%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC218+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:57:12 AM UTC 2026
% Result : Theorem 218.28s 29.59s
% Output : CNFRefutation 218.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 17 unt; 0 def)
% Number of atoms : 135 ( 36 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 139 ( 47 ~; 42 |; 24 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 23 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('theBenchmark.p',ax7) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('theBenchmark.p',ax16) ).
fof(ax21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('theBenchmark.p',ax21) ).
fof(ax58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('theBenchmark.p',ax58) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( neq(U,nil)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ! [X1] :
( ssItem(X1)
=> app(app(Y,cons(X1,nil)),Z) != W )
| app(Y,Z) != X ) ) )
| 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)
=> ( neq(U,nil)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ! [X1] :
( ssItem(X1)
=> app(app(Y,cons(X1,nil)),Z) != W )
| app(Y,Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ~ neq(U,nil)
& ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(Y,cons(X1,nil)),Z) = W
& ssItem(X1) )
& app(Y,Z) = X
& ssList(Z) )
& ssList(Y) )
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ~ neq(sK0,nil)
& app(app(sK1,cons(sK2,nil)),sK3) = sK4
& ssItem(sK2)
& app(sK1,sK3) = sK6
& ssList(sK3)
& ssList(sK1)
& sK4 = sK0
& sK6 = sK5
& ssList(sK6)
& ssList(sK4)
& ssList(sK5)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK5,sK4,sK6,sK1,sK3,sK2]),skolemize(U,sK0),skolemize(V,sK5),skolemize(W,sK4),skolemize(X,sK6),skolemize(Y,sK1),skolemize(Z,sK3),skolemize(X1,sK2)],[nnf_87]) ).
cnf(c_190,negated_conjecture,
~ neq(sK0,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
app(app(sK1,cons(sK2,nil)),sK3) = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
ssItem(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK4 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_196,c_200]) ).
cnf(c_243,plain,
( nil = A
| ~ segmentP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_290,plain,
( cons(B,A) != nil
| ~ ssItem(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax21]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_297,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_298,plain,
( ssList(cons(B,A))
| ~ ssItem(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax16]) ).
cnf(c_299,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_317,plain,
( app(app(C,B),D) != A
| ~ ssList(D)
| ~ ssList(C)
| segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax7]) ).
cnf(c_546,negated_conjecture,
app(app(sK1,cons(sK2,nil)),sK3) = sK0,
inference(paramod,[status(thm)],[c_196,c_191]) ).
cnf(c_2122,plain,
( cons(sK2,A) != nil
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_290,c_192]) ).
cnf(c_2216,plain,
( ssList(cons(A,nil))
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_298,c_297]) ).
cnf(c_13016,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_299,c_201]) ).
cnf(c_2223,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_13016]) ).
cnf(c_13017,negated_conjecture,
( ~ ssList(sK3)
| ~ ssList(sK1)
| segmentP(sK0,cons(sK2,nil))
| ~ ssList(cons(sK2,nil))
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_546,c_317]) ).
cnf(c_13018,negated_conjecture,
( ~ ssList(sK3)
| ~ ssList(sK1)
| segmentP(sK0,cons(sK2,nil))
| ~ ssList(cons(sK2,nil)) ),
inference(resolve,[status(thm)],[c_201,c_13017]) ).
cnf(c_13019,negated_conjecture,
( ~ ssList(sK3)
| segmentP(sK0,cons(sK2,nil))
| ~ ssList(cons(sK2,nil)) ),
inference(resolve,[status(thm)],[c_195,c_13018]) ).
cnf(c_2610,negated_conjecture,
( segmentP(sK0,cons(sK2,nil))
| ~ ssList(cons(sK2,nil)) ),
inference(resolve,[status(thm)],[c_194,c_13019]) ).
cnf(c_13020,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_2223,c_297]) ).
cnf(c_3161,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_190,c_13020]) ).
cnf(c_3162,negated_conjecture,
( segmentP(nil,cons(sK2,nil))
| ~ ssList(cons(sK2,nil)) ),
inference(paramod,[status(thm)],[c_3161,c_2610]) ).
cnf(c_3212,plain,
cons(sK2,nil) != nil,
inference(resolve,[status(thm)],[c_2122,c_297]) ).
cnf(c_12669,plain,
ssList(cons(sK2,nil)),
inference(resolve,[status(thm)],[c_2216,c_192]) ).
cnf(c_12670,negated_conjecture,
segmentP(nil,cons(sK2,nil)),
inference(resolve,[status(thm)],[c_12669,c_3162]) ).
cnf(c_13021,plain,
( nil = cons(sK2,nil)
| ~ segmentP(nil,cons(sK2,nil)) ),
inference(resolve,[status(thm)],[c_12669,c_243]) ).
cnf(c_13022,plain,
( cons(sK2,nil) = nil
| ~ segmentP(nil,cons(sK2,nil)) ),
inference(copy,[status(thm)],[c_13021]) ).
cnf(c_13023,plain,
cons(sK2,nil) = nil,
inference(resolve,[status(thm)],[c_12670,c_13022]) ).
cnf(c_13015,plain,
$false,
inference(resolve,[status(thm)],[c_3212,c_13023]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC218+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 12:37:15 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 877270 was started by sandbox2 on n016,
% 0.11/0.38 % Sat Sep 26 12:37:15 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.42
% 0.11/0.42 % From the command line: assign(max_seconds, 300).
% 218.28/29.59
% 218.28/29.59 % given #500 (I,wt=49): 692 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,D)),cons(C,E)) != A | C != B | ssItem(f34(A)). [factor(361,d,e)].
% 218.28/29.59
% 218.28/29.59 % given #1000 (I,wt=44): 1212 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,C)),cons(B,D)) != A | ssList(f37(A)). [factor(712,c,d)].
% 218.28/29.59
% 218.28/29.59 % given #1500 (F,wt=11): 3110 -neq(c7,nil) | c7 != nil. [resolve(2235,a,297,a)].
% 218.28/29.59
% 218.28/29.59 % given #2000 (W,wt=15): 6068 segmentP(f6(c4,nil),nil). [resolve(2969,a,244,a)].
% 218.28/29.59
% 218.28/29.59 % SZS status Theorem for theBenchmark
% 218.28/29.59
% 218.28/29.59 % Proof 1 at 3.59 (+ 1.36) seconds.
% 218.28/29.59 % Length of proof is 31.
% 218.28/29.59 % Level of proof is 7.
% 218.28/29.59 % Maximum clause weight is 35.000.
% 218.28/29.59 % Given clauses 2176.
% 218.28/29.59
% 218.28/29.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------