%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM436+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:17:00 AM UTC 2026
% Result : Theorem 178.02s 31.46s
% Output : CNFRefutation 178.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 27 unt; 0 def)
% Number of atoms : 176 ( 44 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 181 ( 72 ~; 74 |; 30 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 7 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntNeg,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('theBenchmark.p',mIntNeg) ).
fof(mIntPlus,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mIntPlus) ).
fof(mIntMult,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mIntMult) ).
fof(mDivisor,axiom,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('theBenchmark.p',mDivisor) ).
fof(m__979,axiom,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
file('theBenchmark.p',m__979) ).
fof(m__1003,axiom,
( sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& ? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) )
& sdtasdt0(xp,xq) != sz00 ),
file('theBenchmark.p',m__1003) ).
fof(m__1032,axiom,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
file('theBenchmark.p',m__1032) ).
fof(m__1071,axiom,
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm))
& sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
file('theBenchmark.p',m__1071) ).
fof(m__,conjecture,
( ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) )
& ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) )
& ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_28,plain,
( aInteger0(smndt0(A))
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mIntNeg]) ).
cnf(c_29,plain,
( aInteger0(sdtpldt0(A,B))
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mIntPlus]) ).
cnf(c_30,plain,
( aInteger0(sdtasdt0(A,B))
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mIntMult]) ).
cnf(c_56,plain,
( sdtasdt0(B,C) != A
| ~ aInteger0(C)
| B = sz00
| ~ aInteger0(B)
| aDivisorOf0(B,A)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mDivisor]) ).
cnf(c_57,plain,
( sdtasdt0(B,C) != A
| ~ aInteger0(C)
| sz00 = B
| ~ aInteger0(B)
| aDivisorOf0(B,A)
| ~ aInteger0(A) ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_68,plain,
aInteger0(xa),
inference(clausify,[status(thm)],[m__979]) ).
cnf(c_69,plain,
aInteger0(xb),
inference(clausify,[status(thm)],[m__979]) ).
cnf(c_70,plain,
aInteger0(xp),
inference(clausify,[status(thm)],[m__979]) ).
cnf(c_71,plain,
xp != sz00,
inference(clausify,[status(thm)],[m__979]) ).
cnf(c_72,plain,
aInteger0(xq),
inference(clausify,[status(thm)],[m__979]) ).
cnf(c_73,plain,
xq != sz00,
inference(clausify,[status(thm)],[m__979]) ).
fof(nnf_22,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& ? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) )
& sdtasdt0(xp,xq) != sz00 ),
inference(fof_nnf,[status(thm)],[m__1003]) ).
fof(sk_m__1003,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& sdtasdt0(sdtasdt0(xp,xq),sK0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(sK0)
& sdtasdt0(xp,xq) != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_22]) ).
cnf(c_76,plain,
sdtasdt0(sdtasdt0(xp,xq),sK0) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[sk_m__1003]) ).
cnf(c_77,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(sdtasdt0(xp,xq),sK0),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_81,plain,
aInteger0(xm),
inference(clausify,[status(thm)],[m__1032]) ).
cnf(c_84,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(clausify,[status(thm)],[m__1071]) ).
cnf(c_6339,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtasdt0(sdtasdt0(xp,xq),sK0),
inference(paramod,[status(thm)],[c_77,c_84]) ).
cnf(c_85,plain,
sdtasdt0(sdtasdt0(xp,xq),sK0) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(copy,[status(thm)],[c_6339]) ).
cnf(c_86,plain,
sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(clausify,[status(thm)],[m__1071]) ).
cnf(c_6340,plain,
sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(sdtasdt0(xp,xq),sK0),
inference(paramod,[status(thm)],[c_77,c_86]) ).
cnf(c_6341,plain,
sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(paramod,[status(thm)],[c_85,c_6340]) ).
cnf(c_87,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(copy,[status(thm)],[c_6341]) ).
cnf(c_96,negated_conjecture,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_6342,negated_conjecture,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(xp,sdtasdt0(sdtasdt0(xp,xq),sK0)) ),
inference(paramod,[status(thm)],[c_77,c_96]) ).
cnf(c_6343,negated_conjecture,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(xp,sdtasdt0(xp,sdtasdt0(xq,xm))) ),
inference(paramod,[status(thm)],[c_85,c_6342]) ).
cnf(c_6344,negated_conjecture,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(xp,sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(paramod,[status(thm)],[c_87,c_6343]) ).
cnf(c_6345,negated_conjecture,
( ~ aDivisorOf0(xq,sdtasdt0(sdtasdt0(xp,xq),sK0))
| ~ aDivisorOf0(xp,sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(paramod,[status(thm)],[c_77,c_6344]) ).
cnf(c_6346,negated_conjecture,
( ~ aDivisorOf0(xq,sdtasdt0(xp,sdtasdt0(xq,xm)))
| ~ aDivisorOf0(xp,sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(paramod,[status(thm)],[c_85,c_6345]) ).
cnf(c_97,negated_conjecture,
( ~ aDivisorOf0(xq,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aDivisorOf0(xp,sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(paramod,[status(thm)],[c_87,c_6346]) ).
cnf(c_6347,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(paramod,[status(thm)],[c_85,c_77]) ).
cnf(c_136,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(paramod,[status(thm)],[c_87,c_6347]) ).
cnf(c_521,plain,
aInteger0(smndt0(xb)),
inference(resolve,[status(thm)],[c_69,c_28]) ).
cnf(c_6348,plain,
( aInteger0(sdtasdt0(xq,A))
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_30,c_72]) ).
cnf(c_2622,plain,
aInteger0(sdtasdt0(xq,xm)),
inference(resolve,[status(thm)],[c_6348,c_81]) ).
cnf(c_6349,plain,
( aInteger0(sdtasdt0(xp,A))
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_30,c_70]) ).
cnf(c_2623,plain,
aInteger0(sdtasdt0(xp,xm)),
inference(resolve,[status(thm)],[c_6349,c_81]) ).
cnf(c_6350,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| sz00 = xp
| ~ aInteger0(xp)
| aDivisorOf0(xp,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(resolve,[status(thm)],[c_87,c_57]) ).
cnf(c_6351,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| xp = sz00
| ~ aInteger0(xp)
| aDivisorOf0(xp,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(copy,[status(thm)],[c_6350]) ).
cnf(c_6352,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| xp = sz00
| aDivisorOf0(xp,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(resolve,[status(thm)],[c_70,c_6351]) ).
cnf(c_6353,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| aDivisorOf0(xp,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(resolve,[status(thm)],[c_71,c_6352]) ).
cnf(c_2679,plain,
( aDivisorOf0(xp,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(resolve,[status(thm)],[c_2622,c_6353]) ).
cnf(c_6354,plain,
( A != sdtasdt0(B,C)
| ~ aInteger0(C)
| sz00 = B
| ~ aInteger0(B)
| aDivisorOf0(B,A)
| ~ aInteger0(A) ),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_6355,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| sz00 = xq
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtasdt0(xp,sdtasdt0(xq,xm)))
| ~ aInteger0(sdtasdt0(xp,sdtasdt0(xq,xm))) ),
inference(resolve,[status(thm)],[c_87,c_6354]) ).
cnf(c_6356,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| sz00 = xq
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtasdt0(xp,sdtasdt0(xq,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(paramod,[status(thm)],[c_87,c_6355]) ).
cnf(c_6357,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| sz00 = xq
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(paramod,[status(thm)],[c_87,c_6356]) ).
cnf(c_6358,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| xq = sz00
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(copy,[status(thm)],[c_6357]) ).
cnf(c_6359,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| xq = sz00
| aDivisorOf0(xq,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(resolve,[status(thm)],[c_72,c_6358]) ).
cnf(c_6360,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| aDivisorOf0(xq,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(resolve,[status(thm)],[c_73,c_6359]) ).
cnf(c_2680,plain,
( aDivisorOf0(xq,sdtasdt0(xq,sdtasdt0(xp,xm)))
| ~ aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))) ),
inference(resolve,[status(thm)],[c_2623,c_6360]) ).
cnf(c_6361,plain,
( aInteger0(sdtpldt0(xa,A))
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_29,c_68]) ).
cnf(c_6362,plain,
aInteger0(sdtpldt0(xa,smndt0(xb))),
inference(resolve,[status(thm)],[c_6361,c_521]) ).
cnf(c_6257,plain,
aInteger0(sdtasdt0(xq,sdtasdt0(xp,xm))),
inference(paramod,[status(thm)],[c_136,c_6362]) ).
cnf(c_6335,plain,
aDivisorOf0(xq,sdtasdt0(xq,sdtasdt0(xp,xm))),
inference(resolve,[status(thm)],[c_6257,c_2680]) ).
cnf(c_6336,plain,
aDivisorOf0(xp,sdtasdt0(xq,sdtasdt0(xp,xm))),
inference(resolve,[status(thm)],[c_6257,c_2679]) ).
cnf(c_6363,negated_conjecture,
~ aDivisorOf0(xq,sdtasdt0(xq,sdtasdt0(xp,xm))),
inference(resolve,[status(thm)],[c_6336,c_97]) ).
cnf(c_6338,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_6335,c_6363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM436+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 02:43:59 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 649569 was started by sandbox on n004,
% 0.10/5.38 % Sat Sep 26 02:43:59 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 178.02/31.46
% 178.02/31.46 % SZS status Theorem for theBenchmark
% 178.02/31.46
% 178.02/31.46 % Proof 1 at 1.62 (+ 0.33) seconds.
% 178.02/31.46 % Length of proof is 39.
% 178.02/31.46 % Level of proof is 8.
% 178.02/31.46 % Maximum clause weight is 18.000.
% 178.02/31.46 % Given clauses 96.
% 178.02/31.46
% 178.02/31.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------