%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC292+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 08:57:24 AM UTC 2026
% Result : Theorem 145.22s 20.07s
% Output : CNFRefutation 145.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 20 unt; 0 def)
% Number of atoms : 148 ( 55 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 151 ( 53 ~; 50 |; 34 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 13 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('theBenchmark.p',ax68) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| ( nil = X
& nil != W )
| strictorderedP(U)
| 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(X,nil)
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| ( nil = X
& nil != W )
| strictorderedP(U)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& ~ strictorderedP(U)
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg_sk,plain,
( ( ~ neq(sK2,nil)
| ( memberP(sK2,sK0)
& cons(sK0,nil) = sK1
& ssItem(sK0) ) )
& ( nil != sK2
| nil = sK1 )
& ~ strictorderedP(sK3)
& sK1 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK1)
& ssList(sK4)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK1,sK2,sK0]),skolemize(U,sK3),skolemize(V,sK4),skolemize(W,sK1),skolemize(X,sK2),skolemize(Y,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK2,nil)
| memberP(sK2,sK0) )
& ( ~ neq(sK2,nil)
| cons(sK0,nil) = sK1 )
& ( ~ neq(sK2,nil)
| ssItem(sK0) )
& ( nil != sK2
| nil = sK1 )
& ~ strictorderedP(sK3)
& sK1 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK1)
& ssList(sK4)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK2,nil)
| cons(sK0,nil) = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK2,nil)
| ssItem(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( nil != sK2
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6393,negated_conjecture,
( nil != sK2
| sK1 = nil ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_194,negated_conjecture,
( sK2 != nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_6393]) ).
cnf(c_195,negated_conjecture,
~ strictorderedP(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK2 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
ssList(sK4),
inference(paramod,[status(thm)],[c_197,c_198]) ).
cnf(c_200,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_196,c_200]) ).
fof(ax69,axiom,
strictorderedP(nil),
file('theBenchmark.p',ax69) ).
cnf(c_234,plain,
strictorderedP(nil),
inference(clausify,[status(thm)],[ax69]) ).
cnf(c_235,plain,
( strictorderedP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax68]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_297,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_299,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_300,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_6394,negated_conjecture,
( sK2 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_196,c_194]) ).
cnf(c_546,negated_conjecture,
( sK4 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_197,c_6394]) ).
cnf(c_6395,negated_conjecture,
( ~ neq(sK2,nil)
| cons(sK0,nil) = sK3 ),
inference(paramod,[status(thm)],[c_196,c_191]) ).
cnf(c_547,negated_conjecture,
( ~ neq(sK4,nil)
| cons(sK0,nil) = sK3 ),
inference(paramod,[status(thm)],[c_197,c_6395]) ).
cnf(c_548,negated_conjecture,
( ~ neq(sK4,nil)
| ssItem(sK0) ),
inference(paramod,[status(thm)],[c_197,c_192]) ).
cnf(c_6396,plain,
( A = nil
| neq(nil,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_299,c_297]) ).
cnf(c_1762,plain,
( nil = A
| neq(nil,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6396]) ).
cnf(c_6397,negated_conjecture,
( A = sK4
| neq(sK4,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_299,c_199]) ).
cnf(c_1764,negated_conjecture,
( sK4 = A
| neq(sK4,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6397]) ).
cnf(c_6398,negated_conjecture,
( nil = sK3
| neq(nil,sK3) ),
inference(resolve,[status(thm)],[c_1762,c_201]) ).
cnf(c_5017,negated_conjecture,
( sK3 = nil
| neq(nil,sK3) ),
inference(copy,[status(thm)],[c_6398]) ).
cnf(c_6399,plain,
( ~ strictorderedP(nil)
| neq(nil,sK3) ),
inference(paramod,[status(thm)],[c_5017,c_195]) ).
cnf(c_5019,plain,
neq(nil,sK3),
inference(resolve,[status(thm)],[c_234,c_6399]) ).
cnf(c_6400,plain,
( sK3 != nil
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_5019,c_300]) ).
cnf(c_6401,plain,
( sK3 != nil
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_297,c_6400]) ).
cnf(c_5021,negated_conjecture,
sK3 != nil,
inference(resolve,[status(thm)],[c_201,c_6401]) ).
cnf(c_5046,negated_conjecture,
sK4 != nil,
inference(resolve,[status(thm)],[c_5021,c_546]) ).
cnf(c_6402,plain,
( sK4 = nil
| neq(sK4,nil) ),
inference(resolve,[status(thm)],[c_1764,c_297]) ).
cnf(c_5142,negated_conjecture,
neq(sK4,nil),
inference(resolve,[status(thm)],[c_5046,c_6402]) ).
cnf(c_5145,negated_conjecture,
ssItem(sK0),
inference(resolve,[status(thm)],[c_5142,c_548]) ).
cnf(c_5146,negated_conjecture,
cons(sK0,nil) = sK3,
inference(resolve,[status(thm)],[c_5142,c_547]) ).
cnf(c_6403,negated_conjecture,
strictorderedP(cons(sK0,nil)),
inference(resolve,[status(thm)],[c_5145,c_235]) ).
cnf(c_6404,negated_conjecture,
strictorderedP(sK3),
inference(paramod,[status(thm)],[c_5146,c_6403]) ).
cnf(c_6392,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_195,c_6404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC292+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.63 % Computer : n016.cluster.edu
% 0.15/0.63 % Model : x86_64 x86_64
% 0.15/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.63 % Memory : 8046.5625MB
% 0.15/0.63 % OS : Linux 6.8.0-71-generic
% 0.15/0.63 % CPULimit : 300
% 0.15/0.63 % WCLimit : 300
% 0.15/0.63 % DateTime : Sat Sep 26 12:47:31 UTC 2026
% 0.15/0.63 % CPUTime :
% 0.15/0.63 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.63 % Process 897275 was started by sandbox2 on n016,
% 0.15/0.63 % Sat Sep 26 12:47:31 2026
% 0.15/0.63 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/0.67
% 0.21/0.67 % From the command line: assign(max_seconds, 300).
% 145.22/20.07
% 145.22/20.07 % given #500 (I,wt=47): 703 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,E)) != A | C != B | ssList(f35(A)). [factor(363,e,f)].
% 145.22/20.07
% 145.22/20.07 % given #1000 (I,wt=60): 1228 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,C)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(721,c,e)].
% 145.22/20.07
% 145.22/20.07 % given #1500 (T,wt=11): 5123 frontsegP(c4,c3) | c4 != c3. [resolve(5088,a,300,c),unit_del(b,201),unit_del(c,199)].
% 145.22/20.07
% 145.22/20.07 % SZS status Theorem for theBenchmark
% 145.22/20.07
% 145.22/20.07 % Proof 1 at 2.97 (+ 0.29) seconds.
% 145.22/20.07 % Length of proof is 32.
% 145.22/20.07 % Level of proof is 9.
% 145.22/20.07 % Maximum clause weight is 18.000.
% 145.22/20.07 % Given clauses 1503.
% 145.22/20.07
% 145.22/20.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------