%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM425+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 : n010.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 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 99 ( 20 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 115 ( 48 ~; 44 |; 17 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 19 !; 3 ?)
% 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(m__724,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__724) ).
fof(m__704,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__704) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(m__,conjecture,
? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) ),
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(c_0_7,plain,
! [X69,X70,X71] :
( ( ~ sdteqdtlpzmzozddtrp0(X69,X70,X71)
| aDivisorOf0(X71,sdtpldt0(X69,smndt0(X70)))
| ~ aInteger0(X69)
| ~ aInteger0(X70)
| ~ aInteger0(X71)
| X71 = sz00 )
& ( ~ aDivisorOf0(X71,sdtpldt0(X69,smndt0(X70)))
| sdteqdtlpzmzozddtrp0(X69,X70,X71)
| ~ aInteger0(X69)
| ~ aInteger0(X70)
| ~ aInteger0(X71)
| X71 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
fof(c_0_8,plain,
! [X64,X65,X67,X68] :
( ( aInteger0(X65)
| ~ aDivisorOf0(X65,X64)
| ~ aInteger0(X64) )
& ( X65 != sz00
| ~ aDivisorOf0(X65,X64)
| ~ aInteger0(X64) )
& ( aInteger0(esk1_2(X64,X65))
| ~ aDivisorOf0(X65,X64)
| ~ aInteger0(X64) )
& ( sdtasdt0(X65,esk1_2(X64,X65)) = X64
| ~ aDivisorOf0(X65,X64)
| ~ aInteger0(X64) )
& ( ~ aInteger0(X67)
| X67 = sz00
| ~ aInteger0(X68)
| sdtasdt0(X67,X68) != X64
| aDivisorOf0(X67,X64)
| ~ aInteger0(X64) ) ),
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])])])])])]) ).
cnf(c_0_9,plain,
( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
| X3 = sz00
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(split_conjunct,[status(thm)],[m__724]) ).
cnf(c_0_11,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_12,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_13,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_14,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_15,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,hypothesis,
aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))),
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_9,c_0_10]),c_0_11]),c_0_12]),c_0_13])]),c_0_14]) ).
fof(c_0_17,plain,
! [X40,X41] :
( ~ aInteger0(X40)
| ~ aInteger0(X41)
| aInteger0(sdtpldt0(X40,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
cnf(c_0_18,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_19,negated_conjecture,
~ ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_20,hypothesis,
( sdtasdt0(xq,esk1_2(sdtpldt0(xa,smndt0(xb)),xq)) = sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X39] :
( ~ aInteger0(X39)
| aInteger0(smndt0(X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_23,hypothesis,
( aInteger0(esk1_2(sdtpldt0(xa,smndt0(xb)),xq))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
fof(c_0_24,negated_conjecture,
! [X74] :
( ~ aInteger0(X74)
| sdtasdt0(xq,X74) != sdtpldt0(xa,smndt0(xb)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
cnf(c_0_25,hypothesis,
( sdtasdt0(xq,esk1_2(sdtpldt0(xa,smndt0(xb)),xq)) = sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_13])]) ).
cnf(c_0_26,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,hypothesis,
( aInteger0(esk1_2(sdtpldt0(xa,smndt0(xb)),xq))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_13])]) ).
cnf(c_0_28,negated_conjecture,
( ~ aInteger0(X1)
| sdtasdt0(xq,X1) != sdtpldt0(xa,smndt0(xb)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,hypothesis,
sdtasdt0(xq,esk1_2(sdtpldt0(xa,smndt0(xb)),xq)) = sdtpldt0(xa,smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_12])]) ).
cnf(c_0_30,hypothesis,
aInteger0(esk1_2(sdtpldt0(xa,smndt0(xb)),xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_12])]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM425+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n010.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:31:51 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------