%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG103+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 : n002.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 08:26:39 AM UTC 2026
% Result : Theorem 0.08s 0.45s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 38 ( 19 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 9 |; 5 &)
% ( 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(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__1956,axiom,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('theBenchmark.p',m__1956) ).
fof(m__1979,axiom,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
file('theBenchmark.p',m__1979) ).
fof(m__,conjecture,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_67,negated_conjecture,
sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(xx,xy),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_68,plain,
sdtasdt0(xc,xv) = xy,
inference(clausify,[status(thm)],[m__1979]) ).
cnf(c_69,plain,
xy = sdtasdt0(xc,xv),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_70,plain,
aElement0(xv),
inference(clausify,[status(thm)],[m__1979]) ).
cnf(c_71,plain,
sdtasdt0(xc,xu) = xx,
inference(clausify,[status(thm)],[m__1956]) ).
cnf(c_72,plain,
xx = sdtasdt0(xc,xu),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_73,plain,
aElement0(xu),
inference(clausify,[status(thm)],[m__1956]) ).
fof(m__1905,axiom,
aElement0(xc),
file('theBenchmark.p',m__1905) ).
cnf(c_79,plain,
aElement0(xc),
inference(clausify,[status(thm)],[m__1905]) ).
cnf(c_143,plain,
( sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAMDistr]) ).
cnf(c_144,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(copy,[status(thm)],[c_143]) ).
cnf(c_575,negated_conjecture,
sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xc,xu),xy),
inference(paramod,[status(thm)],[c_72,c_67]) ).
cnf(c_576,negated_conjecture,
sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)),
inference(paramod,[status(thm)],[c_69,c_575]) ).
cnf(c_175,negated_conjecture,
sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(copy,[status(thm)],[c_576]) ).
cnf(c_577,plain,
( sdtpldt0(sdtasdt0(xc,A),sdtasdt0(xc,B)) = sdtasdt0(xc,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_144,c_79]) ).
cnf(c_578,plain,
( sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,A)) = sdtasdt0(xc,sdtpldt0(xu,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_577,c_73]) ).
cnf(c_579,plain,
sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(resolve,[status(thm)],[c_578,c_70]) ).
cnf(c_574,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_175,c_579]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG103+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n002.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 06:08:06 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.38 % Process 1000878 was started by sandbox2 on n002,
% 0.08/0.38 % Sat Sep 26 06:08:06 2026
% 0.08/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 0.08/0.45
% 0.08/0.45 % SZS status Theorem for theBenchmark
% 0.08/0.45
% 0.08/0.45 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.08/0.45 % Length of proof is 16.
% 0.08/0.45 % Level of proof is 4.
% 0.08/0.45 % Maximum clause weight is 34.000.
% 0.08/0.45 % Given clauses 72.
% 0.08/0.45
% 0.08/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------