%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM436+3 : 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 04:57:20 PM UTC 2026
% Result : Theorem 1.27s 1.73s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 80 ( 23 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 104 ( 45 ~; 36 |; 22 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 6 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 6 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',m__1071) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(m__1032,hypothesis,
( aInteger0(xm)
& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1032) ).
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(c_0_5,negated_conjecture,
~ ( ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,negated_conjecture,
! [X92,X93] :
( ( ~ aInteger0(X93)
| sdtasdt0(xq,X93) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X92)
| sdtasdt0(xp,X92) != sdtpldt0(xa,smndt0(xb)) )
& ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(X92)
| sdtasdt0(xp,X92) != sdtpldt0(xa,smndt0(xb)) )
& ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ aInteger0(X92)
| sdtasdt0(xp,X92) != sdtpldt0(xa,smndt0(xb)) )
& ( ~ aInteger0(X93)
| sdtasdt0(xq,X93) != sdtpldt0(xa,smndt0(xb))
| ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) )
& ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) )
& ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) )
& ( ~ aInteger0(X93)
| sdtasdt0(xq,X93) != sdtpldt0(xa,smndt0(xb))
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_7,hypothesis,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[m__1071]) ).
cnf(c_0_8,hypothesis,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[m__1071]) ).
cnf(c_0_9,negated_conjecture,
( ~ aInteger0(X1)
| sdtasdt0(xq,X1) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X2)
| sdtasdt0(xp,X2) != sdtpldt0(xa,smndt0(xb)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( sdtasdt0(xp,X1) != sdtasdt0(xp,sdtasdt0(xq,xm))
| sdtasdt0(xq,X2) != sdtasdt0(xp,sdtasdt0(xq,xm))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_8]),c_0_10]),c_0_8]),c_0_10]) ).
cnf(c_0_12,negated_conjecture,
( sdtasdt0(xq,X1) != sdtasdt0(xp,sdtasdt0(xq,xm))
| ~ aInteger0(sdtasdt0(xq,xm))
| ~ aInteger0(X1) ),
inference(er,[status(thm)],[c_0_11]) ).
fof(c_0_13,plain,
! [X52,X53] :
( ~ aInteger0(X52)
| ~ aInteger0(X53)
| aInteger0(sdtasdt0(X52,X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_14,hypothesis,
( ~ aInteger0(sdtasdt0(xq,xm))
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_15,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,hypothesis,
aInteger0(xm),
inference(split_conjunct,[status(thm)],[m__1032]) ).
cnf(c_0_17,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_18,hypothesis,
~ aInteger0(sdtasdt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_19,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_20,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_16]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM436+3 : 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 : n017.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 00:32:27 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.27/1.73 % Version : CSE_E---1.7
% 1.27/1.73 % Problem : theBenchmark.p
% 1.27/1.73 % SZS status Theorem for theBenchmark.p
% 1.27/1.73 % SZS output start CNFRefutation
% See solution above
% 1.27/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------