%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX186+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 : n007.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 09:16:16 AM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 12 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 9 ~; 1 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 11 sgn 7 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_003,axiom,
! [X,X2] : nil != cons(X,X2),
file('theBenchmark.p',axiom_003) ).
fof(axiom_006,axiom,
! [Z] : drop(s(Z),nil) = nil,
file('theBenchmark.p',axiom_006) ).
fof(axiom_007,axiom,
! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3),
file('theBenchmark.p',axiom_007) ).
fof(axiom_008,axiom,
! [Y] : drop(z,Y) = Y,
file('theBenchmark.p',axiom_008) ).
fof(goal_009,conjecture,
? [N,Xs,Ys] :
~ ( drop(N,Xs) = drop(N,Ys)
=> Xs = Ys ),
file('theBenchmark.p',goal_009) ).
fof(goal_009_neg,negated_conjecture,
~ ? [N,Xs,Ys] :
~ ( drop(N,Xs) = drop(N,Ys)
=> Xs = Ys ),
inference(assume_negation,[status(cth)],[goal_009]) ).
cnf(c_12,plain,
cons(A,B) != nil,
inference(clausify,[status(thm)],[axiom_003]) ).
cnf(c_15,plain,
drop(s(A),nil) = nil,
inference(clausify,[status(thm)],[axiom_006]) ).
cnf(c_16,plain,
drop(s(A),cons(B,C)) = drop(A,C),
inference(clausify,[status(thm)],[axiom_007]) ).
cnf(c_17,plain,
drop(z,A) = A,
inference(clausify,[status(thm)],[axiom_008]) ).
cnf(c_18,negated_conjecture,
( B = C
| drop(A,B) != drop(A,C) ),
inference(clausify,[status(thm)],[goal_009_neg]) ).
cnf(c_20,negated_conjecture,
drop(A,cons(B,C)) != drop(A,nil),
inference(resolve,[status(thm)],[c_18,c_12]) ).
cnf(c_27,plain,
drop(s(A),cons(B,C)) != nil,
inference(paramod,[status(thm)],[c_15,c_20]) ).
cnf(c_25,plain,
drop(A,B) != nil,
inference(paramod,[status(thm)],[c_16,c_27]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX186+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 16:49:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 9886 was started by sandbox2 on n007,
% 0.09/0.36 % Sat Sep 26 16:49:24 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 13.
% 0.09/0.38 % Level of proof is 4.
% 0.09/0.38 % Maximum clause weight is 10.000.
% 0.09/0.38 % Given clauses 11.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------