%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM432+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 : n014.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 04:57:19 PM UTC 2026
% Result : Theorem 1.39s 1.76s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 102 ( 20 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 120 ( 48 ~; 47 |; 19 &)
% ( 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 : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 20 !; 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__924,hypothesis,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__924) ).
fof(m__818,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00
& aInteger0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(m__,conjecture,
sdteqdtlpzmzozddtrp0(xa,xc,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(m__899,hypothesis,
( aInteger0(xm)
& sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__899) ).
fof(m__876,hypothesis,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__876) ).
fof(c_0_9,plain,
! [X71,X72,X73] :
( ( ~ sdteqdtlpzmzozddtrp0(X71,X72,X73)
| aDivisorOf0(X73,sdtpldt0(X71,smndt0(X72)))
| ~ aInteger0(X71)
| ~ aInteger0(X72)
| ~ aInteger0(X73)
| X73 = sz00 )
& ( ~ aDivisorOf0(X73,sdtpldt0(X71,smndt0(X72)))
| sdteqdtlpzmzozddtrp0(X71,X72,X73)
| ~ aInteger0(X71)
| ~ aInteger0(X72)
| ~ aInteger0(X73)
| X73 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
fof(c_0_10,plain,
! [X66,X67,X69,X70] :
( ( aInteger0(X67)
| ~ aDivisorOf0(X67,X66)
| ~ aInteger0(X66) )
& ( X67 != sz00
| ~ aDivisorOf0(X67,X66)
| ~ aInteger0(X66) )
& ( aInteger0(esk1_2(X66,X67))
| ~ aDivisorOf0(X67,X66)
| ~ aInteger0(X66) )
& ( sdtasdt0(X67,esk1_2(X66,X67)) = X66
| ~ aDivisorOf0(X67,X66)
| ~ aInteger0(X66) )
& ( ~ aInteger0(X69)
| X69 = sz00
| ~ aInteger0(X70)
| sdtasdt0(X69,X70) != X66
| aDivisorOf0(X69,X66)
| ~ aInteger0(X66) ) ),
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_11,plain,
! [X44,X45] :
( ~ aInteger0(X44)
| ~ aInteger0(X45)
| aInteger0(sdtasdt0(X44,X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_12,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_9]) ).
cnf(c_0_13,hypothesis,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(split_conjunct,[status(thm)],[m__924]) ).
cnf(c_0_14,hypothesis,
aInteger0(xc),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_15,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_16,plain,
( X1 = sz00
| aDivisorOf0(X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_19,hypothesis,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(xa,xc,X1)
| ~ aDivisorOf0(X1,sdtasdt0(xq,sdtpldt0(xn,xm)))
| ~ aInteger0(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_20,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]) ).
cnf(c_0_21,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_22,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_23,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X42,X43] :
( ~ aInteger0(X42)
| ~ aInteger0(X43)
| aInteger0(sdtpldt0(X42,X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
cnf(c_0_25,hypothesis,
~ aInteger0(sdtpldt0(xn,xm)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22]),c_0_23]) ).
cnf(c_0_26,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,hypothesis,
aInteger0(xm),
inference(split_conjunct,[status(thm)],[m__899]) ).
cnf(c_0_28,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__876]) ).
cnf(c_0_29,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM432+1 : 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 : n014.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 00:33:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.39/1.76 % Version : CSE_E---1.7
% 1.39/1.76 % Problem : theBenchmark.p
% 1.39/1.76 % SZS status Theorem for theBenchmark.p
% 1.39/1.76 % SZS output start CNFRefutation
% See solution above
% 1.39/1.77 % Total time : 1.373s
%------------------------------------------------------------------------------