%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV165+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 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 09:06:56 AM UTC 2026
% Result : Theorem 5.92s 1.76s
% Output : CNFRefutation 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 43 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 11 ~; 6 |; 7 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 15 ( 0 sgn 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X),
file('theBenchmark.p',irreflexivity_gt) ).
fof(leq_succ,axiom,
! [X,Y] :
( leq(X,Y)
=> leq(X,succ(Y)) ),
file('theBenchmark.p',leq_succ) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('theBenchmark.p',leq_succ_gt_equiv) ).
fof(finite_domain_0,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('theBenchmark.p',finite_domain_0) ).
fof(cl5_nebula_init_0001,conjecture,
! [A] :
( ( leq(A,tptp_minus_1)
& leq(n0,A) )
=> uninit = init ),
file('theBenchmark.p',cl5_nebula_init_0001) ).
fof(cl5_nebula_init_0001_neg,negated_conjecture,
~ ! [A] :
( ( leq(A,tptp_minus_1)
& leq(n0,A) )
=> uninit = init ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0001]) ).
cnf(c_63,plain,
~ gt(A,A),
inference(clausify,[status(thm)],[irreflexivity_gt]) ).
cnf(c_71,plain,
( leq(A,succ(B))
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_succ]) ).
cnf(c_72,plain,
( gt(succ(B),A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_succ_gt_equiv]) ).
fof(succ_tptp_minus_1,axiom,
succ(tptp_minus_1) = n0,
file('theBenchmark.p',succ_tptp_minus_1) ).
cnf(c_281,plain,
succ(tptp_minus_1) = n0,
inference(clausify,[status(thm)],[succ_tptp_minus_1]) ).
cnf(c_345,plain,
( n0 = A
| ~ leq(A,n0)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_0]) ).
fof(nnf_56,plain,
? [A] :
( init != uninit
& leq(A,tptp_minus_1)
& leq(n0,A) ),
inference(fof_nnf,[status(thm)],[cl5_nebula_init_0001_neg]) ).
fof(sk_cl5_nebula_init_0001_neg,plain,
( init != uninit
& leq(sK0,tptp_minus_1)
& leq(n0,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_56]) ).
cnf(c_358,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0001_neg]) ).
cnf(c_359,negated_conjecture,
leq(sK0,tptp_minus_1),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0001_neg]) ).
cnf(c_1984,negated_conjecture,
( n0 = sK0
| ~ leq(sK0,n0) ),
inference(resolve,[status(thm)],[c_358,c_345]) ).
cnf(c_1327,negated_conjecture,
( sK0 = n0
| ~ leq(sK0,n0) ),
inference(copy,[status(thm)],[c_1984]) ).
cnf(c_1985,negated_conjecture,
gt(succ(tptp_minus_1),sK0),
inference(resolve,[status(thm)],[c_359,c_72]) ).
cnf(c_1801,negated_conjecture,
gt(n0,sK0),
inference(paramod,[status(thm)],[c_281,c_1985]) ).
cnf(c_1986,negated_conjecture,
leq(sK0,succ(tptp_minus_1)),
inference(resolve,[status(thm)],[c_359,c_71]) ).
cnf(c_1802,negated_conjecture,
leq(sK0,n0),
inference(paramod,[status(thm)],[c_281,c_1986]) ).
cnf(c_1943,negated_conjecture,
sK0 = n0,
inference(resolve,[status(thm)],[c_1802,c_1327]) ).
cnf(c_1987,negated_conjecture,
gt(n0,n0),
inference(paramod,[status(thm)],[c_1943,c_1801]) ).
cnf(c_1983,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_1987]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV165+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 13:17:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2231367 was started by sandbox on n005,
% 0.09/0.37 % Sat Sep 26 13:17:02 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 5.92/1.76
% 5.92/1.76 % SZS status Theorem for theBenchmark
% 5.92/1.76
% 5.92/1.76 % Proof 1 at 0.62 (+ 0.10) seconds.
% 5.92/1.76 % Length of proof is 17.
% 5.92/1.76 % Level of proof is 4.
% 5.92/1.76 % Maximum clause weight is 17.000.
% 5.92/1.76 % Given clauses 285.
% 5.92/1.76
% 5.92/1.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------