%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM443+4 : 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 : n029.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 04:57:21 PM UTC 2026
% Result : Theorem 1.41s 1.76s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 252 ( 42 equ)
% Maximal formula atoms : 50 ( 8 avg)
% Number of connectives : 321 ( 99 ~; 113 |; 90 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 62 ( 0 sgn 34 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xc,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) )
=> ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mEquModTrn,axiom,
! [X1,X2,X3,X4] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00
& aInteger0(X4) )
=> ( ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
& sdteqdtlpzmzozddtrp0(X2,X4,X3) )
=> sdteqdtlpzmzozddtrp0(X1,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModTrn) ).
fof(mEquModSym,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).
fof(m__2010,hypothesis,
( aInteger0(xb)
& aInteger0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2010) ).
fof(m__1962,hypothesis,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1962) ).
fof(mArSeq,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).
fof(c_0_6,negated_conjecture,
~ ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xc,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) )
=> ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X1,xa,xq) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_7,plain,
! [X137,X138,X139,X140] :
( ~ aInteger0(X137)
| ~ aInteger0(X138)
| ~ aInteger0(X139)
| X139 = sz00
| ~ aInteger0(X140)
| ~ sdteqdtlpzmzozddtrp0(X137,X138,X139)
| ~ sdteqdtlpzmzozddtrp0(X138,X140,X139)
| sdteqdtlpzmzozddtrp0(X137,X140,X139) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModTrn])]) ).
fof(c_0_8,negated_conjecture,
! [X205,X207,X208,X210,X212,X213] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ( aInteger0(X205)
| ~ aElementOf0(X205,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aInteger0(esk16_1(X205))
| ~ aElementOf0(X205,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( sdtasdt0(xq,esk16_1(X205)) = sdtpldt0(X205,smndt0(xa))
| ~ aElementOf0(X205,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aDivisorOf0(xq,sdtpldt0(X205,smndt0(xa)))
| ~ aElementOf0(X205,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( sdteqdtlpzmzozddtrp0(X205,xa,xq)
| ~ aElementOf0(X205,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aInteger0(X208)
| sdtasdt0(xq,X208) != sdtpldt0(X207,smndt0(xa))
| ~ aInteger0(X207)
| aElementOf0(X207,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aDivisorOf0(xq,sdtpldt0(X207,smndt0(xa)))
| ~ aInteger0(X207)
| aElementOf0(X207,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ sdteqdtlpzmzozddtrp0(X207,xa,xq)
| ~ aInteger0(X207)
| aElementOf0(X207,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aInteger0(esk17_0)
& sdtasdt0(xq,esk17_0) = sdtpldt0(xc,smndt0(xb))
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ( aInteger0(X210)
| ~ aElementOf0(X210,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aInteger0(esk18_1(X210))
| ~ aElementOf0(X210,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( sdtasdt0(xq,esk18_1(X210)) = sdtpldt0(X210,smndt0(xa))
| ~ aElementOf0(X210,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aDivisorOf0(xq,sdtpldt0(X210,smndt0(xa)))
| ~ aElementOf0(X210,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( sdteqdtlpzmzozddtrp0(X210,xa,xq)
| ~ aElementOf0(X210,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aInteger0(X213)
| sdtasdt0(xq,X213) != sdtpldt0(X212,smndt0(xa))
| ~ aInteger0(X212)
| aElementOf0(X212,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aDivisorOf0(xq,sdtpldt0(X212,smndt0(xa)))
| ~ aInteger0(X212)
| aElementOf0(X212,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ sdteqdtlpzmzozddtrp0(X212,xa,xq)
| ~ aInteger0(X212)
| aElementOf0(X212,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])]) ).
fof(c_0_9,plain,
! [X134,X135,X136] :
( ~ aInteger0(X134)
| ~ aInteger0(X135)
| ~ aInteger0(X136)
| X136 = sz00
| ~ sdteqdtlpzmzozddtrp0(X134,X135,X136)
| sdteqdtlpzmzozddtrp0(X135,X134,X136) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModSym])]) ).
cnf(c_0_10,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X1,X4,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ sdteqdtlpzmzozddtrp0(X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__2010]) ).
cnf(c_0_13,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__1962]) ).
cnf(c_0_14,hypothesis,
aInteger0(xc),
inference(split_conjunct,[status(thm)],[m__2010]) ).
cnf(c_0_15,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__1962]) ).
cnf(c_0_16,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
( sdteqdtlpzmzozddtrp0(X1,xa,xq)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__1962]) ).
cnf(c_0_19,negated_conjecture,
( aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_20,plain,
! [X184,X185,X186,X187,X188,X189] :
( ( aSet0(X186)
| X186 != szAzrzSzezqlpdtcmdtrp0(X184,X185)
| ~ aInteger0(X184)
| ~ aInteger0(X185)
| X185 = sz00 )
& ( aInteger0(X187)
| ~ aElementOf0(X187,X186)
| X186 != szAzrzSzezqlpdtcmdtrp0(X184,X185)
| ~ aInteger0(X184)
| ~ aInteger0(X185)
| X185 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X187,X184,X185)
| ~ aElementOf0(X187,X186)
| X186 != szAzrzSzezqlpdtcmdtrp0(X184,X185)
| ~ aInteger0(X184)
| ~ aInteger0(X185)
| X185 = sz00 )
& ( ~ aInteger0(X188)
| ~ sdteqdtlpzmzozddtrp0(X188,X184,X185)
| aElementOf0(X188,X186)
| X186 != szAzrzSzezqlpdtcmdtrp0(X184,X185)
| ~ aInteger0(X184)
| ~ aInteger0(X185)
| X185 = sz00 )
& ( ~ aElementOf0(esk11_3(X184,X185,X189),X189)
| ~ aInteger0(esk11_3(X184,X185,X189))
| ~ sdteqdtlpzmzozddtrp0(esk11_3(X184,X185,X189),X184,X185)
| ~ aSet0(X189)
| X189 = szAzrzSzezqlpdtcmdtrp0(X184,X185)
| ~ aInteger0(X184)
| ~ aInteger0(X185)
| X185 = sz00 )
& ( aInteger0(esk11_3(X184,X185,X189))
| aElementOf0(esk11_3(X184,X185,X189),X189)
| ~ aSet0(X189)
| X189 = szAzrzSzezqlpdtcmdtrp0(X184,X185)
| ~ aInteger0(X184)
| ~ aInteger0(X185)
| X185 = sz00 )
& ( sdteqdtlpzmzozddtrp0(esk11_3(X184,X185,X189),X184,X185)
| aElementOf0(esk11_3(X184,X185,X189),X189)
| ~ aSet0(X189)
| X189 = szAzrzSzezqlpdtcmdtrp0(X184,X185)
| ~ aInteger0(X184)
| ~ aInteger0(X185)
| X185 = sz00 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mArSeq])])])])])]) ).
cnf(c_0_21,negated_conjecture,
( sdteqdtlpzmzozddtrp0(X1,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(X1,xc,xq)
| ~ aInteger0(X1) ),
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_10,c_0_11]),c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( sdteqdtlpzmzozddtrp0(xa,X1,xq)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(csr,[status(thm)],[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_17]),c_0_13]),c_0_18])]),c_0_15]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,plain,
( aElementOf0(X1,X4)
| X3 = sz00
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_18]),c_0_23])]) ).
cnf(c_0_26,plain,
( X1 = sz00
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X3)
| ~ aInteger0(X2) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
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_25]),c_0_13]),c_0_12]),c_0_18])]),c_0_15]) ).
cnf(c_0_28,negated_conjecture,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,negated_conjecture,
$false,
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_26,c_0_27]),c_0_13]),c_0_18]),c_0_12])]),c_0_15]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM443+4 : 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
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:34:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.41/1.76 % Version : CSE_E---1.7
% 1.41/1.76 % Problem : theBenchmark.p
% 1.41/1.76 % SZS status Theorem for theBenchmark.p
% 1.41/1.76 % SZS output start CNFRefutation
% See solution above
% 1.41/1.76 % Total time : 1.374s
%------------------------------------------------------------------------------