%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM434+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 : n017.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 1.31s 1.74s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 138 ( 40 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 157 ( 61 ~; 66 |; 21 &)
% ( 2 <=>; 7 =>; 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 27 !; 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(m__1003,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1003) ).
fof(m__979,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__979) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
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(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(sdtasdt0(xp,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(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(c_0_9,plain,
! [X77,X78,X79] :
( ( ~ sdteqdtlpzmzozddtrp0(X77,X78,X79)
| aDivisorOf0(X79,sdtpldt0(X77,smndt0(X78)))
| ~ aInteger0(X77)
| ~ aInteger0(X78)
| ~ aInteger0(X79)
| X79 = sz00 )
& ( ~ aDivisorOf0(X79,sdtpldt0(X77,smndt0(X78)))
| sdteqdtlpzmzozddtrp0(X77,X78,X79)
| ~ aInteger0(X77)
| ~ aInteger0(X78)
| ~ aInteger0(X79)
| X79 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_10,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_9]) ).
cnf(c_0_11,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(split_conjunct,[status(thm)],[m__1003]) ).
cnf(c_0_12,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_13,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__979]) ).
fof(c_0_14,plain,
! [X50,X51] :
( ~ aInteger0(X50)
| ~ aInteger0(X51)
| aInteger0(sdtasdt0(X50,X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
fof(c_0_15,plain,
! [X72,X73,X75,X76] :
( ( aInteger0(X73)
| ~ aDivisorOf0(X73,X72)
| ~ aInteger0(X72) )
& ( X73 != sz00
| ~ aDivisorOf0(X73,X72)
| ~ aInteger0(X72) )
& ( aInteger0(esk1_2(X72,X73))
| ~ aDivisorOf0(X73,X72)
| ~ aInteger0(X72) )
& ( sdtasdt0(X73,esk1_2(X72,X73)) = X72
| ~ aDivisorOf0(X73,X72)
| ~ aInteger0(X72) )
& ( ~ aInteger0(X75)
| X75 = sz00
| ~ aInteger0(X76)
| sdtasdt0(X75,X76) != X72
| aDivisorOf0(X75,X72)
| ~ aInteger0(X72) ) ),
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_16,hypothesis,
( sdtasdt0(xp,xq) = sz00
| aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtasdt0(xp,xq)) ),
inference(cn,[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])]) ).
cnf(c_0_17,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_19,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_20,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,hypothesis,
( sdtasdt0(xp,xq) = sz00
| aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).
fof(c_0_22,plain,
! [X48,X49] :
( ~ aInteger0(X48)
| ~ aInteger0(X49)
| aInteger0(sdtpldt0(X48,X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
cnf(c_0_23,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_24,negated_conjecture,
~ ? [X1] :
( aInteger0(X1)
& sdtasdt0(sdtasdt0(xp,xq),X1) = sdtpldt0(xa,smndt0(xb)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_25,hypothesis,
( sdtasdt0(sdtasdt0(xp,xq),esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) = sdtpldt0(xa,smndt0(xb))
| sdtasdt0(xp,xq) = sz00
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,plain,
! [X47] :
( ~ aInteger0(X47)
| aInteger0(smndt0(X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_28,hypothesis,
( sdtasdt0(xp,xq) = sz00
| aInteger0(esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq)))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
fof(c_0_29,negated_conjecture,
! [X89] :
( ~ aInteger0(X89)
| sdtasdt0(sdtasdt0(xp,xq),X89) != sdtpldt0(xa,smndt0(xb)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).
cnf(c_0_30,hypothesis,
( sdtasdt0(sdtasdt0(xp,xq),esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) = sdtpldt0(xa,smndt0(xb))
| sdtasdt0(xp,xq) = sz00
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_13])]) ).
cnf(c_0_31,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,hypothesis,
( sdtasdt0(xp,xq) = sz00
| aInteger0(esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq)))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_13])]) ).
fof(c_0_33,plain,
! [X70,X71] :
( ~ aInteger0(X70)
| ~ aInteger0(X71)
| sdtasdt0(X70,X71) != sz00
| X70 = sz00
| X71 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).
cnf(c_0_34,negated_conjecture,
( ~ aInteger0(X1)
| sdtasdt0(sdtasdt0(xp,xq),X1) != sdtpldt0(xa,smndt0(xb)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,hypothesis,
( sdtasdt0(sdtasdt0(xp,xq),esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) = sdtpldt0(xa,smndt0(xb))
| sdtasdt0(xp,xq) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_12])]) ).
cnf(c_0_36,hypothesis,
( sdtasdt0(xp,xq) = sz00
| aInteger0(esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_12])]) ).
cnf(c_0_37,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
sdtasdt0(xp,xq) = sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_40,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_18]),c_0_19])]),c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM434+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
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 00:33:27 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.31/1.74 % Version : CSE_E---1.7
% 1.31/1.74 % Problem : theBenchmark.p
% 1.31/1.74 % SZS status Theorem for theBenchmark.p
% 1.31/1.74 % SZS output start CNFRefutation
% See solution above
% 1.31/1.74 % Total time : 1.374s
%------------------------------------------------------------------------------