%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM465+2 : 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 : n006.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 04:57:26 PM UTC 2026
% Result : Theorem 3.79s 3.16s
% Output : CNFRefutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 127 ( 33 unt; 0 def)
% Number of atoms : 445 ( 172 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 545 ( 227 ~; 237 |; 54 &)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 168 ( 0 sgn 74 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( xm != sz00
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = sdtasdt0(xn,xm) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1007,hypothesis,
( xm != sz00
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sz10,X1) = xm )
& sdtlseqdt0(sz10,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1007) ).
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(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(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__987,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
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(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_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(c_0_21,negated_conjecture,
~ ( xm != sz00
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = sdtasdt0(xn,xm) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_22,hypothesis,
( ( aNaturalNumber0(esk2_0)
| xm = sz00 )
& ( sdtpldt0(sz10,esk2_0) = xm
| xm = sz00 )
& ( sdtlseqdt0(sz10,xm)
| xm = sz00 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1007])])])]) ).
fof(c_0_23,negated_conjecture,
! [X111] :
( xm != sz00
& ( ~ aNaturalNumber0(X111)
| sdtpldt0(xn,X111) != sdtasdt0(xn,xm) )
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_24,plain,
! [X88,X89,X91] :
( ( aNaturalNumber0(esk1_2(X88,X89))
| ~ sdtlseqdt0(X88,X89)
| ~ aNaturalNumber0(X88)
| ~ aNaturalNumber0(X89) )
& ( sdtpldt0(X88,esk1_2(X88,X89)) = X89
| ~ sdtlseqdt0(X88,X89)
| ~ aNaturalNumber0(X88)
| ~ aNaturalNumber0(X89) )
& ( ~ aNaturalNumber0(X91)
| sdtpldt0(X88,X91) != X89
| sdtlseqdt0(X88,X89)
| ~ aNaturalNumber0(X88)
| ~ aNaturalNumber0(X89) ) ),
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_25,plain,
! [X58,X59] :
( ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X59)
| aNaturalNumber0(sdtpldt0(X58,X59)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_26,plain,
! [X78,X79,X80] :
( ( sdtpldt0(X78,X79) != sdtpldt0(X78,X80)
| X79 = X80
| ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79)
| ~ aNaturalNumber0(X80) )
& ( sdtpldt0(X79,X78) != sdtpldt0(X80,X78)
| X79 = X80
| ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79)
| ~ aNaturalNumber0(X80) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_27,hypothesis,
( sdtpldt0(sz10,esk2_0) = xm
| xm = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,hypothesis,
( aNaturalNumber0(esk2_0)
| xm = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X62,X63] :
( ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63)
| sdtpldt0(X62,X63) = sdtpldt0(X63,X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_33,plain,
! [X81,X82,X83] :
( ( sdtasdt0(X81,X82) != sdtasdt0(X81,X83)
| X82 = X83
| ~ aNaturalNumber0(X82)
| ~ aNaturalNumber0(X83)
| X81 = sz00
| ~ aNaturalNumber0(X81) )
& ( sdtasdt0(X82,X81) != sdtasdt0(X83,X81)
| X82 = X83
| ~ aNaturalNumber0(X82)
| ~ aNaturalNumber0(X83)
| X81 = sz00
| ~ aNaturalNumber0(X81) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_34,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,hypothesis,
sdtpldt0(sz10,esk2_0) = xm,
inference(sr,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_37,hypothesis,
aNaturalNumber0(esk2_0),
inference(sr,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_38,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_30]),c_0_31]) ).
cnf(c_0_39,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__987]) ).
fof(c_0_42,plain,
! [X73] :
( ( sdtasdt0(X73,sz10) = X73
| ~ aNaturalNumber0(X73) )
& ( X73 = sdtasdt0(sz10,X73)
| ~ aNaturalNumber0(X73) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_43,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_44,hypothesis,
( X1 = sz10
| sdtpldt0(X1,esk2_0) != xm
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]) ).
cnf(c_0_45,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,hypothesis,
( X1 = xm
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_49,plain,
! [X60,X61] :
( ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61)
| aNaturalNumber0(sdtasdt0(X60,X61)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_50,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_43]) ).
cnf(c_0_51,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_52,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__987]) ).
fof(c_0_53,plain,
! [X75,X76,X77] :
( ( sdtasdt0(X75,sdtpldt0(X76,X77)) = sdtpldt0(sdtasdt0(X75,X76),sdtasdt0(X75,X77))
| ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77) )
& ( sdtasdt0(sdtpldt0(X76,X77),X75) = sdtpldt0(sdtasdt0(X76,X75),sdtasdt0(X77,X75))
| ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_54,hypothesis,
( X1 = sz10
| sdtpldt0(esk2_0,X1) != xm
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_39]),c_0_37])]) ).
cnf(c_0_55,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_56,hypothesis,
sdtlseqdt0(esk2_0,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_35]),c_0_37]),c_0_36])]) ).
fof(c_0_57,plain,
! [X70,X71,X72] :
( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X72)
| sdtasdt0(sdtasdt0(X70,X71),X72) = sdtasdt0(X70,sdtasdt0(X71,X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_58,plain,
! [X74] :
( ( sdtasdt0(X74,sz00) = sz00
| ~ aNaturalNumber0(X74) )
& ( sz00 = sdtasdt0(sz00,X74)
| ~ aNaturalNumber0(X74) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
fof(c_0_59,plain,
! [X68,X69] :
( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X69)
| sdtasdt0(X68,X69) = sdtasdt0(X69,X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_60,hypothesis,
( sdtasdt0(sz10,xm) = xm
| ~ aNaturalNumber0(sdtasdt0(sz10,xm)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_36])]),c_0_48])]) ).
cnf(c_0_61,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_62,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aNaturalNumber0(sdtasdt0(sz10,sz00)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_47]),c_0_36])]),c_0_48])]) ).
cnf(c_0_63,hypothesis,
( X1 = esk2_0
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(esk2_0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_37]) ).
cnf(c_0_64,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_65,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xn,X1) != sdtasdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_66,plain,
! [X64,X65,X66] :
( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65)
| ~ aNaturalNumber0(X66)
| sdtpldt0(sdtpldt0(X64,X65),X66) = sdtpldt0(X64,sdtpldt0(X65,X66)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_67,plain,
! [X92,X93,X94] :
( ( aNaturalNumber0(X94)
| X94 != sdtmndt0(X93,X92)
| ~ sdtlseqdt0(X92,X93)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) )
& ( sdtpldt0(X92,X94) = X93
| X94 != sdtmndt0(X93,X92)
| ~ sdtlseqdt0(X92,X93)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) )
& ( ~ aNaturalNumber0(X94)
| sdtpldt0(X92,X94) != X93
| X94 = sdtmndt0(X93,X92)
| ~ sdtlseqdt0(X92,X93)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_68,hypothesis,
( X1 = xn
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_52]) ).
cnf(c_0_69,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_70,plain,
! [X67] :
( ( sdtpldt0(X67,sz00) = X67
| ~ aNaturalNumber0(X67) )
& ( X67 = sdtpldt0(sz00,X67)
| ~ aNaturalNumber0(X67) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_71,hypothesis,
( esk1_2(esk2_0,xm) = sz10
| ~ aNaturalNumber0(esk1_2(esk2_0,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_37])])]),c_0_41])]),c_0_56])]) ).
cnf(c_0_72,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_73,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_74,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_75,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_76,hypothesis,
sdtasdt0(sz10,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_41]),c_0_36])]) ).
cnf(c_0_77,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_43]),c_0_36])]) ).
cnf(c_0_78,hypothesis,
( sdtasdt0(esk2_0,sz10) = esk2_0
| ~ aNaturalNumber0(sdtasdt0(esk2_0,sz10)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_36])]),c_0_48])]) ).
cnf(c_0_79,negated_conjecture,
( sdtpldt0(X1,xn) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_39]),c_0_52])]) ).
cnf(c_0_80,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_81,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_67]) ).
cnf(c_0_82,hypothesis,
( sdtasdt0(sz10,xn) = xn
| ~ aNaturalNumber0(sdtasdt0(sz10,xn)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_47]),c_0_36])]),c_0_48])]) ).
cnf(c_0_83,plain,
( sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz10,X1),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_47]),c_0_36])]) ).
cnf(c_0_84,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
fof(c_0_85,plain,
! [X101,X102] :
( ( X102 != X101
| sdtlseqdt0(X101,X102)
| ~ aNaturalNumber0(X101)
| ~ aNaturalNumber0(X102) )
& ( sdtlseqdt0(X102,X101)
| sdtlseqdt0(X101,X102)
| ~ aNaturalNumber0(X101)
| ~ aNaturalNumber0(X102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
fof(c_0_86,plain,
! [X106,X107,X108] :
( ( sdtasdt0(X106,X107) != sdtasdt0(X106,X108)
| X106 = sz00
| X107 = X108
| ~ sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) )
& ( sdtlseqdt0(sdtasdt0(X106,X107),sdtasdt0(X106,X108))
| X106 = sz00
| X107 = X108
| ~ sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) )
& ( sdtasdt0(X107,X106) != sdtasdt0(X108,X106)
| X106 = sz00
| X107 = X108
| ~ sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) )
& ( sdtlseqdt0(sdtasdt0(X107,X106),sdtasdt0(X108,X106))
| X106 = sz00
| X107 = X108
| ~ sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_87,hypothesis,
( sdtlseqdt0(sz10,xm)
| xm = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_88,hypothesis,
( X1 = xn
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(xn,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_89,hypothesis,
esk1_2(esk2_0,xm) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_56]),c_0_41]),c_0_37])]) ).
cnf(c_0_90,plain,
( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_43])]) ).
cnf(c_0_91,hypothesis,
sdtasdt0(xm,sz10) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_41]),c_0_36])]) ).
cnf(c_0_92,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_77]),c_0_43]),c_0_36])]) ).
cnf(c_0_93,hypothesis,
sdtasdt0(esk2_0,sz10) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_61]),c_0_36]),c_0_37])]) ).
cnf(c_0_94,negated_conjecture,
( sdtpldt0(X1,sdtpldt0(X2,xn)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_52])]),c_0_31]) ).
cnf(c_0_95,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_81]),c_0_31]),c_0_38]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_61]),c_0_52]),c_0_36])]) ).
cnf(c_0_97,plain,
( sdtasdt0(sz10,X1) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_77]),c_0_43])]) ).
cnf(c_0_98,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_99,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_100,hypothesis,
sdtlseqdt0(sz10,xm),
inference(sr,[status(thm)],[c_0_87,c_0_28]) ).
cnf(c_0_101,hypothesis,
( sdtasdt0(xn,sz10) = xn
| ~ aNaturalNumber0(sdtasdt0(xn,sz10)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_64]),c_0_36])]),c_0_48])]) ).
cnf(c_0_102,plain,
( sdtasdt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz00,X1),sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_74]),c_0_43])]) ).
cnf(c_0_103,hypothesis,
sdtpldt0(esk2_0,sz10) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_89]),c_0_56]),c_0_41]),c_0_37])]) ).
cnf(c_0_104,hypothesis,
sdtasdt0(sz00,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_36]),c_0_41])]) ).
cnf(c_0_105,hypothesis,
sdtasdt0(sz00,esk2_0) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_93]),c_0_92]),c_0_36]),c_0_37])]) ).
cnf(c_0_106,negated_conjecture,
( sdtpldt0(X1,sdtpldt0(xn,X2)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_39]),c_0_52])]) ).
cnf(c_0_107,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_80]),c_0_31]) ).
cnf(c_0_108,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_109,plain,
( sdtmndt0(sdtpldt0(X1,X2),X2) = X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_39]) ).
cnf(c_0_110,hypothesis,
sdtpldt0(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_52])]) ).
cnf(c_0_111,hypothesis,
( sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_52]) ).
cnf(c_0_112,hypothesis,
( sz10 = xm
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_41]),c_0_36])]) ).
cnf(c_0_113,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_61]),c_0_36]),c_0_52])]) ).
cnf(c_0_114,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_115,hypothesis,
sdtpldt0(sz00,sz00) = sz00,
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_102,c_0_103]),c_0_104]),c_0_105]),c_0_36]),c_0_37])]) ).
cnf(c_0_116,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(X1,X2)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_52])]) ).
cnf(c_0_117,plain,
( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_108]) ).
cnf(c_0_118,hypothesis,
sdtmndt0(xn,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_52]),c_0_43])]) ).
cnf(c_0_119,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_111,c_0_52]) ).
cnf(c_0_120,hypothesis,
( xn = sz00
| sz10 = xm ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_52]),c_0_113]),c_0_114]) ).
cnf(c_0_121,hypothesis,
sdtlseqdt0(sz00,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_115]),c_0_43])]) ).
cnf(c_0_122,negated_conjecture,
sdtasdt0(xn,xm) != sdtpldt0(xn,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_115]),c_0_43])]) ).
cnf(c_0_123,hypothesis,
sdtpldt0(xn,sz00) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]),c_0_52])]) ).
cnf(c_0_124,negated_conjecture,
sz10 = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_120]),c_0_104]),c_0_121])]) ).
cnf(c_0_125,negated_conjecture,
sdtasdt0(xn,xm) != xn,
inference(rw,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_126,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_124]),c_0_125]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM465+2 : 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
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:39:16 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.79/3.16 % Version : CSE_E---1.7
% 3.79/3.16 % Problem : theBenchmark.p
% 3.79/3.16 % SZS status Theorem for theBenchmark.p
% 3.79/3.16 % SZS output start CNFRefutation
% See solution above
% 3.79/3.18 % Total time : 2.375s
%------------------------------------------------------------------------------