%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM475+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:17:07 AM UTC 2026
% Result : Theorem 39.98s 5.44s
% Output : CNFRefutation 39.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 39 unt; 0 def)
% Number of atoms : 130 ( 65 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 106 ( 44 ~; 39 |; 17 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mAddComm,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('theBenchmark.p',mAddComm) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
file('theBenchmark.p',mAddAsso) ).
fof(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mAMDistr) ).
fof(mAddCanc,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('theBenchmark.p',mAddCanc) ).
fof(m__1324,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('theBenchmark.p',m__1324) ).
fof(m__1360,axiom,
( xp = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,xp)
& aNaturalNumber0(xp) ),
file('theBenchmark.p',m__1360) ).
fof(m__1379,axiom,
( xq = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& aNaturalNumber0(xq) ),
file('theBenchmark.p',m__1379) ).
fof(m__1422,axiom,
( xr = sdtmndt0(xq,xp)
& sdtpldt0(xp,xr) = xq
& aNaturalNumber0(xr) ),
file('theBenchmark.p',m__1422) ).
fof(m__,conjecture,
xn = sdtasdt0(xl,xr),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_40,negated_conjecture,
sdtasdt0(xl,xr) != xn,
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__1459,axiom,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('theBenchmark.p',m__1459) ).
cnf(c_41,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(clausify,[status(thm)],[m__1459]) ).
cnf(c_44,plain,
aNaturalNumber0(xr),
inference(clausify,[status(thm)],[m__1422]) ).
cnf(c_49,plain,
sdtasdt0(xl,xq) = sdtpldt0(xm,xn),
inference(clausify,[status(thm)],[m__1379]) ).
cnf(c_50,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_51,plain,
aNaturalNumber0(xq),
inference(clausify,[status(thm)],[m__1379]) ).
cnf(c_53,plain,
sdtasdt0(xl,xp) = xm,
inference(clausify,[status(thm)],[m__1360]) ).
cnf(c_64,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_65,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_66,plain,
aNaturalNumber0(xl),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_104,plain,
( C = B
| sdtpldt0(A,C) != sdtpldt0(A,B)
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mAddCanc]) ).
cnf(c_107,plain,
( sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mAMDistr]) ).
cnf(c_108,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_107]) ).
cnf(c_117,plain,
( sdtpldt0(sdtpldt0(A,B),C) = sdtpldt0(A,sdtpldt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mAddAsso]) ).
cnf(c_118,plain,
( sdtpldt0(B,A) = sdtpldt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mAddComm]) ).
cnf(c_119,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_12581,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(paramod,[status(thm)],[c_53,c_41]) ).
cnf(c_12582,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtpldt0(xm,xn),
inference(paramod,[status(thm)],[c_53,c_12581]) ).
cnf(c_125,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtasdt0(xl,xq),
inference(paramod,[status(thm)],[c_50,c_12582]) ).
cnf(c_12583,plain,
( sdtpldt0(sdtasdt0(xl,A),sdtasdt0(xl,B)) = sdtasdt0(xl,sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_108,c_66]) ).
cnf(c_12584,plain,
( sdtpldt0(sdtasdt0(xl,xq),sdtasdt0(xl,A)) = sdtasdt0(xl,sdtpldt0(xq,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_12583,c_51]) ).
cnf(c_945,plain,
sdtpldt0(sdtasdt0(xl,xq),sdtasdt0(xl,xr)) = sdtasdt0(xl,sdtpldt0(xq,xr)),
inference(resolve,[status(thm)],[c_12584,c_44]) ).
cnf(c_12585,plain,
( sdtpldt0(sdtpldt0(xm,A),B) = sdtpldt0(xm,sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_117,c_65]) ).
cnf(c_12586,plain,
( sdtpldt0(sdtpldt0(xm,xn),A) = sdtpldt0(xm,sdtpldt0(xn,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_12585,c_64]) ).
cnf(c_12587,plain,
sdtpldt0(sdtpldt0(xm,xn),xn) = sdtpldt0(xm,sdtpldt0(xn,xn)),
inference(resolve,[status(thm)],[c_12586,c_64]) ).
cnf(c_2061,plain,
sdtpldt0(sdtasdt0(xl,xq),xn) = sdtpldt0(xm,sdtpldt0(xn,xn)),
inference(paramod,[status(thm)],[c_50,c_12587]) ).
cnf(c_12588,plain,
( sdtpldt0(sdtpldt0(xn,A),B) = sdtpldt0(xn,sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_117,c_64]) ).
cnf(c_12589,plain,
( sdtpldt0(sdtpldt0(xn,xm),A) = sdtpldt0(xn,sdtpldt0(xm,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_12588,c_65]) ).
cnf(c_12590,plain,
sdtpldt0(sdtpldt0(xn,xm),xn) = sdtpldt0(xn,sdtpldt0(xm,xn)),
inference(resolve,[status(thm)],[c_12589,c_64]) ).
cnf(c_2091,plain,
sdtpldt0(sdtpldt0(xn,xm),xn) = sdtpldt0(xn,sdtasdt0(xl,xq)),
inference(paramod,[status(thm)],[c_50,c_12590]) ).
cnf(c_12591,plain,
( sdtpldt0(A,xm) = sdtpldt0(xm,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_118,c_65]) ).
cnf(c_12592,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolve,[status(thm)],[c_12591,c_64]) ).
cnf(c_2256,plain,
sdtpldt0(xn,xm) = sdtasdt0(xl,xq),
inference(paramod,[status(thm)],[c_50,c_12592]) ).
cnf(c_12593,plain,
sdtpldt0(sdtasdt0(xl,xq),xn) = sdtpldt0(xn,sdtasdt0(xl,xq)),
inference(paramod,[status(thm)],[c_2256,c_2091]) ).
cnf(c_12594,plain,
sdtpldt0(xm,sdtpldt0(xn,xn)) = sdtpldt0(xn,sdtasdt0(xl,xq)),
inference(paramod,[status(thm)],[c_2061,c_12593]) ).
cnf(c_2352,plain,
sdtpldt0(xn,sdtasdt0(xl,xq)) = sdtpldt0(xm,sdtpldt0(xn,xn)),
inference(copy,[status(thm)],[c_12594]) ).
cnf(c_12595,plain,
( aNaturalNumber0(sdtasdt0(xl,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_119,c_66]) ).
cnf(c_2534,plain,
aNaturalNumber0(sdtasdt0(xl,xq)),
inference(resolve,[status(thm)],[c_12595,c_51]) ).
cnf(c_12596,plain,
( aNaturalNumber0(sdtasdt0(xl,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_119,c_66]) ).
cnf(c_2535,plain,
aNaturalNumber0(sdtasdt0(xl,xr)),
inference(resolve,[status(thm)],[c_12596,c_44]) ).
cnf(c_12597,plain,
( sdtpldt0(sdtpldt0(xn,A),B) = sdtpldt0(xn,sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_117,c_64]) ).
cnf(c_12598,plain,
( sdtpldt0(sdtpldt0(xn,xm),A) = sdtpldt0(xn,sdtpldt0(xm,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_12597,c_65]) ).
cnf(c_12599,plain,
sdtpldt0(sdtpldt0(xn,xm),sdtasdt0(xl,xr)) = sdtpldt0(xn,sdtpldt0(xm,sdtasdt0(xl,xr))),
inference(resolve,[status(thm)],[c_12598,c_2535]) ).
cnf(c_12600,plain,
sdtpldt0(sdtasdt0(xl,xq),sdtasdt0(xl,xr)) = sdtpldt0(xn,sdtpldt0(xm,sdtasdt0(xl,xr))),
inference(paramod,[status(thm)],[c_2256,c_12599]) ).
cnf(c_12601,plain,
sdtasdt0(xl,sdtpldt0(xq,xr)) = sdtpldt0(xn,sdtpldt0(xm,sdtasdt0(xl,xr))),
inference(paramod,[status(thm)],[c_945,c_12600]) ).
cnf(c_12602,plain,
sdtasdt0(xl,sdtpldt0(xq,xr)) = sdtpldt0(xn,sdtasdt0(xl,xq)),
inference(paramod,[status(thm)],[c_125,c_12601]) ).
cnf(c_12603,plain,
sdtasdt0(xl,sdtpldt0(xq,xr)) = sdtpldt0(xm,sdtpldt0(xn,xn)),
inference(paramod,[status(thm)],[c_2352,c_12602]) ).
cnf(c_12169,plain,
sdtpldt0(xm,sdtpldt0(xn,xn)) = sdtasdt0(xl,sdtpldt0(xq,xr)),
inference(copy,[status(thm)],[c_12603]) ).
cnf(c_12604,plain,
( B = A
| sdtpldt0(sdtasdt0(xl,xq),B) != sdtpldt0(sdtasdt0(xl,xq),A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_104,c_2534]) ).
cnf(c_12605,plain,
( A = xn
| sdtpldt0(sdtasdt0(xl,xq),A) != sdtpldt0(sdtasdt0(xl,xq),xn)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_12604,c_64]) ).
cnf(c_12606,plain,
( sdtasdt0(xl,xr) = xn
| sdtpldt0(sdtasdt0(xl,xq),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xq),xn) ),
inference(resolve,[status(thm)],[c_12605,c_2535]) ).
cnf(c_12607,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xq),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xq),xn),
inference(resolve,[status(thm)],[c_12606,c_40]) ).
cnf(c_12608,negated_conjecture,
sdtasdt0(xl,sdtpldt0(xq,xr)) != sdtpldt0(sdtasdt0(xl,xq),xn),
inference(paramod,[status(thm)],[c_945,c_12607]) ).
cnf(c_12609,negated_conjecture,
sdtasdt0(xl,sdtpldt0(xq,xr)) != sdtpldt0(xm,sdtpldt0(xn,xn)),
inference(paramod,[status(thm)],[c_2061,c_12608]) ).
cnf(c_12610,negated_conjecture,
sdtasdt0(xl,sdtpldt0(xq,xr)) != sdtasdt0(xl,sdtpldt0(xq,xr)),
inference(paramod,[status(thm)],[c_12169,c_12609]) ).
cnf(c_12580,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_12610]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM475+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n004.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 26 02:54:22 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 666308 was started by sandbox2 on n004,
% 0.11/0.36 % Sat Sep 26 02:54:22 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 39.98/5.44
% 39.98/5.44 % given #500 (T,wt=11): 5595 doDivides0(xr,xp) | xr != xp. [resolve(5032,a,54,a)].
% 39.98/5.44
% 39.98/5.44 % SZS status Theorem for theBenchmark
% 39.98/5.44
% 39.98/5.44 % Proof 1 at 4.50 (+ 0.54) seconds.
% 39.98/5.44 % Length of proof is 36.
% 39.98/5.44 % Level of proof is 6.
% 39.98/5.44 % Maximum clause weight is 42.000.
% 39.98/5.44 % Given clauses 581.
% 39.98/5.44
% 39.98/5.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------