%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM448+5 : 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 04:57:22 PM UTC 2026
% Result : Theorem 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 7 unt; 0 def)
% Number of atoms : 275 ( 63 equ)
% Maximal formula atoms : 102 ( 6 avg)
% Number of connectives : 363 ( 130 ~; 141 |; 71 &)
% ( 7 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 21 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ! [X1] :
( aInteger0(X1)
=> ( ( ( ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) )
| aElementOf0(X1,sbsmnsldt0(xS)) )
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 )
& aDivisorOf0(X2,X1)
& isPrime0(X2) ) )
& ( ? [X2] :
( ( ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) )
| aDivisorOf0(X2,X1) )
& isPrime0(X2) )
=> ( ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) )
& aElementOf0(X1,sbsmnsldt0(xS)) ) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) ) )
=> ( ( aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
| stldt0(sbsmnsldt0(xS)) = cS2076 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mPrimeDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ( ? [X2] :
( aDivisorOf0(X2,X1)
& isPrime0(X2) )
<=> ( X1 != sz10
& X1 != smndt0(sz10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimeDivisor) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(c_0_4,negated_conjecture,
~ ( ! [X1] :
( aInteger0(X1)
=> ( ( ( ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) )
| aElementOf0(X1,sbsmnsldt0(xS)) )
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 )
& aDivisorOf0(X2,X1)
& isPrime0(X2) ) )
& ( ? [X2] :
( ( ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) )
| aDivisorOf0(X2,X1) )
& isPrime0(X2) )
=> ( ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) )
& aElementOf0(X1,sbsmnsldt0(xS)) ) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) ) )
=> ( ( aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
| stldt0(sbsmnsldt0(xS)) = cS2076 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_5,negated_conjecture,
! [X234,X235,X238,X239,X241,X243,X244,X245] :
( ( aInteger0(esk19_1(X234))
| ~ aElementOf0(X235,xS)
| ~ aElementOf0(X234,X235)
| ~ aInteger0(X234) )
& ( esk19_1(X234) != sz00
| ~ aElementOf0(X235,xS)
| ~ aElementOf0(X234,X235)
| ~ aInteger0(X234) )
& ( aInteger0(esk20_1(X234))
| ~ aElementOf0(X235,xS)
| ~ aElementOf0(X234,X235)
| ~ aInteger0(X234) )
& ( sdtasdt0(esk19_1(X234),esk20_1(X234)) = X234
| ~ aElementOf0(X235,xS)
| ~ aElementOf0(X234,X235)
| ~ aInteger0(X234) )
& ( aDivisorOf0(esk19_1(X234),X234)
| ~ aElementOf0(X235,xS)
| ~ aElementOf0(X234,X235)
| ~ aInteger0(X234) )
& ( isPrime0(esk19_1(X234))
| ~ aElementOf0(X235,xS)
| ~ aElementOf0(X234,X235)
| ~ aInteger0(X234) )
& ( aInteger0(esk19_1(X234))
| ~ aElementOf0(X234,sbsmnsldt0(xS))
| ~ aInteger0(X234) )
& ( esk19_1(X234) != sz00
| ~ aElementOf0(X234,sbsmnsldt0(xS))
| ~ aInteger0(X234) )
& ( aInteger0(esk20_1(X234))
| ~ aElementOf0(X234,sbsmnsldt0(xS))
| ~ aInteger0(X234) )
& ( sdtasdt0(esk19_1(X234),esk20_1(X234)) = X234
| ~ aElementOf0(X234,sbsmnsldt0(xS))
| ~ aInteger0(X234) )
& ( aDivisorOf0(esk19_1(X234),X234)
| ~ aElementOf0(X234,sbsmnsldt0(xS))
| ~ aInteger0(X234) )
& ( isPrime0(esk19_1(X234))
| ~ aElementOf0(X234,sbsmnsldt0(xS))
| ~ aInteger0(X234) )
& ( aElementOf0(esk21_1(X234),xS)
| ~ aInteger0(X238)
| X238 = sz00
| ~ aInteger0(X239)
| sdtasdt0(X238,X239) != X234
| ~ isPrime0(X238)
| ~ aInteger0(X234) )
& ( aElementOf0(X234,esk21_1(X234))
| ~ aInteger0(X238)
| X238 = sz00
| ~ aInteger0(X239)
| sdtasdt0(X238,X239) != X234
| ~ isPrime0(X238)
| ~ aInteger0(X234) )
& ( aElementOf0(X234,sbsmnsldt0(xS))
| ~ aInteger0(X238)
| X238 = sz00
| ~ aInteger0(X239)
| sdtasdt0(X238,X239) != X234
| ~ isPrime0(X238)
| ~ aInteger0(X234) )
& ( aElementOf0(esk21_1(X234),xS)
| ~ aDivisorOf0(X238,X234)
| ~ isPrime0(X238)
| ~ aInteger0(X234) )
& ( aElementOf0(X234,esk21_1(X234))
| ~ aDivisorOf0(X238,X234)
| ~ isPrime0(X238)
| ~ aInteger0(X234) )
& ( aElementOf0(X234,sbsmnsldt0(xS))
| ~ aDivisorOf0(X238,X234)
| ~ isPrime0(X238)
| ~ aInteger0(X234) )
& aSet0(sbsmnsldt0(xS))
& ( aInteger0(X241)
| ~ aElementOf0(X241,sbsmnsldt0(xS)) )
& ( aElementOf0(esk22_1(X241),xS)
| ~ aElementOf0(X241,sbsmnsldt0(xS)) )
& ( aElementOf0(X241,esk22_1(X241))
| ~ aElementOf0(X241,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X243)
| ~ aElementOf0(X244,xS)
| ~ aElementOf0(X243,X244)
| aElementOf0(X243,sbsmnsldt0(xS)) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ( aInteger0(X245)
| ~ aElementOf0(X245,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X245,sbsmnsldt0(xS))
| ~ aElementOf0(X245,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X245)
| aElementOf0(X245,sbsmnsldt0(xS))
| aElementOf0(X245,stldt0(sbsmnsldt0(xS))) )
& ( esk23_0 != sz10
| ~ aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS))) )
& ( esk23_0 != smndt0(sz10)
| ~ aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS))) )
& ( aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS)))
| esk23_0 = sz10
| esk23_0 = smndt0(sz10) )
& stldt0(sbsmnsldt0(xS)) != cS2076 ),
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_4])])])])])]) ).
fof(c_0_6,plain,
! [X114] :
( ~ aInteger0(X114)
| aInteger0(smndt0(X114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_7,negated_conjecture,
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS)))
| esk23_0 = sz10
| esk23_0 = smndt0(sz10) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X160,X161] :
( ( X160 != sz10
| ~ aDivisorOf0(X161,X160)
| ~ isPrime0(X161)
| ~ aInteger0(X160) )
& ( X160 != smndt0(sz10)
| ~ aDivisorOf0(X161,X160)
| ~ isPrime0(X161)
| ~ aInteger0(X160) )
& ( aDivisorOf0(esk2_1(X160),X160)
| X160 = sz10
| X160 = smndt0(sz10)
| ~ aInteger0(X160) )
& ( isPrime0(esk2_1(X160))
| X160 = sz10
| X160 = smndt0(sz10)
| ~ aInteger0(X160) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrimeDivisor])])])])]) ).
cnf(c_0_10,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( smndt0(sz10) = esk23_0
| esk23_0 = sz10
| aInteger0(esk23_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_13,plain,
( X1 != smndt0(sz10)
| ~ aDivisorOf0(X2,X1)
| ~ isPrime0(X2)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( aDivisorOf0(esk19_1(X1),X1)
| ~ aElementOf0(X1,sbsmnsldt0(xS))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( aInteger0(X1)
| ~ aElementOf0(X1,sbsmnsldt0(xS)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
( isPrime0(esk19_1(X1))
| ~ aElementOf0(X1,sbsmnsldt0(xS))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,plain,
( aDivisorOf0(esk2_1(X1),X1)
| X1 = sz10
| X1 = smndt0(sz10)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( esk23_0 = sz10
| aInteger0(esk23_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_19,plain,
( isPrime0(esk2_1(X1))
| X1 = sz10
| X1 = smndt0(sz10)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
( ~ aElementOf0(X1,sbsmnsldt0(xS))
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
( aElementOf0(X1,sbsmnsldt0(xS))
| aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,plain,
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_23,negated_conjecture,
( aDivisorOf0(esk19_1(X1),X1)
| ~ aElementOf0(X1,sbsmnsldt0(xS)) ),
inference(csr,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( isPrime0(esk19_1(X1))
| ~ aElementOf0(X1,sbsmnsldt0(xS)) ),
inference(csr,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_25,negated_conjecture,
( aElementOf0(X1,sbsmnsldt0(xS))
| ~ aDivisorOf0(X2,X1)
| ~ isPrime0(X2)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,negated_conjecture,
( smndt0(sz10) = esk23_0
| esk23_0 = sz10
| aDivisorOf0(esk2_1(esk23_0),esk23_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( smndt0(sz10) = esk23_0
| esk23_0 = sz10
| isPrime0(esk2_1(esk23_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( smndt0(sz10) = esk23_0
| esk23_0 = sz10
| ~ aElementOf0(esk23_0,sbsmnsldt0(xS)) ),
inference(spm,[status(thm)],[c_0_20,c_0_8]) ).
cnf(c_0_29,plain,
( X1 != sz10
| ~ aDivisorOf0(X2,X1)
| ~ isPrime0(X2)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,negated_conjecture,
( esk23_0 != smndt0(sz10)
| ~ aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_31,negated_conjecture,
( esk23_0 = sz10
| aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS)))
| aElementOf0(esk23_0,sbsmnsldt0(xS)) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_32,negated_conjecture,
~ aElementOf0(smndt0(sz10),sbsmnsldt0(xS)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_15]),c_0_24]) ).
cnf(c_0_33,negated_conjecture,
( smndt0(sz10) = esk23_0
| esk23_0 = sz10 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_18]),c_0_27]),c_0_28]) ).
cnf(c_0_34,plain,
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_12])]) ).
cnf(c_0_35,negated_conjecture,
( esk23_0 = sz10
| aElementOf0(esk23_0,sbsmnsldt0(xS))
| smndt0(sz10) != esk23_0 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( esk23_0 = sz10
| ~ aElementOf0(esk23_0,sbsmnsldt0(xS)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
~ aElementOf0(sz10,sbsmnsldt0(xS)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_23]),c_0_24]) ).
cnf(c_0_38,negated_conjecture,
( esk23_0 != sz10
| ~ aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_39,negated_conjecture,
esk23_0 = sz10,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_36]) ).
cnf(c_0_40,negated_conjecture,
aElementOf0(sz10,stldt0(sbsmnsldt0(xS))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_12]),c_0_37]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM448+5 : 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
% 0.14/0.33 % Computer : n029.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 00:34:59 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.33/1.73 % Version : CSE_E---1.7
% 1.33/1.73 % Problem : theBenchmark.p
% 1.33/1.73 % SZS status Theorem for theBenchmark.p
% 1.33/1.73 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------