%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG103+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.15s 5.64s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 38 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 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,negated_conjecture,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_69,plain,
sdtasdt0(xc,xv) = xy,
inference(clausify,[status(thm)],[m__1979]) ).
cnf(c_70,plain,
xy = sdtasdt0(xc,xv),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_71,plain,
aElement0(xv),
inference(clausify,[status(thm)],[m__1979]) ).
cnf(c_72,plain,
sdtasdt0(xc,xu) = xx,
inference(clausify,[status(thm)],[m__1956]) ).
cnf(c_73,plain,
xx = sdtasdt0(xc,xu),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_74,plain,
aElement0(xu),
inference(clausify,[status(thm)],[m__1956]) ).
fof(m__1905,axiom,
aElement0(xc),
file('theBenchmark.p',m__1905) ).
cnf(c_84,plain,
aElement0(xc),
inference(clausify,[status(thm)],[m__1905]) ).
cnf(c_148,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_149,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(copy,[status(thm)],[c_148]) ).
cnf(c_263,plain,
sdtpldt0(xx,sdtasdt0(xc,xv)) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_70,c_68]) ).
cnf(c_1019,plain,
sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_73,c_263]) ).
cnf(c_1064,plain,
( sdtpldt0(sdtasdt0(A,xu),sdtasdt0(A,B)) = sdtasdt0(A,sdtpldt0(xu,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_149,c_74]) ).
cnf(c_1065,plain,
( sdtpldt0(sdtasdt0(A,xu),sdtasdt0(A,xv)) = sdtasdt0(A,sdtpldt0(xu,xv))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_1064,c_71]) ).
cnf(c_1066,plain,
~ aElement0(xc),
inference(resolve,[status(thm)],[c_1065,c_1019]) ).
cnf(c_1063,plain,
$false,
inference(resolve,[status(thm)],[c_84,c_1066]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG103+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.39 % Computer : n016.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Sat Sep 26 06:11:05 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.40 % Process 165474 was started by sandbox on n016,
% 0.10/5.40 % Sat Sep 26 06:11:05 2026
% 0.10/5.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.40
% 0.15/5.40 % From the command line: assign(max_seconds, 300).
% 0.15/5.64
% 0.15/5.64 % SZS status Theorem for theBenchmark
% 0.15/5.64
% 0.15/5.64 % Proof 1 at 0.08 (+ 0.01) seconds.
% 0.15/5.64 % Length of proof is 18.
% 0.15/5.64 % Level of proof is 5.
% 0.15/5.64 % Maximum clause weight is 34.000.
% 0.15/5.64 % Given clauses 196.
% 0.15/5.64
% 0.15/5.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------