%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM475+1 : 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 : n011.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 7.20s 6.32s
% Output : CNFRefutation 7.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 38 unt; 0 def)
% Number of atoms : 174 ( 77 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 167 ( 68 ~; 77 |; 12 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
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(mDefDiff,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefDiff) ).
fof(mDefQuot,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefQuot) ).
fof(m__1324,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('theBenchmark.p',m__1324) ).
fof(m__1324_04,axiom,
( doDivides0(xl,sdtpldt0(xm,xn))
& doDivides0(xl,xm) ),
file('theBenchmark.p',m__1324_04) ).
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_36,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_37,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(clausify,[status(thm)],[m__1459]) ).
fof(m__1422,axiom,
xr = sdtmndt0(xq,xp),
file('theBenchmark.p',m__1422) ).
cnf(c_38,plain,
xr = sdtmndt0(xq,xp),
inference(clausify,[status(thm)],[m__1422]) ).
fof(m__1395,axiom,
sdtlseqdt0(xp,xq),
file('theBenchmark.p',m__1395) ).
cnf(c_39,plain,
sdtlseqdt0(xp,xq),
inference(clausify,[status(thm)],[m__1395]) ).
fof(m__1379,axiom,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('theBenchmark.p',m__1379) ).
cnf(c_40,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(clausify,[status(thm)],[m__1379]) ).
cnf(c_41,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
inference(copy,[status(thm)],[c_40]) ).
fof(m__1360,axiom,
xp = sdtsldt0(xm,xl),
file('theBenchmark.p',m__1360) ).
cnf(c_42,plain,
xp = sdtsldt0(xm,xl),
inference(clausify,[status(thm)],[m__1360]) ).
cnf(c_43,plain,
sdtsldt0(xm,xl) = xp,
inference(copy,[status(thm)],[c_42]) ).
fof(m__1347,axiom,
xl != sz00,
file('theBenchmark.p',m__1347) ).
cnf(c_44,plain,
xl != sz00,
inference(clausify,[status(thm)],[m__1347]) ).
cnf(c_45,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(clausify,[status(thm)],[m__1324_04]) ).
cnf(c_46,plain,
doDivides0(xl,xm),
inference(clausify,[status(thm)],[m__1324_04]) ).
cnf(c_47,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_48,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_49,plain,
aNaturalNumber0(xl),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_53,plain,
( sdtasdt0(A,C) = B
| sdtsldt0(B,A) != C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_54,plain,
( aNaturalNumber0(C)
| sdtsldt0(B,A) != C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_75,plain,
( aNaturalNumber0(C)
| sdtmndt0(B,A) != C
| ~ sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_87,plain,
( C = B
| sdtpldt0(A,C) != sdtpldt0(A,B)
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mAddCanc]) ).
cnf(c_102,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_103,plain,
( aNaturalNumber0(sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB]) ).
cnf(c_107,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,sdtmndt0(xq,xp))) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(paramod,[status(thm)],[c_38,c_37]) ).
cnf(c_108,negated_conjecture,
sdtasdt0(xl,sdtmndt0(xq,xp)) != xn,
inference(paramod,[status(thm)],[c_38,c_36]) ).
cnf(c_2998,plain,
( sdtasdt0(xl,B) = A
| sdtsldt0(A,xl) != B
| ~ doDivides0(xl,A)
| sz00 = xl
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_53,c_49]) ).
cnf(c_2999,plain,
( sdtasdt0(xl,A) = xm
| sdtsldt0(xm,xl) != A
| ~ doDivides0(xl,xm)
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2998,c_48]) ).
cnf(c_3000,plain,
( sdtasdt0(xl,A) = xm
| sdtsldt0(xm,xl) != A
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2999,c_46]) ).
cnf(c_3001,plain,
( sdtasdt0(xl,xp) = xm
| sz00 = xl ),
inference(resolve,[status(thm)],[c_3000,c_43]) ).
cnf(c_3002,plain,
( sdtasdt0(xl,xp) = xm
| xl = sz00 ),
inference(copy,[status(thm)],[c_3001]) ).
cnf(c_203,plain,
sdtasdt0(xl,xp) = xm,
inference(resolve,[status(thm)],[c_44,c_3002]) ).
cnf(c_3003,plain,
sdtpldt0(xm,sdtasdt0(xl,sdtmndt0(xq,xp))) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(paramod,[status(thm)],[c_203,c_107]) ).
cnf(c_204,plain,
sdtpldt0(xm,sdtasdt0(xl,sdtmndt0(xq,xp))) = sdtpldt0(xm,xn),
inference(paramod,[status(thm)],[c_203,c_3003]) ).
cnf(c_3004,plain,
( aNaturalNumber0(A)
| sdtsldt0(sdtpldt0(xm,xn),xl) != A
| sz00 = xl
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl) ),
inference(resolve,[status(thm)],[c_54,c_45]) ).
cnf(c_3005,plain,
( aNaturalNumber0(A)
| xq != A
| sz00 = xl
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl) ),
inference(paramod,[status(thm)],[c_41,c_3004]) ).
cnf(c_3006,plain,
( aNaturalNumber0(A)
| xq != A
| xl = sz00
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl) ),
inference(copy,[status(thm)],[c_3005]) ).
cnf(c_3007,plain,
( aNaturalNumber0(A)
| xq != A
| xl = sz00
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolve,[status(thm)],[c_49,c_3006]) ).
cnf(c_206,plain,
( aNaturalNumber0(A)
| xq != A
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolve,[status(thm)],[c_44,c_3007]) ).
cnf(c_3008,plain,
( aNaturalNumber0(B)
| sdtsldt0(A,xl) != B
| ~ doDivides0(xl,A)
| sz00 = xl
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_54,c_49]) ).
cnf(c_3009,plain,
( aNaturalNumber0(A)
| sdtsldt0(xm,xl) != A
| ~ doDivides0(xl,xm)
| sz00 = xl ),
inference(resolve,[status(thm)],[c_3008,c_48]) ).
cnf(c_3010,plain,
( aNaturalNumber0(A)
| sdtsldt0(xm,xl) != A
| sz00 = xl ),
inference(resolve,[status(thm)],[c_3009,c_46]) ).
cnf(c_3011,plain,
( aNaturalNumber0(xp)
| sz00 = xl ),
inference(resolve,[status(thm)],[c_3010,c_43]) ).
cnf(c_3012,plain,
( aNaturalNumber0(xp)
| xl = sz00 ),
inference(copy,[status(thm)],[c_3011]) ).
cnf(c_207,plain,
aNaturalNumber0(xp),
inference(resolve,[status(thm)],[c_44,c_3012]) ).
cnf(c_3013,plain,
( aNaturalNumber0(sdtpldt0(xm,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_103,c_48]) ).
cnf(c_687,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(resolve,[status(thm)],[c_3013,c_47]) ).
cnf(c_691,plain,
( aNaturalNumber0(A)
| xq != A ),
inference(resolve,[status(thm)],[c_687,c_206]) ).
cnf(c_3014,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_3015,plain,
aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)),
inference(resolve,[status(thm)],[c_691,c_3014]) ).
cnf(c_1684,plain,
aNaturalNumber0(xq),
inference(paramod,[status(thm)],[c_41,c_3015]) ).
cnf(c_3016,plain,
( aNaturalNumber0(B)
| sdtmndt0(A,xp) != B
| ~ sdtlseqdt0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_75,c_207]) ).
cnf(c_3017,plain,
( aNaturalNumber0(A)
| sdtmndt0(xq,xp) != A
| ~ sdtlseqdt0(xp,xq) ),
inference(resolve,[status(thm)],[c_3016,c_1684]) ).
cnf(c_3018,plain,
( aNaturalNumber0(A)
| sdtmndt0(xq,xp) != A ),
inference(resolve,[status(thm)],[c_3017,c_39]) ).
cnf(c_3019,plain,
sdtmndt0(xq,xp) = xr,
inference(copy,[status(thm)],[c_38]) ).
cnf(c_3020,plain,
aNaturalNumber0(xr),
inference(resolve,[status(thm)],[c_3018,c_3019]) ).
cnf(c_2202,plain,
aNaturalNumber0(sdtmndt0(xq,xp)),
inference(paramod,[status(thm)],[c_38,c_3020]) ).
cnf(c_3021,plain,
( B = A
| sdtpldt0(xm,B) != sdtpldt0(xm,A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_87,c_48]) ).
cnf(c_3022,plain,
( A = xn
| sdtpldt0(xm,A) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_3021,c_47]) ).
cnf(c_3023,plain,
( sdtasdt0(xl,sdtmndt0(xq,xp)) = xn
| ~ aNaturalNumber0(sdtasdt0(xl,sdtmndt0(xq,xp))) ),
inference(resolve,[status(thm)],[c_3022,c_204]) ).
cnf(c_2986,negated_conjecture,
~ aNaturalNumber0(sdtasdt0(xl,sdtmndt0(xq,xp))),
inference(resolve,[status(thm)],[c_3023,c_108]) ).
cnf(c_3024,plain,
( aNaturalNumber0(sdtasdt0(xl,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_102,c_49]) ).
cnf(c_3025,plain,
~ aNaturalNumber0(sdtmndt0(xq,xp)),
inference(resolve,[status(thm)],[c_3024,c_2986]) ).
cnf(c_2997,plain,
$false,
inference(resolve,[status(thm)],[c_2202,c_3025]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM475+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n011.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sat Sep 26 02:54:05 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 3640803 was started by sandbox2 on n011,
% 0.11/5.38 % Sat Sep 26 02:54:05 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 7.20/6.32
% 7.20/6.32 % SZS status Theorem for theBenchmark
% 7.20/6.32
% 7.20/6.32 % Proof 1 at 0.78 (+ 0.14) seconds.
% 7.20/6.32 % Length of proof is 40.
% 7.20/6.32 % Level of proof is 6.
% 7.20/6.32 % Maximum clause weight is 35.000.
% 7.20/6.32 % Given clauses 217.
% 7.20/6.32
% 7.20/6.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------