%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM471+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 : n001.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 04:57:27 PM UTC 2026
% Result : Theorem 5.60s 4.38s
% Output : CNFRefutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 22 unt; 0 def)
% Number of atoms : 171 ( 49 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 198 ( 78 ~; 80 |; 31 &)
% ( 1 <=>; 8 =>; 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; 6 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 26 !; 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(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__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(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(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_12,plain,
! [X120,X121] :
( ( X121 != X120
| sdtlseqdt0(X120,X121)
| ~ aNaturalNumber0(X120)
| ~ aNaturalNumber0(X121) )
& ( sdtlseqdt0(X121,X120)
| sdtlseqdt0(X120,X121)
| ~ aNaturalNumber0(X120)
| ~ aNaturalNumber0(X121) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
fof(c_0_13,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xq )
| sdtlseqdt0(xp,xq) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_14,plain,
! [X107,X108,X110] :
( ( aNaturalNumber0(esk1_2(X107,X108))
| ~ sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) )
& ( sdtpldt0(X107,esk1_2(X107,X108)) = X108
| ~ sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) )
& ( ~ aNaturalNumber0(X110)
| sdtpldt0(X107,X110) != X108
| sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) ) ),
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_15,plain,
! [X77,X78] :
( ~ aNaturalNumber0(X77)
| ~ aNaturalNumber0(X78)
| aNaturalNumber0(sdtpldt0(X77,X78)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_16,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__1379]) ).
fof(c_0_18,negated_conjecture,
! [X148] :
( ( ~ aNaturalNumber0(X148)
| sdtpldt0(xp,X148) != xq )
& ~ sdtlseqdt0(xp,xq) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_19,plain,
! [X86] :
( ( sdtpldt0(X86,sz00) = X86
| ~ aNaturalNumber0(X86) )
& ( X86 = sdtpldt0(sz00,X86)
| ~ aNaturalNumber0(X86) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_20,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X125,X126,X127] :
( ( sdtasdt0(X125,X126) != sdtasdt0(X125,X127)
| X125 = sz00
| X126 = X127
| ~ sdtlseqdt0(X126,X127)
| ~ aNaturalNumber0(X125)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127) )
& ( sdtlseqdt0(sdtasdt0(X125,X126),sdtasdt0(X125,X127))
| X125 = sz00
| X126 = X127
| ~ sdtlseqdt0(X126,X127)
| ~ aNaturalNumber0(X125)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127) )
& ( sdtasdt0(X126,X125) != sdtasdt0(X127,X125)
| X125 = sz00
| X126 = X127
| ~ sdtlseqdt0(X126,X127)
| ~ aNaturalNumber0(X125)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127) )
& ( sdtlseqdt0(sdtasdt0(X126,X125),sdtasdt0(X127,X125))
| X125 = sz00
| X126 = X127
| ~ sdtlseqdt0(X126,X127)
| ~ aNaturalNumber0(X125)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_23,hypothesis,
( sdtlseqdt0(X1,xq)
| sdtlseqdt0(xq,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_25,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xp,X1) != xq ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_29,plain,
! [X115,X116] :
( ~ aNaturalNumber0(X115)
| ~ aNaturalNumber0(X116)
| ~ sdtlseqdt0(X115,X116)
| ~ sdtlseqdt0(X116,X115)
| X115 = X116 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_30,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]) ).
cnf(c_0_31,hypothesis,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(split_conjunct,[status(thm)],[m__1379]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xn),
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_22]) ).
cnf(c_0_35,hypothesis,
sdtlseqdt0(xq,xp),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
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_26,c_0_27]),c_0_28]),c_0_24])]) ).
cnf(c_0_37,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,hypothesis,
sdtlseqdt0(xm,sdtasdt0(xl,xq)),
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_39,hypothesis,
aNaturalNumber0(sdtasdt0(xl,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_31]),c_0_33]),c_0_32])]) ).
cnf(c_0_40,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_24]),c_0_17])]),c_0_36]) ).
cnf(c_0_41,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_42,hypothesis,
xm = sdtasdt0(xl,xp),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_43,hypothesis,
xl != sz00,
inference(split_conjunct,[status(thm)],[m__1347]) ).
cnf(c_0_44,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(split_conjunct,[status(thm)],[m__1379]) ).
cnf(c_0_45,hypothesis,
( sdtasdt0(xl,xq) = xm
| ~ sdtlseqdt0(sdtasdt0(xl,xq),xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_32]),c_0_39])]) ).
cnf(c_0_46,hypothesis,
sdtlseqdt0(sdtasdt0(xl,xq),xm),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]) ).
cnf(c_0_47,hypothesis,
sdtsldt0(sdtasdt0(xl,xq),xl) = xq,
inference(rw,[status(thm)],[c_0_44,c_0_31]) ).
cnf(c_0_48,hypothesis,
sdtasdt0(xl,xq) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_49,hypothesis,
xp = sdtsldt0(xm,xl),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_50,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM471+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
% 0.14/0.31 % Computer : n001.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue May 5 00:37:48 EDT 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.32 % start to proof: theBenchmark
% 5.60/4.38 % Version : CSE_E---1.7
% 5.60/4.38 % Problem : theBenchmark.p
% 5.60/4.38 % SZS status Theorem for theBenchmark.p
% 5.60/4.38 % SZS output start CNFRefutation
% See solution above
% 5.60/4.39 % Total time : 3.373s
%------------------------------------------------------------------------------