%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM473+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 : n028.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 04:57:28 PM UTC 2026
% Result : Theorem 4.34s 3.31s
% Output : CNFRefutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 51 ( 20 unt; 0 def)
% Number of atoms : 179 ( 61 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 207 ( 79 ~; 84 |; 33 &)
% ( 0 <=>; 11 =>; 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xq )
| sdtlseqdt0(xp,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1379,hypothesis,
( aNaturalNumber0(xq)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& xq = sdtsldt0(sdtpldt0(xm,xn),xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
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(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m__1409,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = sdtpldt0(xm,xn) )
& sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).
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__1360,hypothesis,
( aNaturalNumber0(xp)
& xm = sdtasdt0(xl,xp)
& xp = sdtsldt0(xm,xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
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(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
fof(m__1347,hypothesis,
xl != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).
fof(c_0_13,plain,
! [X121,X122] :
( ( X122 != X121
| sdtlseqdt0(X121,X122)
| ~ aNaturalNumber0(X121)
| ~ aNaturalNumber0(X122) )
& ( sdtlseqdt0(X122,X121)
| sdtlseqdt0(X121,X122)
| ~ aNaturalNumber0(X121)
| ~ aNaturalNumber0(X122) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
fof(c_0_14,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xq )
| sdtlseqdt0(xp,xq) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_15,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__1379]) ).
fof(c_0_17,negated_conjecture,
! [X150] :
( ( ~ aNaturalNumber0(X150)
| sdtpldt0(xp,X150) != xq )
& ~ sdtlseqdt0(xp,xq) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_18,plain,
! [X87] :
( ( sdtpldt0(X87,sz00) = X87
| ~ aNaturalNumber0(X87) )
& ( X87 = sdtpldt0(sz00,X87)
| ~ aNaturalNumber0(X87) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_19,plain,
! [X78,X79] :
( ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79)
| aNaturalNumber0(sdtpldt0(X78,X79)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_20,hypothesis,
( aNaturalNumber0(esk5_0)
& sdtpldt0(xm,esk5_0) = sdtpldt0(xm,xn)
& sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1409])]) ).
fof(c_0_21,plain,
! [X126,X127,X128] :
( ( sdtasdt0(X126,X127) != sdtasdt0(X126,X128)
| X126 = sz00
| X127 = X128
| ~ sdtlseqdt0(X127,X128)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127)
| ~ aNaturalNumber0(X128) )
& ( sdtlseqdt0(sdtasdt0(X126,X127),sdtasdt0(X126,X128))
| X126 = sz00
| X127 = X128
| ~ sdtlseqdt0(X127,X128)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127)
| ~ aNaturalNumber0(X128) )
& ( sdtasdt0(X127,X126) != sdtasdt0(X128,X126)
| X126 = sz00
| X127 = X128
| ~ sdtlseqdt0(X127,X128)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127)
| ~ aNaturalNumber0(X128) )
& ( sdtlseqdt0(sdtasdt0(X127,X126),sdtasdt0(X128,X126))
| X126 = sz00
| X127 = X128
| ~ sdtlseqdt0(X127,X128)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127)
| ~ aNaturalNumber0(X128) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_22,hypothesis,
( sdtlseqdt0(X1,xq)
| sdtlseqdt0(xq,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_24,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xp,X1) != xq ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_28,plain,
! [X101,X102,X103] :
( ( sdtasdt0(X101,X102) != sdtasdt0(X101,X103)
| X102 = X103
| ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| X101 = sz00
| ~ aNaturalNumber0(X101) )
& ( sdtasdt0(X102,X101) != sdtasdt0(X103,X101)
| X102 = X103
| ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| X101 = sz00
| ~ aNaturalNumber0(X101) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
fof(c_0_29,plain,
! [X116,X117] :
( ~ aNaturalNumber0(X116)
| ~ aNaturalNumber0(X117)
| ~ sdtlseqdt0(X116,X117)
| ~ sdtlseqdt0(X117,X116)
| X116 = X117 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_30,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,hypothesis,
sdtpldt0(xm,esk5_0) = sdtpldt0(xm,xn),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_34,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_21]) ).
cnf(c_0_35,hypothesis,
sdtlseqdt0(xq,xp),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_36,negated_conjecture,
xq != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_23])]) ).
cnf(c_0_37,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,hypothesis,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_41,hypothesis,
( X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,xq),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_23]),c_0_16])]),c_0_36]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_43,hypothesis,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(split_conjunct,[status(thm)],[m__1379]) ).
cnf(c_0_44,hypothesis,
xm = sdtasdt0(xl,xp),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_45,hypothesis,
xl != sz00,
inference(split_conjunct,[status(thm)],[m__1347]) ).
cnf(c_0_46,hypothesis,
( X1 = xp
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_47,hypothesis,
( sdtpldt0(xm,xn) = xm
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_33]),c_0_40])]) ).
cnf(c_0_48,hypothesis,
sdtlseqdt0(sdtpldt0(xm,xn),xm),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_49,hypothesis,
sdtpldt0(xm,xn) != xm,
inference(sr,[status(thm)],[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_46,c_0_43]),c_0_44]),c_0_16]),c_0_42])]),c_0_36]),c_0_45]) ).
cnf(c_0_50,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM473+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n028.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:37:15 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 4.34/3.31 % Version : CSE_E---1.7
% 4.34/3.31 % Problem : theBenchmark.p
% 4.34/3.31 % SZS status Theorem for theBenchmark.p
% 4.34/3.31 % SZS output start CNFRefutation
% See solution above
% 4.34/3.32 % Total time : 2.373s
%------------------------------------------------------------------------------