%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC019+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 : n013.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 08:56:33 AM UTC 2026
% Result : Theorem 17.99s 3.01s
% Output : CNFRefutation 17.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 17 unt; 0 def)
% Number of atoms : 106 ( 40 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 115 ( 44 ~; 35 |; 24 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 25 ( 0 sgn 13 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('theBenchmark.p',ax42) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = U
& nil = V )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| X != W
| 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)
=> ( ( nil = U
& nil = V )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| X != W
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != U
| nil != V )
& ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& X = W
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ( nil != sK1
| nil != sK0 )
& ! [Y] :
( ~ frontsegP(sK1,Y)
| ~ frontsegP(sK0,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK2 = sK3
& sK3 = sK1
& sK2 = sK0
& ssList(sK2)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK3,sK2]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK3),skolemize(X,sK2)],[nnf_87]) ).
cnf(c_190,negated_conjecture,
( nil != sK1
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6052,negated_conjecture,
( nil != sK1
| sK0 != nil ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_191,negated_conjecture,
( sK1 != nil
| sK0 != nil ),
inference(copy,[status(thm)],[c_6052]) ).
cnf(c_192,negated_conjecture,
( ~ frontsegP(sK1,A)
| ~ frontsegP(sK0,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
sK3 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
sK2 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_261,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax42]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_295,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_297,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_1640,plain,
sK2 = sK1,
inference(paramod,[status(thm)],[c_194,c_193]) ).
cnf(c_1790,plain,
frontsegP(sK1,sK1),
inference(resolve,[status(thm)],[c_261,c_199]) ).
cnf(c_1791,plain,
frontsegP(sK0,sK0),
inference(resolve,[status(thm)],[c_261,c_198]) ).
cnf(c_6053,negated_conjecture,
( A = sK1
| neq(sK1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_297,c_199]) ).
cnf(c_1851,negated_conjecture,
( sK1 = A
| neq(sK1,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6053]) ).
cnf(c_6054,plain,
sK1 = sK0,
inference(paramod,[status(thm)],[c_1640,c_195]) ).
cnf(c_4854,plain,
sK0 = sK1,
inference(copy,[status(thm)],[c_6054]) ).
cnf(c_6055,plain,
( sK1 != nil
| sK1 != nil ),
inference(paramod,[status(thm)],[c_4854,c_191]) ).
cnf(c_5409,plain,
sK1 != nil,
inference(copy,[status(thm)],[c_6055]) ).
cnf(c_5415,plain,
frontsegP(sK0,sK1),
inference(paramod,[status(thm)],[c_4854,c_1791]) ).
cnf(c_6056,plain,
( sK1 = nil
| neq(sK1,nil) ),
inference(resolve,[status(thm)],[c_1851,c_295]) ).
cnf(c_6050,plain,
neq(sK1,nil),
inference(resolve,[status(thm)],[c_5409,c_6056]) ).
cnf(c_6057,negated_conjecture,
( ~ frontsegP(sK1,sK1)
| ~ frontsegP(sK0,sK1)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_6050,c_192]) ).
cnf(c_6058,negated_conjecture,
( ~ frontsegP(sK1,sK1)
| ~ frontsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_199,c_6057]) ).
cnf(c_6059,negated_conjecture,
~ frontsegP(sK1,sK1),
inference(resolve,[status(thm)],[c_5415,c_6058]) ).
cnf(c_6051,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1790,c_6059]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC019+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 12:04:07 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 2686658 was started by sandbox2 on n013,
% 0.08/0.37 % Sat Sep 26 12:04:07 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 17.99/3.01
% 17.99/3.01 % given #500 (I,wt=49): 697 -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(361,e,f)].
% 17.99/3.01
% 17.99/3.01 % given #1000 (I,wt=64): 1222 -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(715,c,e)].
% 17.99/3.01
% 17.99/3.01 % given #1500 (W,wt=8): 5118 frontsegP(c4,c6). [para(195(a,1),1793(a,1))].
% 17.99/3.01
% 17.99/3.01 % SZS status Theorem for theBenchmark
% 17.99/3.01
% 17.99/3.01 % Proof 1 at 2.36 (+ 0.21) seconds.
% 17.99/3.01 % Length of proof is 23.
% 17.99/3.01 % Level of proof is 6.
% 17.99/3.01 % Maximum clause weight is 16.000.
% 17.99/3.01 % Given clauses 1628.
% 17.99/3.01
% 17.99/3.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------