%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM436+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.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 04:57:20 PM UTC 2026
% Result : Theorem 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 16 unt; 0 def)
% Number of atoms : 107 ( 25 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 123 ( 51 ~; 46 |; 21 &)
% ( 2 <=>; 3 =>; 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(m__1071,hypothesis,
( sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb))
& sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1071) ).
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/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(m__979,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__979) ).
fof(m__,conjecture,
( sdteqdtlpzmzozddtrp0(xa,xb,xp)
& sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1032,hypothesis,
( aInteger0(xm)
& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1032) ).
fof(c_0_7,plain,
! [X71,X72,X74,X75] :
( ( aInteger0(X72)
| ~ aDivisorOf0(X72,X71)
| ~ aInteger0(X71) )
& ( X72 != sz00
| ~ aDivisorOf0(X72,X71)
| ~ aInteger0(X71) )
& ( aInteger0(esk1_2(X71,X72))
| ~ aDivisorOf0(X72,X71)
| ~ aInteger0(X71) )
& ( sdtasdt0(X72,esk1_2(X71,X72)) = X71
| ~ aDivisorOf0(X72,X71)
| ~ aInteger0(X71) )
& ( ~ aInteger0(X74)
| X74 = sz00
| ~ aInteger0(X75)
| sdtasdt0(X74,X75) != X71
| aDivisorOf0(X74,X71)
| ~ aInteger0(X71) ) ),
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_8,plain,
! [X49,X50] :
( ~ aInteger0(X49)
| ~ aInteger0(X50)
| aInteger0(sdtasdt0(X49,X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_9,hypothesis,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[m__1071]) ).
cnf(c_0_10,hypothesis,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[m__1071]) ).
cnf(c_0_11,plain,
( X1 = sz00
| aDivisorOf0(X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X76,X77,X78] :
( ( ~ sdteqdtlpzmzozddtrp0(X76,X77,X78)
| aDivisorOf0(X78,sdtpldt0(X76,smndt0(X77)))
| ~ aInteger0(X76)
| ~ aInteger0(X77)
| ~ aInteger0(X78)
| X78 = sz00 )
& ( ~ aDivisorOf0(X78,sdtpldt0(X76,smndt0(X77)))
| sdteqdtlpzmzozddtrp0(X76,X77,X78)
| ~ aInteger0(X76)
| ~ aInteger0(X77)
| ~ aInteger0(X78)
| X78 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_14,hypothesis,
sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_11]),c_0_12]) ).
cnf(c_0_16,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_17,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__979]) ).
fof(c_0_18,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
& sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_19,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_13]) ).
cnf(c_0_20,hypothesis,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(rw,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_21,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_22,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_23,hypothesis,
( aDivisorOf0(xq,sdtasdt0(xp,sdtasdt0(xq,xm)))
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_16])]),c_0_17]) ).
cnf(c_0_24,hypothesis,
aInteger0(xm),
inference(split_conjunct,[status(thm)],[m__1032]) ).
cnf(c_0_25,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[m__979]) ).
fof(c_0_26,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_27,hypothesis,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(xa,xb,X1)
| ~ aDivisorOf0(X1,sdtasdt0(xp,sdtasdt0(xq,xm)))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_28,hypothesis,
aDivisorOf0(xq,sdtasdt0(xp,sdtasdt0(xq,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_12]),c_0_24]),c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_16])]),c_0_17]) ).
cnf(c_0_31,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_32,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xb,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_33,hypothesis,
~ aInteger0(sdtasdt0(xq,xm)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_15]),c_0_25])]),c_0_31]),c_0_32]) ).
cnf(c_0_34,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_12]),c_0_24]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM436+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:34:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Theorem for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------