%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX190+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 09:16:17 AM UTC 2026
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 32 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 3 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 52 ( 18 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_008,axiom,
! [X,X2,X3] : n(X) != x(X2,X3),
file('theBenchmark.p',axiom_008) ).
fof(axiom_009,axiom,
! [X,X2,X3] : n(X) != y(X2,X3),
file('theBenchmark.p',axiom_009) ).
fof(axiom_039,axiom,
! [Y] : d(n(Y)) = n(z),
file('theBenchmark.p',axiom_039) ).
fof(axiom_040,axiom,
! [F,G] : d(x(F,G)) = x(d(F),d(G)),
file('theBenchmark.p',axiom_040) ).
fof(axiom_041,axiom,
! [H,G2] : d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))),
file('theBenchmark.p',axiom_041) ).
fof(axiom_047,axiom,
! [X] :
( X != x(proj1(X),proj2(X))
=> ( X != y(proj12(X),proj22(X))
=> opt(X) = X ) ),
file('theBenchmark.p',axiom_047) ).
fof(axiom_050,axiom,
! [E] : opt(x(n(z),E)) = E,
file('theBenchmark.p',axiom_050) ).
fof(axiom_053,axiom,
! [E2] : opt(y(n(z),E2)) = n(z),
file('theBenchmark.p',axiom_053) ).
fof(goal_054,conjecture,
? [E] : opt(d(E)) != opt(d(opt(E))),
file('theBenchmark.p',goal_054) ).
fof(goal_054_neg,negated_conjecture,
~ ? [E] : opt(d(E)) != opt(d(opt(E))),
inference(assume_negation,[status(cth)],[goal_054]) ).
cnf(c_61,plain,
x(A,B) != n(C),
inference(clausify,[status(thm)],[axiom_008]) ).
cnf(c_62,plain,
y(A,B) != n(C),
inference(clausify,[status(thm)],[axiom_009]) ).
cnf(c_103,plain,
d(n(A)) = n(z),
inference(clausify,[status(thm)],[axiom_039]) ).
cnf(c_104,plain,
d(x(A,B)) = x(d(A),d(B)),
inference(clausify,[status(thm)],[axiom_040]) ).
cnf(c_105,plain,
x(d(A),d(B)) = d(x(A,B)),
inference(copy,[status(thm)],[c_104]) ).
cnf(c_106,plain,
d(y(A,B)) = x(y(d(A),B),y(A,d(B))),
inference(clausify,[status(thm)],[axiom_041]) ).
cnf(c_107,plain,
x(y(d(A),B),y(A,d(B))) = d(y(A,B)),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_116,plain,
( opt(A) = A
| y(proj12(A),proj22(A)) = A
| x(proj1(A),proj2(A)) = A ),
inference(clausify,[status(thm)],[axiom_047]) ).
cnf(c_121,plain,
opt(x(n(z),A)) = A,
inference(clausify,[status(thm)],[axiom_050]) ).
cnf(c_126,plain,
opt(y(n(z),A)) = n(z),
inference(clausify,[status(thm)],[axiom_053]) ).
cnf(c_127,negated_conjecture,
opt(d(opt(A))) = opt(d(A)),
inference(clausify,[status(thm)],[goal_054_neg]) ).
cnf(c_272,plain,
x(n(z),d(A)) = d(x(n(B),A)),
inference(paramod,[status(thm)],[c_103,c_105]) ).
cnf(c_206,plain,
d(x(n(A),B)) = x(n(z),d(B)),
inference(copy,[status(thm)],[c_272]) ).
cnf(c_210,plain,
d(y(A,B)) != n(C),
inference(paramod,[status(thm)],[c_107,c_61]) ).
cnf(c_273,plain,
( opt(n(A)) = n(A)
| x(proj1(n(A)),proj2(n(A))) = n(A) ),
inference(resolve,[status(thm)],[c_116,c_62]) ).
cnf(c_243,plain,
opt(n(A)) = n(A),
inference(resolve,[status(thm)],[c_61,c_273]) ).
cnf(c_274,plain,
opt(d(A)) = opt(d(x(n(z),A))),
inference(paramod,[status(thm)],[c_121,c_127]) ).
cnf(c_275,plain,
opt(d(A)) = opt(x(n(z),d(A))),
inference(paramod,[status(thm)],[c_206,c_274]) ).
cnf(c_269,plain,
opt(d(A)) = d(A),
inference(paramod,[status(thm)],[c_121,c_275]) ).
cnf(c_276,plain,
opt(d(n(z))) = opt(d(y(n(z),A))),
inference(paramod,[status(thm)],[c_126,c_127]) ).
cnf(c_277,plain,
opt(n(z)) = opt(d(y(n(z),A))),
inference(paramod,[status(thm)],[c_103,c_276]) ).
cnf(c_278,plain,
n(z) = opt(d(y(n(z),A))),
inference(paramod,[status(thm)],[c_243,c_277]) ).
cnf(c_279,plain,
n(z) = d(y(n(z),A)),
inference(paramod,[status(thm)],[c_269,c_278]) ).
cnf(c_280,plain,
d(y(n(z),A)) = n(z),
inference(copy,[status(thm)],[c_279]) ).
cnf(c_271,plain,
$false,
inference(resolve,[status(thm)],[c_210,c_280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX190+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n005.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 16:53:48 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2592170 was started by sandbox2 on n005,
% 0.19/0.45 % Sat Sep 26 16:53:48 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.50
% 0.19/0.50 % SZS status Theorem for theBenchmark
% 0.19/0.50
% 0.19/0.50 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.19/0.50 % Length of proof is 25.
% 0.19/0.50 % Level of proof is 5.
% 0.19/0.50 % Maximum clause weight is 34.000.
% 0.19/0.50 % Given clauses 52.
% 0.19/0.50
% 0.19/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------