%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC135+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:56:57 AM UTC 2026
% Result : Theorem 11.12s 6.84s
% Output : CNFRefutation 11.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 59 ( 15 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 55 ( 17 ~; 13 |; 14 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 17 ( 0 sgn 10 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( cyclefreeP(V)
| neq(X,nil)
| U != W
| V != X ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( cyclefreeP(V)
| neq(X,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_209,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_211,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
fof(ax60,axiom,
cyclefreeP(nil),
file('theBenchmark.p',ax60) ).
cnf(c_268,plain,
cyclefreeP(nil),
inference(clausify,[status(thm)],[ax60]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ~ cyclefreeP(V)
& ~ neq(X,nil)
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ~ cyclefreeP(sK0)
& ~ neq(sK1,nil)
& sK3 = sK2
& sK1 = sK0
& ssList(sK1)
& ssList(sK3)
& ssList(sK0)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK3,sK1]),skolemize(U,sK2),skolemize(V,sK0),skolemize(W,sK3),skolemize(X,sK1)],[nnf_87]) ).
cnf(c_310,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_313,negated_conjecture,
sK1 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_315,negated_conjecture,
~ neq(sK1,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_316,negated_conjecture,
~ cyclefreeP(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2289,plain,
( nil = A
| neq(A,nil)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_211,c_209]) ).
cnf(c_2758,plain,
~ neq(sK0,nil),
inference(paramod,[status(thm)],[c_313,c_315]) ).
cnf(c_5550,negated_conjecture,
( nil = sK0
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_2289,c_310]) ).
cnf(c_5551,negated_conjecture,
( sK0 = nil
| neq(sK0,nil) ),
inference(copy,[status(thm)],[c_5550]) ).
cnf(c_5505,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_2758,c_5551]) ).
cnf(c_5552,plain,
~ cyclefreeP(nil),
inference(paramod,[status(thm)],[c_5505,c_316]) ).
cnf(c_5549,plain,
$false,
inference(resolve,[status(thm)],[c_268,c_5552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC135+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n008.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 12:20:17 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.39 % Process 3640895 was started by sandbox on n008,
% 0.10/5.39 % Sat Sep 26 12:20:17 2026
% 0.10/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.41
% 0.16/5.41 % From the command line: assign(max_seconds, 300).
% 11.12/6.84
% 11.12/6.84 % given #500 (I,wt=55): 682 -ssList(cons(A,nil)) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(cons(A,nil),cons(A,C)),cons(B,D)) != cons(A,nil) | lt(A,B) | lt(B,A). [factor(387,b,i)].
% 11.12/6.84
% 11.12/6.84 % given #1000 (I,wt=45): 1203 -ssList(A) | ssItem(f34(A)) | -ssItem(B) | -ssItem(C) | app(app(A,cons(B,A)),cons(C,A)) != A | C != B. [factor(947,a,e)].
% 11.12/6.84
% 11.12/6.84 % SZS status Theorem for theBenchmark
% 11.12/6.84
% 11.12/6.84 % Proof 1 at 1.29 (+ 0.11) seconds.
% 11.12/6.84 % Length of proof is 13.
% 11.12/6.84 % Level of proof is 4.
% 11.12/6.84 % Maximum clause weight is 15.000.
% 11.12/6.84 % Given clauses 1299.
% 11.12/6.84
% 11.12/6.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------