%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM463+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 : n005.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 04:57:25 PM UTC 2026
% Result : Theorem 1.16s 1.73s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 12 unt; 0 def)
% Number of atoms : 154 ( 57 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 174 ( 66 ~; 75 |; 23 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mLENTr,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sz00
| X1 = sz10
| ( sz10 != X1
& sdtlseqdt0(sz10,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
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(m__987,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
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(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(mLERefl,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
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(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_11,negated_conjecture,
~ ( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,plain,
! [X107] :
( ( sz10 != X107
| X107 = sz00
| X107 = sz10
| ~ aNaturalNumber0(X107) )
& ( sdtlseqdt0(sz10,X107)
| X107 = sz00
| X107 = sz10
| ~ aNaturalNumber0(X107) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLENTr])])]) ).
fof(c_0_13,negated_conjecture,
( xm != sz00
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X104,X105,X106] :
( ( sdtasdt0(X104,X105) != sdtasdt0(X104,X106)
| X104 = sz00
| X105 = X106
| ~ sdtlseqdt0(X105,X106)
| ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106) )
& ( sdtlseqdt0(sdtasdt0(X104,X105),sdtasdt0(X104,X106))
| X104 = sz00
| X105 = X106
| ~ sdtlseqdt0(X105,X106)
| ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106) )
& ( sdtasdt0(X105,X104) != sdtasdt0(X106,X104)
| X104 = sz00
| X105 = X106
| ~ sdtlseqdt0(X105,X106)
| ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106) )
& ( sdtlseqdt0(sdtasdt0(X105,X104),sdtasdt0(X106,X104))
| X104 = sz00
| X105 = X106
| ~ sdtlseqdt0(X105,X106)
| ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_15,plain,
( sdtlseqdt0(sz10,X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__987]) ).
cnf(c_0_17,negated_conjecture,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,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_14]) ).
cnf(c_0_19,hypothesis,
( xm = sz10
| sdtlseqdt0(sz10,xm) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_21,hypothesis,
( xm = sz10
| 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_18,c_0_19]),c_0_16]),c_0_20])]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__987]) ).
fof(c_0_23,plain,
! [X71] :
( ( sdtasdt0(X71,sz10) = X71
| ~ aNaturalNumber0(X71) )
& ( X71 = sdtasdt0(sz10,X71)
| ~ aNaturalNumber0(X71) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_24,hypothesis,
( xn = sz00
| xm = sz10
| sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,hypothesis,
( xm = sz10
| xn = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_22])]),c_0_26]) ).
fof(c_0_28,plain,
! [X72] :
( ( sdtasdt0(X72,sz00) = sz00
| ~ aNaturalNumber0(X72) )
& ( sz00 = sdtasdt0(sz00,X72)
| ~ aNaturalNumber0(X72) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
fof(c_0_29,plain,
! [X66,X67] :
( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67)
| sdtasdt0(X66,X67) = sdtasdt0(X67,X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_30,negated_conjecture,
( xm = sz10
| ~ sdtlseqdt0(sz00,sdtasdt0(sz00,xm)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,plain,
! [X93] :
( ~ aNaturalNumber0(X93)
| sdtlseqdt0(X93,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])]) ).
fof(c_0_33,plain,
! [X99,X100] :
( ( X100 != X99
| sdtlseqdt0(X99,X100)
| ~ aNaturalNumber0(X99)
| ~ aNaturalNumber0(X100) )
& ( sdtlseqdt0(X100,X99)
| sdtlseqdt0(X99,X100)
| ~ aNaturalNumber0(X99)
| ~ aNaturalNumber0(X100) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_34,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( xm = sz10
| ~ sdtlseqdt0(sz00,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_16])]) ).
cnf(c_0_36,plain,
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_38,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_34]),c_0_22]),c_0_16])]) ).
cnf(c_0_40,negated_conjecture,
xm = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_41,hypothesis,
( sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_42,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(sz10,xn)),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_44,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_41,c_0_22]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM463+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % 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
% 0.10/0.32 % Computer : n005.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 5 00:35:45 EDT 2026
% 0.10/0.32 % CPUTime :
% 0.10/0.34 % start to proof: theBenchmark
% 1.16/1.73 % Version : CSE_E---1.7
% 1.16/1.73 % Problem : theBenchmark.p
% 1.16/1.73 % SZS status Theorem for theBenchmark.p
% 1.16/1.73 % SZS output start CNFRefutation
% See solution above
% 1.16/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------