%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM473+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 : n016.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 08:17:06 AM UTC 2026
% Result : Theorem 4.76s 1.12s
% Output : CNFRefutation 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 21 unt; 0 def)
% Number of atoms : 166 ( 63 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 170 ( 63 ~; 74 |; 23 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mMulCanc,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 != sz00
=> ! [W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0)
| sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
=> W1 = W2 ) ) ) ),
file('theBenchmark.p',mMulCanc) ).
fof(mLEAsym,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLEAsym) ).
fof(mLETotal,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
file('theBenchmark.p',mLETotal) ).
fof(mMonMul,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& W1 != W2
& W0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) ) ) ),
file('theBenchmark.p',mMonMul) ).
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__1409,axiom,
( sdtlseqdt0(xm,sdtpldt0(xm,xn))
& ? [W0] :
( sdtpldt0(xm,W0) = sdtpldt0(xm,xn)
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__1409) ).
fof(m__,conjecture,
( sdtlseqdt0(xp,xq)
| ? [W0] :
( sdtpldt0(xp,W0) = xq
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdtlseqdt0(xp,xq)
| ? [W0] :
( sdtpldt0(xp,W0) = xq
& aNaturalNumber0(W0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_39,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_41,plain,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(clausify,[status(thm)],[m__1409]) ).
cnf(c_46,plain,
sdtasdt0(xl,xq) = sdtpldt0(xm,xn),
inference(clausify,[status(thm)],[m__1379]) ).
cnf(c_47,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_48,plain,
aNaturalNumber0(xq),
inference(clausify,[status(thm)],[m__1379]) ).
cnf(c_50,plain,
sdtasdt0(xl,xp) = xm,
inference(clausify,[status(thm)],[m__1360]) ).
cnf(c_51,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1360]) ).
fof(m__1347,axiom,
xl != sz00,
file('theBenchmark.p',m__1347) ).
cnf(c_52,plain,
xl != sz00,
inference(clausify,[status(thm)],[m__1347]) ).
cnf(c_62,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_63,plain,
aNaturalNumber0(xl),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_76,plain,
( sdtlseqdt0(sdtasdt0(A,B),sdtasdt0(A,C))
| ~ sdtlseqdt0(B,C)
| C = B
| sz00 = A
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMonMul]) ).
cnf(c_82,plain,
( sdtlseqdt0(B,A)
| sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLETotal]) ).
cnf(c_83,plain,
( B != A
| sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLETotal]) ).
cnf(c_85,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLEAsym]) ).
cnf(c_99,plain,
( C = B
| sdtasdt0(A,C) != sdtasdt0(A,B)
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| sz00 = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulCanc]) ).
cnf(c_116,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_123,plain,
sdtlseqdt0(xm,sdtasdt0(xl,xq)),
inference(paramod,[status(thm)],[c_47,c_41]) ).
cnf(c_3548,plain,
( sdtlseqdt0(A,xp)
| sdtlseqdt0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_82,c_51]) ).
cnf(c_3549,plain,
( sdtlseqdt0(xq,xp)
| sdtlseqdt0(xp,xq) ),
inference(resolve,[status(thm)],[c_3548,c_48]) ).
cnf(c_375,negated_conjecture,
sdtlseqdt0(xq,xp),
inference(resolve,[status(thm)],[c_39,c_3549]) ).
cnf(c_3550,plain,
( A != xp
| sdtlseqdt0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_83,c_51]) ).
cnf(c_3551,plain,
( xq != xp
| sdtlseqdt0(xp,xq) ),
inference(resolve,[status(thm)],[c_3550,c_48]) ).
cnf(c_394,negated_conjecture,
xq != xp,
inference(resolve,[status(thm)],[c_3551,c_39]) ).
cnf(c_3552,plain,
( aNaturalNumber0(sdtasdt0(xl,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_116,c_63]) ).
cnf(c_2478,plain,
aNaturalNumber0(sdtasdt0(xl,xq)),
inference(resolve,[status(thm)],[c_3552,c_48]) ).
cnf(c_3553,plain,
( xm = sdtasdt0(xl,xq)
| ~ sdtlseqdt0(sdtasdt0(xl,xq),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xq)) ),
inference(resolve,[status(thm)],[c_123,c_85]) ).
cnf(c_3554,plain,
( sdtasdt0(xl,xq) = xm
| ~ sdtlseqdt0(sdtasdt0(xl,xq),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xq)) ),
inference(copy,[status(thm)],[c_3553]) ).
cnf(c_3555,plain,
( sdtasdt0(xl,xq) = xm
| ~ sdtlseqdt0(sdtasdt0(xl,xq),xm)
| ~ aNaturalNumber0(xm) ),
inference(resolve,[status(thm)],[c_2478,c_3554]) ).
cnf(c_3278,plain,
( sdtasdt0(xl,xq) = xm
| ~ sdtlseqdt0(sdtasdt0(xl,xq),xm) ),
inference(resolve,[status(thm)],[c_62,c_3555]) ).
cnf(c_3556,plain,
( B = A
| sdtasdt0(xl,B) != sdtasdt0(xl,A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A)
| sz00 = xl ),
inference(resolve,[status(thm)],[c_99,c_63]) ).
cnf(c_3557,plain,
sz00 != xl,
inference(copy,[status(thm)],[c_52]) ).
cnf(c_3558,plain,
( B = A
| sdtasdt0(xl,B) != sdtasdt0(xl,A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_3556,c_3557]) ).
cnf(c_3559,plain,
( A = xp
| sdtasdt0(xl,A) != sdtasdt0(xl,xp)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_3558,c_51]) ).
cnf(c_3560,plain,
( xq = xp
| sdtasdt0(xl,xq) != sdtasdt0(xl,xp) ),
inference(resolve,[status(thm)],[c_3559,c_48]) ).
cnf(c_3561,plain,
sdtasdt0(xl,xq) != sdtasdt0(xl,xp),
inference(resolve,[status(thm)],[c_3560,c_394]) ).
cnf(c_3482,plain,
sdtasdt0(xl,xq) != xm,
inference(paramod,[status(thm)],[c_50,c_3561]) ).
cnf(c_3491,plain,
~ sdtlseqdt0(sdtasdt0(xl,xq),xm),
inference(resolve,[status(thm)],[c_3482,c_3278]) ).
cnf(c_3562,plain,
( sdtlseqdt0(sdtasdt0(xl,A),sdtasdt0(xl,B))
| ~ sdtlseqdt0(A,B)
| B = A
| sz00 = xl
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_76,c_63]) ).
cnf(c_3563,plain,
( sdtlseqdt0(sdtasdt0(xl,xq),sdtasdt0(xl,A))
| ~ sdtlseqdt0(xq,A)
| A = xq
| sz00 = xl
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_3562,c_48]) ).
cnf(c_3564,plain,
( sdtlseqdt0(sdtasdt0(xl,xq),sdtasdt0(xl,xp))
| ~ sdtlseqdt0(xq,xp)
| xp = xq
| sz00 = xl ),
inference(resolve,[status(thm)],[c_3563,c_51]) ).
cnf(c_3565,plain,
( sdtlseqdt0(sdtasdt0(xl,xq),sdtasdt0(xl,xp))
| xp = xq
| sz00 = xl ),
inference(resolve,[status(thm)],[c_3564,c_375]) ).
cnf(c_3566,plain,
( sdtlseqdt0(sdtasdt0(xl,xq),xm)
| xp = xq
| sz00 = xl ),
inference(paramod,[status(thm)],[c_50,c_3565]) ).
cnf(c_3567,plain,
( sdtlseqdt0(sdtasdt0(xl,xq),xm)
| xp = xq
| xl = sz00 ),
inference(copy,[status(thm)],[c_3566]) ).
cnf(c_3568,plain,
( sdtlseqdt0(sdtasdt0(xl,xq),xm)
| xq = xp
| xl = sz00 ),
inference(copy,[status(thm)],[c_3567]) ).
cnf(c_3569,plain,
( sdtlseqdt0(sdtasdt0(xl,xq),xm)
| xq = xp ),
inference(resolve,[status(thm)],[c_52,c_3568]) ).
cnf(c_3570,plain,
sdtlseqdt0(sdtasdt0(xl,xq),xm),
inference(resolve,[status(thm)],[c_394,c_3569]) ).
cnf(c_3547,plain,
$false,
inference(resolve,[status(thm)],[c_3491,c_3570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM473+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 02:58:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 4049917 was started by sandbox2 on n016,
% 0.11/0.38 % Sat Sep 26 02:58:31 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 4.76/1.12
% 4.76/1.12 % SZS status Theorem for theBenchmark
% 4.76/1.12
% 4.76/1.12 % Proof 1 at 0.57 (+ 0.14) seconds.
% 4.76/1.12 % Length of proof is 34.
% 4.76/1.12 % Level of proof is 6.
% 4.76/1.12 % Maximum clause weight is 32.000.
% 4.76/1.12 % Given clauses 149.
% 4.76/1.12
% 4.76/1.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------