%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM474+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.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 3.96s 3.21s
% Output : CNFRefutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 27 unt; 0 def)
% Number of atoms : 152 ( 53 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 179 ( 77 ~; 77 |; 17 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(m__,conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1324_04,hypothesis,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(m__1360,hypothesis,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(m__1347,hypothesis,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
fof(m__1379,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
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/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(m__1422,hypothesis,
xr = sdtmndt0(xq,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1422) ).
fof(m__1395,hypothesis,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1395) ).
fof(c_0_12,plain,
! [X134,X135,X136] :
( ( aNaturalNumber0(X136)
| X136 != sdtsldt0(X135,X134)
| X134 = sz00
| ~ doDivides0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( X135 = sdtasdt0(X134,X136)
| X136 != sdtsldt0(X135,X134)
| X134 = sz00
| ~ doDivides0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( ~ aNaturalNumber0(X136)
| X135 != sdtasdt0(X134,X136)
| X136 = sdtsldt0(X135,X134)
| X134 = sz00
| ~ doDivides0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_13,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_14,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_16,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,hypothesis,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[m__1324_04]) ).
cnf(c_0_18,hypothesis,
xp = sdtsldt0(xm,xl),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_21,hypothesis,
xl != sz00,
inference(split_conjunct,[status(thm)],[m__1347]) ).
cnf(c_0_22,hypothesis,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[m__1324_04]) ).
cnf(c_0_23,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(split_conjunct,[status(thm)],[m__1379]) ).
fof(c_0_24,plain,
! [X74,X75] :
( ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X75)
| aNaturalNumber0(sdtpldt0(X74,X75)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_25,plain,
! [X108,X109,X110] :
( ( aNaturalNumber0(X110)
| X110 != sdtmndt0(X109,X108)
| ~ sdtlseqdt0(X108,X109)
| ~ aNaturalNumber0(X108)
| ~ aNaturalNumber0(X109) )
& ( sdtpldt0(X108,X110) = X109
| X110 != sdtmndt0(X109,X108)
| ~ sdtlseqdt0(X108,X109)
| ~ aNaturalNumber0(X108)
| ~ aNaturalNumber0(X109) )
& ( ~ aNaturalNumber0(X110)
| sdtpldt0(X108,X110) != X109
| X110 = sdtmndt0(X109,X108)
| ~ sdtlseqdt0(X108,X109)
| ~ aNaturalNumber0(X108)
| ~ aNaturalNumber0(X109) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_26,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_27,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,hypothesis,
sdtasdt0(xl,xp) = xm,
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_16,c_0_17]),c_0_18]),c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_29,hypothesis,
( sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_22]),c_0_23]),c_0_19])]),c_0_21]) ).
cnf(c_0_30,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1324]) ).
fof(c_0_32,plain,
! [X91,X92,X93] :
( ( sdtasdt0(X91,sdtpldt0(X92,X93)) = sdtpldt0(sdtasdt0(X91,X92),sdtasdt0(X91,X93))
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) )
& ( sdtasdt0(sdtpldt0(X92,X93),X91) = sdtpldt0(sdtasdt0(X92,X91),sdtasdt0(X93,X91))
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_33,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,hypothesis,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_23]),c_0_19])]),c_0_21]) ).
cnf(c_0_35,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,negated_conjecture,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtpldt0(xm,xn),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_37,hypothesis,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_20])]) ).
cnf(c_0_38,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_32]) ).
cnf(c_0_39,hypothesis,
aNaturalNumber0(xp),
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_26,c_0_17]),c_0_18]),c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_40,plain,
( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_41,hypothesis,
xr = sdtmndt0(xq,xp),
inference(split_conjunct,[status(thm)],[m__1422]) ).
cnf(c_0_42,hypothesis,
sdtlseqdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__1395]) ).
cnf(c_0_43,hypothesis,
aNaturalNumber0(xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_31]),c_0_20])]) ).
cnf(c_0_44,plain,
( aNaturalNumber0(sdtmndt0(X1,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_45,negated_conjecture,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtasdt0(xl,xq),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,hypothesis,
( sdtpldt0(xm,sdtasdt0(xl,X1)) = sdtasdt0(xl,sdtpldt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_28]),c_0_19])]),c_0_39])]) ).
cnf(c_0_47,hypothesis,
sdtpldt0(xp,xr) = xq,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),c_0_43]),c_0_39])]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_41]),c_0_42])]),c_0_39]),c_0_43])]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM474+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n026.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 00:37:08 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 3.96/3.21 % Version : CSE_E---1.7
% 3.96/3.21 % Problem : theBenchmark.p
% 3.96/3.21 % SZS status Theorem for theBenchmark.p
% 3.96/3.21 % SZS output start CNFRefutation
% See solution above
% 3.96/3.22 % Total time : 2.372s
%------------------------------------------------------------------------------