 17
% 0.14/10.58 % Backward-rewritten : 89
% 0.14/10.58 % Generated clauses : 16244
% 0.14/10.58 % ...of the previous two non-redundant : 13331
% 0.14/10.58 % ...aggressively subsumed : 0
% 0.14/10.58 % Contextual simplify-reflections : 87
% 0.14/10.58 % Paramodulations : 16142
% 0.14/10.58 % Factorizations : 0
% 0.14/10.58 % NegExts : 0
% 0.14/10.58 % Equation resolutions : 102
% 0.14/10.58 % Disequality decompositions : 0
% 0.14/10.58 % Total rewrite steps : 20496
% 0.14/10.58 % ...of those cached : 20279
% 0.14/10.58 % Propositional unsat checks : 0
% 0.14/10.58 % Propositional check models : 0
% 0.14/10.58 % Propositional check unsatisfiable : 0
% 0.14/10.58 % Propositional clauses : 0
% 0.14/10.58 % Propositional clauses after purity: 0
% 0.14/10.58 % Propositional unsat core size : 0
% 0.14/10.58 % Propositional preprocessing time : 0.000
% 0.14/10.58 % Propositional encoding time : 0.000
% 0.14/10.58 % Propositional solver time : 0.000
% 0.14/10.58 % Success case prop preproc time : 0.000
% 0.14/10.58 % Success case prop encoding time : 0.000
% 0.14/10.58 % Success case prop solver time : 0.000
% 0.14/10.58 % Current number of processed clauses : 547
% 0.14/10.58 % Positive orientable unit clauses : 211
% 0.14/10.58 % Positive unorientable unit clauses: 0
% 0.14/10.58 % Negative unit clauses : 36
% 0.14/10.58 % Non-unit-clauses : 300
% 0.14/10.58 % Current number of unprocessed clauses: 11350
% 0.14/10.58 % ...number of literals in the above : 51603
% 0.14/10.58 % Current number of archived formulas : 0
% 0.14/10.58 % Current number of archived clauses : 106
% 0.14/10.58 % Clause-clause subsumption calls (NU) : 17219
% 0.14/10.58 % Rec. Clause-clause subsumption calls : 11037
% 0.14/10.58 % Non-unit clause-clause subsumptions : 885
% 0.14/10.58 % Unit Clause-clause subsumption calls : 1898
% 0.14/10.58 % Rewrite failures with RHS unbound : 0
% 0.14/10.58 % BW rewrite match attempts : 414
% 0.14/10.58 % BW rewrite match successes : 21
% 0.14/10.58 % Condensation attempts : 0
% 0.14/10.58 % Condensation successes : 0
% 0.14/10.58 % Termbank termtop insertions : 259122
% 0.14/10.58 % Search garbage collected termcells : 550
% 0.14/10.58
% 0.14/10.58 % -------------------------------------------------
% 0.14/10.58 % User time : 0.124 s
% 0.14/10.58 % System time : 0.010 s
% 0.14/10.58 % Total time : 0.134 s
% 0.14/10.58 % Maximum resident set size: 3600 pages
% 0.14/10.58
% 0.14/10.58 % -------------------------------------------------
% 0.14/10.58 % User time : 0.606 s
% 0.14/10.58 % System time : 0.044 s
% 0.14/10.58 % Total time : 0.650 s
% 0.14/10.58 % Maximum resident set size: 4608 pages
% 0.14/10.58 % E exiting
%------------------------------------------------------------------------------