%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM435+3 : 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 : n008.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 08:16:59 AM UTC 2026
% Result : Theorem 0.16s 5.92s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 42 ( 19 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 33 ( 13 ~; 9 |; 9 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ),
file('theBenchmark.p',mMulAsso) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(m__979,axiom,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
file('theBenchmark.p',m__979) ).
fof(m__1032,axiom,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
file('theBenchmark.p',m__1032) ).
fof(m__,conjecture,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_36,plain,
( sdtasdt0(sdtasdt0(A,B),C) = sdtasdt0(A,sdtasdt0(B,C))
| ~ aInteger0(C)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mMulAsso]) ).
cnf(c_37,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_69,plain,
aInteger0(xp),
inference(clausify,[status(thm)],[m__979]) ).
cnf(c_71,plain,
aInteger0(xq),
inference(clausify,[status(thm)],[m__979]) ).
cnf(c_78,plain,
aInteger0(xm),
inference(clausify,[status(thm)],[m__1032]) ).
cnf(c_79,plain,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)),
inference(clausify,[status(thm)],[m__1032]) ).
cnf(c_80,negated_conjecture,
sdtasdt0(xq,sdtasdt0(xp,xm)) != sdtpldt0(xa,smndt0(xb)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_2225,plain,
( sdtasdt0(A,xp) = sdtasdt0(xp,A)
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_37,c_69]) ).
cnf(c_1025,plain,
sdtasdt0(xq,xp) = sdtasdt0(xp,xq),
inference(resolve,[status(thm)],[c_2225,c_71]) ).
cnf(c_2226,plain,
( sdtasdt0(sdtasdt0(xq,A),B) = sdtasdt0(xq,sdtasdt0(A,B))
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_36,c_71]) ).
cnf(c_2227,plain,
( sdtasdt0(sdtasdt0(xq,xp),A) = sdtasdt0(xq,sdtasdt0(xp,A))
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_2226,c_69]) ).
cnf(c_2228,plain,
sdtasdt0(sdtasdt0(xq,xp),xm) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(resolve,[status(thm)],[c_2227,c_78]) ).
cnf(c_2229,plain,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(paramod,[status(thm)],[c_1025,c_2228]) ).
cnf(c_2230,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(paramod,[status(thm)],[c_79,c_2229]) ).
cnf(c_2231,plain,
sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(copy,[status(thm)],[c_2230]) ).
cnf(c_2224,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_80,c_2231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM435+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n008.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Sat Sep 26 02:45:04 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.40 % Process 2626957 was started by sandbox2 on n008,
% 0.12/5.40 % Sat Sep 26 02:45:04 2026
% 0.12/5.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.41
% 0.16/5.41 % From the command line: assign(max_seconds, 300).
% 0.16/5.92
% 0.16/5.92 % Assigning unary symbol smndt0 kb_weight 0 and highest precedence (16).
% 0.16/5.92
% 0.16/5.92 % SZS status Theorem for theBenchmark
% 0.16/5.92
% 0.16/5.92 % Proof 1 at 0.38 (+ 0.11) seconds.
% 0.16/5.92 % Length of proof is 14.
% 0.16/5.92 % Level of proof is 3.
% 0.16/5.92 % Maximum clause weight is 42.000.
% 0.16/5.92 % Given clauses 44.
% 0.16/5.92
% 0.16/5.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------