%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG091+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 : n005.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 08:26:37 AM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 59 ( 20 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 64 ( 28 ~; 24 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 0 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__994,axiom,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('theBenchmark.p',m__994) ).
fof(m__1021,axiom,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('theBenchmark.p',m__1021) ).
fof(m__,conjecture,
( ( aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = sdtasdt0(xz,xx)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) )
& ( aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(xx,xy)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = sdtasdt0(xz,xx)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) )
& ( aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(xx,xy)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_59,negated_conjecture,
( sdtasdt0(xz,xx) != sdtpldt0(C,D)
| ~ aElementOf0(D,xJ)
| ~ aElementOf0(C,xI)
| sdtpldt0(xx,xy) != sdtpldt0(A,B)
| ~ aElementOf0(B,xJ)
| ~ aElementOf0(A,xI) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_60,negated_conjecture,
( sdtpldt0(C,D) != sdtasdt0(xz,xx)
| ~ aElementOf0(D,xJ)
| ~ aElementOf0(C,xI)
| sdtpldt0(xx,xy) != sdtpldt0(A,B)
| ~ aElementOf0(B,xJ)
| ~ aElementOf0(A,xI) ),
inference(copy,[status(thm)],[c_59]) ).
fof(m__1098,axiom,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('theBenchmark.p',m__1098) ).
cnf(c_61,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(clausify,[status(thm)],[m__1098]) ).
cnf(c_62,plain,
sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) = sdtasdt0(xz,xx),
inference(copy,[status(thm)],[c_61]) ).
fof(m__1061,axiom,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('theBenchmark.p',m__1061) ).
cnf(c_63,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(clausify,[status(thm)],[m__1061]) ).
cnf(c_64,plain,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xx,xy),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_65,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(clausify,[status(thm)],[m__1021]) ).
cnf(c_66,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(clausify,[status(thm)],[m__1021]) ).
cnf(c_67,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(clausify,[status(thm)],[m__994]) ).
cnf(c_68,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(clausify,[status(thm)],[m__994]) ).
cnf(c_296,negated_conjecture,
( sdtpldt0(B,C) != sdtasdt0(xz,xx)
| ~ aElementOf0(C,xJ)
| ~ aElementOf0(B,xI)
| sdtpldt0(xx,xy) != sdtpldt0(A,sdtpldt0(xl,xn))
| ~ aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_60,c_67]) ).
cnf(c_297,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_298,negated_conjecture,
( sdtpldt0(A,B) != sdtasdt0(xz,xx)
| ~ aElementOf0(B,xJ)
| ~ aElementOf0(A,xI)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(resolve,[status(thm)],[c_296,c_297]) ).
cnf(c_299,negated_conjecture,
( sdtpldt0(sdtasdt0(xz,xk),A) != sdtasdt0(xz,xx)
| ~ aElementOf0(A,xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(resolve,[status(thm)],[c_298,c_66]) ).
cnf(c_300,negated_conjecture,
( sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) != sdtasdt0(xz,xx)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(resolve,[status(thm)],[c_299,c_65]) ).
cnf(c_301,negated_conjecture,
~ aElementOf0(sdtpldt0(xk,xm),xI),
inference(resolve,[status(thm)],[c_300,c_62]) ).
cnf(c_295,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_68,c_301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG091+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 06:02:31 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 1370557 was started by sandbox on n005,
% 0.16/0.44 % Sat Sep 26 06:02:31 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.48
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48
% 0.16/0.48 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.16/0.48 % Length of proof is 14.
% 0.16/0.48 % Level of proof is 3.
% 0.16/0.48 % Maximum clause weight is 36.000.
% 0.16/0.48 % Given clauses 25.
% 0.16/0.48
% 0.16/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------