%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM474+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 1.53s 0.66s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 17 unt; 0 def)
% Number of atoms : 47 ( 25 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 35 ( 14 ~; 9 |; 11 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 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 : 12 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_40,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_42,plain,
sdtpldt0(xp,xr) = xq,
inference(clausify,[status(thm)],[m__1422]) ).
cnf(c_43,plain,
aNaturalNumber0(xr),
inference(clausify,[status(thm)],[m__1422]) ).
cnf(c_48,plain,
sdtasdt0(xl,xq) = sdtpldt0(xm,xn),
inference(clausify,[status(thm)],[m__1379]) ).
cnf(c_49,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_52,plain,
sdtasdt0(xl,xp) = xm,
inference(clausify,[status(thm)],[m__1360]) ).
cnf(c_53,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1360]) ).
cnf(c_65,plain,
aNaturalNumber0(xl),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_106,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_107,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_940,negated_conjecture,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(paramod,[status(thm)],[c_52,c_40]) ).
cnf(c_941,negated_conjecture,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtpldt0(xm,xn),
inference(paramod,[status(thm)],[c_52,c_940]) ).
cnf(c_124,negated_conjecture,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtasdt0(xl,xq),
inference(paramod,[status(thm)],[c_49,c_941]) ).
cnf(c_942,plain,
( sdtpldt0(sdtasdt0(xl,A),sdtasdt0(xl,B)) = sdtasdt0(xl,sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_107,c_65]) ).
cnf(c_943,plain,
( sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,A)) = sdtasdt0(xl,sdtpldt0(xp,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_942,c_53]) ).
cnf(c_944,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtasdt0(xl,sdtpldt0(xp,xr)),
inference(resolve,[status(thm)],[c_943,c_43]) ).
cnf(c_945,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtasdt0(xl,sdtpldt0(xp,xr)),
inference(paramod,[status(thm)],[c_52,c_944]) ).
cnf(c_946,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtasdt0(xl,xq),
inference(paramod,[status(thm)],[c_42,c_945]) ).
cnf(c_939,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_124,c_946]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM474+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 02:54:06 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 665754 was started by sandbox2 on n004,
% 0.12/0.37 % Sat Sep 26 02:54:06 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 1.53/0.66
% 1.53/0.66 % SZS status Theorem for theBenchmark
% 1.53/0.66
% 1.53/0.66 % Proof 1 at 0.19 (+ 0.06) seconds.
% 1.53/0.66 % Length of proof is 18.
% 1.53/0.66 % Level of proof is 4.
% 1.53/0.66 % Maximum clause weight is 34.000.
% 1.53/0.66 % Given clauses 55.
% 1.53/0.66
% 1.53/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------