%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM461+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 : n008.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 3.90s 3.26s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 172 ( 68 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 222 ( 89 ~; 93 |; 32 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 27 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(xm,xl),X1) = sdtpldt0(xm,xn) )
| sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(xl,xm),X1) = sdtpldt0(xn,xm) )
| sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ),
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__873,hypothesis,
aNaturalNumber0(xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__873) ).
fof(m__840,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__840) ).
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(m__840_03,hypothesis,
( xl != xn
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xl,X1) = xn )
& sdtlseqdt0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__840_03) ).
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(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(c_0_9,negated_conjecture,
~ ( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(xm,xl),X1) = sdtpldt0(xm,xn) )
| sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(xl,xm),X1) = sdtpldt0(xn,xm) )
| sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_10,negated_conjecture,
! [X98,X99] :
( ( ~ aNaturalNumber0(X99)
| sdtpldt0(sdtpldt0(xl,xm),X99) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X98)
| sdtpldt0(sdtpldt0(xm,xl),X98) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
& ( ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X98)
| sdtpldt0(sdtpldt0(xm,xl),X98) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
& ( ~ aNaturalNumber0(X99)
| sdtpldt0(sdtpldt0(xl,xm),X99) != sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
& ( ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_11,plain,
! [X56,X57] :
( ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X57)
| sdtpldt0(X56,X57) = sdtpldt0(X57,X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_12,negated_conjecture,
( sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(xl,xm),X1) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__873]) ).
cnf(c_0_15,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__840]) ).
fof(c_0_16,plain,
! [X58,X59,X60] :
( ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X59)
| ~ aNaturalNumber0(X60)
| sdtpldt0(sdtpldt0(X58,X59),X60) = sdtpldt0(X58,sdtpldt0(X59,X60)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_17,negated_conjecture,
( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xn,xm) = sdtpldt0(xm,xl)
| sdtpldt0(sdtpldt0(xm,xl),X1) != sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_18,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,hypothesis,
( xl != xn
& aNaturalNumber0(esk2_0)
& sdtpldt0(xl,esk2_0) = xn
& sdtlseqdt0(xl,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__840_03])]) ).
cnf(c_0_20,negated_conjecture,
( sdtpldt0(xn,xm) = sdtpldt0(xm,xl)
| sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xm,sdtpldt0(xl,X1)) != sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_15]),c_0_14])]) ).
cnf(c_0_21,hypothesis,
sdtpldt0(xl,esk2_0) = xn,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X82,X83,X85] :
( ( aNaturalNumber0(esk1_2(X82,X83))
| ~ sdtlseqdt0(X82,X83)
| ~ aNaturalNumber0(X82)
| ~ aNaturalNumber0(X83) )
& ( sdtpldt0(X82,esk1_2(X82,X83)) = X83
| ~ sdtlseqdt0(X82,X83)
| ~ aNaturalNumber0(X82)
| ~ aNaturalNumber0(X83) )
& ( ~ aNaturalNumber0(X85)
| sdtpldt0(X82,X85) != X83
| sdtlseqdt0(X82,X83)
| ~ aNaturalNumber0(X82)
| ~ aNaturalNumber0(X83) ) ),
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_24,plain,
! [X52,X53] :
( ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| aNaturalNumber0(sdtpldt0(X52,X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_25,hypothesis,
( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xn,xm) = sdtpldt0(xm,xl)
| sdtpldt0(sdtpldt0(xm,xl),X1) != sdtpldt0(xm,xn)
| sdtpldt0(xn,xm) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__840]) ).
fof(c_0_27,plain,
! [X86,X87,X88] :
( ( aNaturalNumber0(X88)
| X88 != sdtmndt0(X87,X86)
| ~ sdtlseqdt0(X86,X87)
| ~ aNaturalNumber0(X86)
| ~ aNaturalNumber0(X87) )
& ( sdtpldt0(X86,X88) = X87
| X88 != sdtmndt0(X87,X86)
| ~ sdtlseqdt0(X86,X87)
| ~ aNaturalNumber0(X86)
| ~ aNaturalNumber0(X87) )
& ( ~ aNaturalNumber0(X88)
| sdtpldt0(X86,X88) != X87
| X88 = sdtmndt0(X87,X86)
| ~ sdtlseqdt0(X86,X87)
| ~ aNaturalNumber0(X86)
| ~ aNaturalNumber0(X87) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_28,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,hypothesis,
( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(sdtpldt0(xm,xl),X1) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_13]),c_0_14]),c_0_26])]) ).
cnf(c_0_31,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_27]) ).
cnf(c_0_32,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_29]) ).
cnf(c_0_33,hypothesis,
( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xm,sdtpldt0(xl,X1)) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_18]),c_0_15]),c_0_14])]) ).
cnf(c_0_34,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_31]),c_0_29]),c_0_32]) ).
cnf(c_0_35,hypothesis,
sdtpldt0(xm,xn) = sdtpldt0(xm,xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_21]),c_0_22])]) ).
cnf(c_0_36,hypothesis,
sdtmndt0(sdtpldt0(xm,xl),xm) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_14]),c_0_26])]) ).
cnf(c_0_37,hypothesis,
xl != xn,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_38,hypothesis,
$false,
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_36]),c_0_14]),c_0_15])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM461+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 : n008.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 00:36:28 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.90/3.26 % Version : CSE_E---1.7
% 3.90/3.26 % Problem : theBenchmark.p
% 3.90/3.26 % SZS status Theorem for theBenchmark.p
% 3.90/3.26 % SZS output start CNFRefutation
% See solution above
% 3.90/3.27 % Total time : 2.371s
%------------------------------------------------------------------------------