%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG045+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 : n001.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 08:26:29 AM UTC 2026
% Result : Theorem 0.22s 0.49s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 17 unt; 0 def)
% Number of atoms : 44 ( 20 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 37 ( 18 ~; 12 |; 6 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDistr,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mDistr) ).
fof(m__674,axiom,
( aScalar0(xv)
& aScalar0(xu)
& aScalar0(xy)
& aScalar0(xx) ),
file('theBenchmark.p',m__674) ).
fof(m__,conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_16,negated_conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_17,negated_conjecture,
sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(copy,[status(thm)],[c_16]) ).
fof(m__733,axiom,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
file('theBenchmark.p',m__733) ).
cnf(c_18,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
inference(clausify,[status(thm)],[m__733]) ).
cnf(c_19,plain,
sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) = sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_20,plain,
aScalar0(xv),
inference(clausify,[status(thm)],[m__674]) ).
cnf(c_21,plain,
aScalar0(xu),
inference(clausify,[status(thm)],[m__674]) ).
cnf(c_22,plain,
aScalar0(xy),
inference(clausify,[status(thm)],[m__674]) ).
cnf(c_23,plain,
aScalar0(xx),
inference(clausify,[status(thm)],[m__674]) ).
cnf(c_26,plain,
( sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))
| ~ aScalar0(C)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mDistr]) ).
cnf(c_27,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aScalar0(C)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_250,plain,
( sdtpldt0(sdtasdt0(xx,A),sdtasdt0(xx,B)) = sdtasdt0(xx,sdtpldt0(A,B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_251,plain,
( sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,A)) = sdtasdt0(xx,sdtpldt0(xu,A))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_250,c_21]) ).
cnf(c_181,plain,
sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) = sdtasdt0(xx,sdtpldt0(xu,xv)),
inference(resolve,[status(thm)],[c_251,c_20]) ).
cnf(c_252,plain,
( sdtpldt0(sdtasdt0(xy,A),sdtasdt0(xy,B)) = sdtasdt0(xy,sdtpldt0(A,B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_27,c_22]) ).
cnf(c_253,plain,
( sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,A)) = sdtasdt0(xy,sdtpldt0(xu,A))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_252,c_21]) ).
cnf(c_197,plain,
sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) = sdtasdt0(xy,sdtpldt0(xu,xv)),
inference(resolve,[status(thm)],[c_253,c_20]) ).
cnf(c_254,negated_conjecture,
sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_181,c_17]) ).
cnf(c_255,negated_conjecture,
sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_197,c_254]) ).
cnf(c_256,negated_conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_19,c_255]) ).
cnf(c_249,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG045+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n001.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 05:57:27 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1044728 was started by sandbox2 on n001,
% 0.17/0.44 % Sat Sep 26 05:57:27 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.22/0.49
% 0.22/0.49 % SZS status Theorem for theBenchmark
% 0.22/0.49
% 0.22/0.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.22/0.49 % Length of proof is 16.
% 0.22/0.49 % Level of proof is 4.
% 0.22/0.49 % Maximum clause weight is 53.000.
% 0.22/0.49 % Given clauses 8.
% 0.22/0.49
% 0.22/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------