%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM494+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 : Tue May 5 04:57:33 PM UTC 2026
% Result : Theorem 1.39s 1.77s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 92 ( 31 unt; 0 def)
% Number of atoms : 295 ( 86 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 361 ( 158 ~; 154 |; 33 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 99 ( 0 sgn 45 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__,conjecture,
( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m__1894,hypothesis,
( xr != xn
& sdtlseqdt0(xr,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1894) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(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(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(c_0_15,plain,
! [X123,X124,X125] :
( ( aNaturalNumber0(X125)
| X125 != sdtmndt0(X124,X123)
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( sdtpldt0(X123,X125) = X124
| X125 != sdtmndt0(X124,X123)
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( ~ aNaturalNumber0(X125)
| sdtpldt0(X123,X125) != X124
| X125 = sdtmndt0(X124,X123)
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
fof(c_0_16,negated_conjecture,
~ ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_17,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,negated_conjecture,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(fof_nnf,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X93,X94] :
( ~ aNaturalNumber0(X93)
| ~ aNaturalNumber0(X94)
| sdtpldt0(X93,X94) = sdtpldt0(X94,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_20,plain,
( aNaturalNumber0(sdtmndt0(X1,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_22,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_25,negated_conjecture,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
fof(c_0_29,plain,
! [X95,X96,X97] :
( ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X97)
| sdtpldt0(sdtpldt0(X95,X96),X97) = sdtpldt0(X95,sdtpldt0(X96,X97)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_30,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,negated_conjecture,
( sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_28])]) ).
cnf(c_0_32,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_30]) ).
fof(c_0_34,plain,
! [X134,X135,X136] :
( ( sdtpldt0(X136,X134) != sdtpldt0(X136,X135)
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( sdtlseqdt0(sdtpldt0(X136,X134),sdtpldt0(X136,X135))
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( sdtpldt0(X134,X136) != sdtpldt0(X135,X136)
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( sdtlseqdt0(sdtpldt0(X134,X136),sdtpldt0(X135,X136))
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
cnf(c_0_35,negated_conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,sdtpldt0(xr,xp))
| ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_23]),c_0_28]),c_0_27])]) ).
cnf(c_0_36,hypothesis,
sdtpldt0(xp,xr) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_21]),c_0_22]),c_0_24]),c_0_23])]) ).
fof(c_0_37,plain,
! [X119,X120,X122] :
( ( aNaturalNumber0(esk1_2(X119,X120))
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( sdtpldt0(X119,esk1_2(X119,X120)) = X120
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( ~ aNaturalNumber0(X122)
| sdtpldt0(X119,X122) != X120
| sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) ) ),
inference(distribute,[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_38,plain,
! [X89,X90] :
( ~ aNaturalNumber0(X89)
| ~ aNaturalNumber0(X90)
| aNaturalNumber0(sdtpldt0(X89,X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_39,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| X2 = X3
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,hypothesis,
sdtlseqdt0(xr,xn),
inference(split_conjunct,[status(thm)],[m__1894]) ).
cnf(c_0_41,hypothesis,
xr != xn,
inference(split_conjunct,[status(thm)],[m__1894]) ).
fof(c_0_42,plain,
! [X98] :
( ( sdtpldt0(X98,sz00) = X98
| ~ aNaturalNumber0(X98) )
& ( X98 = sdtpldt0(sz00,X98)
| ~ aNaturalNumber0(X98) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_43,negated_conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,xn)
| ~ sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
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_35,c_0_26]),c_0_36]),c_0_36]),c_0_23]),c_0_28])]) ).
cnf(c_0_44,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,hypothesis,
( sdtlseqdt0(sdtpldt0(X1,xr),sdtpldt0(X1,xn))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_24]),c_0_28])]),c_0_41]) ).
cnf(c_0_47,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_49,negated_conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_26]),c_0_24]),c_0_27])]) ).
cnf(c_0_50,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_44]),c_0_45]) ).
cnf(c_0_51,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,xr),xn),
inference(cn,[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_24])]) ).
cnf(c_0_52,negated_conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_23])]) ).
fof(c_0_53,plain,
! [X109,X110,X111] :
( ( sdtpldt0(X109,X110) != sdtpldt0(X109,X111)
| X110 = X111
| ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X110)
| ~ aNaturalNumber0(X111) )
& ( sdtpldt0(X110,X109) != sdtpldt0(X111,X109)
| X110 = X111
| ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X110)
| ~ aNaturalNumber0(X111) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_54,hypothesis,
( aNaturalNumber0(sdtmndt0(xn,sdtpldt0(sz00,xr)))
| ~ aNaturalNumber0(sdtpldt0(sz00,xr)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_51]),c_0_24])]) ).
cnf(c_0_55,negated_conjecture,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_45]),c_0_27]),c_0_24])]) ).
cnf(c_0_56,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,hypothesis,
sdtpldt0(xr,sdtmndt0(xn,xr)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_24]),c_0_28])]) ).
cnf(c_0_58,hypothesis,
aNaturalNumber0(sdtmndt0(xn,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_47]),c_0_28])]) ).
cnf(c_0_59,negated_conjecture,
sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(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_55]),c_0_23]),c_0_27]),c_0_24])]) ).
cnf(c_0_60,hypothesis,
( sdtmndt0(xn,xr) = X1
| sdtpldt0(xr,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_28])]) ).
cnf(c_0_61,negated_conjecture,
( aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xm,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_59]),c_0_24])]) ).
cnf(c_0_62,hypothesis,
( sdtmndt0(xn,xr) = X1
| sdtpldt0(X1,xr) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_26]),c_0_28])]) ).
cnf(c_0_63,negated_conjecture,
( sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_23])]) ).
cnf(c_0_64,negated_conjecture,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_45]),c_0_23]),c_0_27])]) ).
cnf(c_0_65,hypothesis,
sdtmndt0(xn,xr) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_36]),c_0_23])]) ).
fof(c_0_66,plain,
! [X129,X130,X131] :
( ~ aNaturalNumber0(X129)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131)
| ~ sdtlseqdt0(X129,X130)
| ~ sdtlseqdt0(X130,X131)
| sdtlseqdt0(X129,X131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_67,negated_conjecture,
( sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
cnf(c_0_68,hypothesis,
sdtpldt0(xr,xp) = xn,
inference(rw,[status(thm)],[c_0_57,c_0_65]) ).
cnf(c_0_69,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_70,negated_conjecture,
( sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(xm,xn)
| ~ sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_32]),c_0_68]),c_0_68]),c_0_23]),c_0_28]),c_0_27])]) ).
cnf(c_0_71,hypothesis,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,sdtpldt0(sz00,xr))
| ~ aNaturalNumber0(sdtpldt0(sz00,xr))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_51]),c_0_24])]) ).
cnf(c_0_72,negated_conjecture,
( sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_26]),c_0_24]),c_0_27])]) ).
cnf(c_0_73,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_74,hypothesis,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_47]),c_0_28])]) ).
cnf(c_0_75,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_47]),c_0_48])]) ).
cnf(c_0_76,plain,
( X1 = sdtmndt0(X3,X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_77,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_78,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_79,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_80,negated_conjecture,
sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_64]),c_0_23])]) ).
cnf(c_0_81,hypothesis,
sdtlseqdt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_48]),c_0_28])]) ).
cnf(c_0_82,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_76]),c_0_45]),c_0_50]) ).
cnf(c_0_83,hypothesis,
sdtpldt0(xp,esk1_2(xp,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_21]),c_0_24]),c_0_23])]) ).
cnf(c_0_84,hypothesis,
aNaturalNumber0(esk1_2(xp,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_21]),c_0_24]),c_0_23])]) ).
cnf(c_0_85,negated_conjecture,
( X1 = xp
| sdtpldt0(X1,sdtpldt0(xn,xm)) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_23]),c_0_64])]) ).
cnf(c_0_86,hypothesis,
sdtpldt0(sz00,esk1_2(sz00,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_81]),c_0_24]),c_0_48])]) ).
cnf(c_0_87,hypothesis,
aNaturalNumber0(esk1_2(sz00,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_81]),c_0_24]),c_0_48])]) ).
cnf(c_0_88,hypothesis,
esk1_2(xp,xn) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_22]),c_0_23]),c_0_84])]) ).
cnf(c_0_89,negated_conjecture,
xp = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_47]),c_0_48]),c_0_64])]) ).
cnf(c_0_90,hypothesis,
esk1_2(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_86]),c_0_87])]) ).
cnf(c_0_91,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89]),c_0_90]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM494+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:38:11 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.39/1.77 % Version : CSE_E---1.7
% 1.39/1.77 % Problem : theBenchmark.p
% 1.39/1.77 % SZS status Theorem for theBenchmark.p
% 1.39/1.77 % SZS output start CNFRefutation
% See solution above
% 1.39/1.77 % Total time : 1.376s
%------------------------------------------------------------------------------