%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC101+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 : n003.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 08:56:49 AM UTC 2026
% Result : Theorem 95.66s 13.51s
% Output : CNFRefutation 95.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 18 unt; 0 def)
% Number of atoms : 176 ( 85 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 206 ( 75 ~; 64 |; 51 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 23 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('theBenchmark.p',ax5) ).
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)
=> ( ( frontsegP(V,U)
& neq(U,nil) )
| ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != 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)
=> ( ( frontsegP(V,U)
& neq(U,nil) )
| ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != X ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ frontsegP(V,U)
| ~ neq(U,nil) )
& ( nil != U
| nil != V )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(W)
& app(W,Y) = X
& 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_sk,plain,
( ( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil) )
& ( nil != sK0
| nil != sK1 )
& ( nil != sK3
| nil = sK2 )
& ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != sK3
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != sK4
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(sK3)
& app(sK3,sK4) = sK2
& ssList(sK4)
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2,sK4]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil) )
& ( nil != sK0
| nil != sK1 )
& ( nil != sK3
| nil = sK2 )
& ! [VAR_0,VAR_1,VAR_2] :
( app(VAR_2,cons(VAR_0,nil)) != sK3
| ~ ssList(VAR_2)
| app(cons(VAR_0,nil),VAR_1) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& equalelemsP(sK3)
& app(sK3,sK4) = sK2
& ssList(sK4)
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( nil != sK0
| nil != sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_4287,negated_conjecture,
( nil != sK0
| sK1 != nil ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_194,negated_conjecture,
( sK0 != nil
| sK1 != nil ),
inference(copy,[status(thm)],[c_4287]) ).
cnf(c_195,negated_conjecture,
( nil != sK3
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_4288,negated_conjecture,
( nil != sK3
| sK2 = nil ),
inference(copy,[status(thm)],[c_195]) ).
cnf(c_196,negated_conjecture,
( sK3 != nil
| sK2 = nil ),
inference(copy,[status(thm)],[c_4288]) ).
cnf(c_198,negated_conjecture,
app(sK3,sK4) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_201,c_202]) ).
cnf(c_204,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_200,c_204]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_301,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_303,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_328,plain,
( app(B,C) != A
| ~ ssList(C)
| frontsegP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_4289,negated_conjecture,
app(sK0,sK4) = sK2,
inference(paramod,[status(thm)],[c_200,c_198]) ).
cnf(c_554,negated_conjecture,
app(sK0,sK4) = sK1,
inference(paramod,[status(thm)],[c_201,c_4289]) ).
cnf(c_4290,negated_conjecture,
( sK3 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_201,c_196]) ).
cnf(c_556,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_200,c_4290]) ).
cnf(c_4291,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_303,c_205]) ).
cnf(c_4292,negated_conjecture,
( nil = sK0
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_4291,c_301]) ).
cnf(c_1899,negated_conjecture,
( sK0 = nil
| neq(sK0,nil) ),
inference(copy,[status(thm)],[c_4292]) ).
cnf(c_4293,negated_conjecture,
( app(A,B) != sK1
| ~ ssList(B)
| frontsegP(sK1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_328,c_203]) ).
cnf(c_4294,negated_conjecture,
( app(sK0,A) != sK1
| ~ ssList(A)
| frontsegP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_4293,c_205]) ).
cnf(c_4295,negated_conjecture,
( app(sK0,sK4) != sK1
| frontsegP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_4294,c_199]) ).
cnf(c_4267,negated_conjecture,
frontsegP(sK1,sK0),
inference(resolve,[status(thm)],[c_4295,c_554]) ).
cnf(c_4270,negated_conjecture,
~ neq(sK0,nil),
inference(resolve,[status(thm)],[c_4267,c_192]) ).
cnf(c_4271,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_4270,c_1899]) ).
cnf(c_4296,negated_conjecture,
( nil != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_4271,c_556]) ).
cnf(c_4282,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_4296]) ).
cnf(c_4297,negated_conjecture,
( sK0 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_4282,c_194]) ).
cnf(c_4298,negated_conjecture,
( nil != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_4271,c_4297]) ).
cnf(c_4299,negated_conjecture,
nil != nil,
inference(copy,[status(thm)],[c_4298]) ).
cnf(c_4286,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_4299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC101+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n003.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 12:16:54 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 2842689 was started by sandbox on n003,
% 0.16/0.42 % Sat Sep 26 12:16:54 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 95.66/13.51
% 95.66/13.51 % SZS status Theorem for theBenchmark
% 95.66/13.51
% 95.66/13.51 % Proof 1 at 4.79 (+ 0.15) seconds.
% 95.66/13.51 % Length of proof is 27.
% 95.66/13.51 % Level of proof is 7.
% 95.66/13.51 % Maximum clause weight is 24.000.
% 95.66/13.51 % Given clauses 354.
% 95.66/13.51
% 95.66/13.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------