%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM427+1 : 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 : n019.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 04:57:17 PM UTC 2026
% Result : Theorem 1.33s 1.75s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 95 ( 19 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 113 ( 46 ~; 45 |; 16 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 18 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(m__767,hypothesis,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__767) ).
fof(m__704,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__704) ).
fof(m__,conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
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(m__747,hypothesis,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__747) ).
fof(c_0_8,plain,
! [X68,X69,X70] :
( ( ~ sdteqdtlpzmzozddtrp0(X68,X69,X70)
| aDivisorOf0(X70,sdtpldt0(X68,smndt0(X69)))
| ~ aInteger0(X68)
| ~ aInteger0(X69)
| ~ aInteger0(X70)
| X70 = sz00 )
& ( ~ aDivisorOf0(X70,sdtpldt0(X68,smndt0(X69)))
| sdteqdtlpzmzozddtrp0(X68,X69,X70)
| ~ aInteger0(X68)
| ~ aInteger0(X69)
| ~ aInteger0(X70)
| X70 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
fof(c_0_9,plain,
! [X63,X64,X66,X67] :
( ( aInteger0(X64)
| ~ aDivisorOf0(X64,X63)
| ~ aInteger0(X63) )
& ( X64 != sz00
| ~ aDivisorOf0(X64,X63)
| ~ aInteger0(X63) )
& ( aInteger0(esk1_2(X63,X64))
| ~ aDivisorOf0(X64,X63)
| ~ aInteger0(X63) )
& ( sdtasdt0(X64,esk1_2(X63,X64)) = X63
| ~ aDivisorOf0(X64,X63)
| ~ aInteger0(X63) )
& ( ~ aInteger0(X66)
| X66 = sz00
| ~ aInteger0(X67)
| sdtasdt0(X66,X67) != X63
| aDivisorOf0(X66,X63)
| ~ aInteger0(X63) ) ),
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)],[mDivisor])])])])])]) ).
fof(c_0_10,plain,
! [X41,X42] :
( ~ aInteger0(X41)
| ~ aInteger0(X42)
| aInteger0(sdtasdt0(X41,X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_11,plain,
( sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(split_conjunct,[status(thm)],[m__767]) ).
cnf(c_0_13,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_14,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_15,plain,
( X1 = sz00
| aDivisorOf0(X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_18,hypothesis,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(xb,xa,X1)
| ~ aDivisorOf0(X1,sdtasdt0(xq,smndt0(xn)))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_19,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]) ).
cnf(c_0_20,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_21,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_22,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X38] :
( ~ aInteger0(X38)
| aInteger0(smndt0(X38)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_24,hypothesis,
~ aInteger0(smndt0(xn)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_21]),c_0_22]) ).
cnf(c_0_25,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__747]) ).
cnf(c_0_27,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM427+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % 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
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 00:33:29 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.33/1.75 % Version : CSE_E---1.7
% 1.33/1.75 % Problem : theBenchmark.p
% 1.33/1.75 % SZS status Theorem for theBenchmark.p
% 1.33/1.75 % SZS output start CNFRefutation
% See solution above
% 1.33/1.75 % Total time : 1.375s
%------------------------------------------------------------------------------