%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC017+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 : n019.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 08:56:32 AM UTC 2026
% Result : Theorem 20.14s 5.55s
% Output : CNFRefutation 20.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 72 ( 16 unt; 0 def)
% Number of atoms : 259 ( 87 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 296 ( 109 ~; 130 |; 46 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 35 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('theBenchmark.p',ax41) ).
fof(ax42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('theBenchmark.p',ax42) ).
fof(ax45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('theBenchmark.p',ax45) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ( ( ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& 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 ) )
& ( ( ! [Y] :
( ~ frontsegP(sK2,Y)
| ~ frontsegP(sK3,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK3,nil) )
| ( nil != sK2
& nil = sK3 ) )
& sK0 = sK2
& sK1 = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0,sK1]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( frontsegP(sK1,sK0)
| nil = sK0 )
& ( neq(sK0,nil)
| nil = sK0 )
& ( frontsegP(sK1,sK0)
| nil = sK1 )
& ( neq(sK0,nil)
| nil = sK1 )
& ! [VAR_0] :
( ~ frontsegP(sK2,VAR_0)
| ~ frontsegP(sK3,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil != sK2 )
& ( neq(sK3,nil)
| nil != sK2 )
& ! [VAR_0] :
( ~ frontsegP(sK2,VAR_0)
| ~ frontsegP(sK3,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sK3 )
& ( neq(sK3,nil)
| nil = sK3 )
& sK0 = sK2
& sK1 = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( frontsegP(sK1,sK0)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( frontsegP(sK1,sK0)
| sK0 = nil ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_192,negated_conjecture,
( neq(sK0,nil)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( neq(sK0,nil)
| sK0 = nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_194,negated_conjecture,
( frontsegP(sK1,sK0)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( frontsegP(sK1,sK0)
| sK1 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_196,negated_conjecture,
( neq(sK0,nil)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( neq(sK0,nil)
| sK1 = nil ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_198,negated_conjecture,
( ~ frontsegP(sK2,A)
| ~ frontsegP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil != sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
( ~ frontsegP(sK2,A)
| ~ frontsegP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sK2 != nil ),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_200,negated_conjecture,
( neq(sK3,nil)
| nil != sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
( neq(sK3,nil)
| sK2 != nil ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_202,negated_conjecture,
( ~ frontsegP(sK2,A)
| ~ frontsegP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
( ~ frontsegP(sK2,A)
| ~ frontsegP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sK3 = nil ),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_206,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_208,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_209,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_207,c_208]) ).
cnf(c_210,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_211,negated_conjecture,
ssList(sK2),
inference(paramod,[status(thm)],[c_206,c_210]) ).
cnf(c_268,plain,
( frontsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax45]) ).
cnf(c_273,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax42]) ).
cnf(c_274,plain,
( B = A
| ~ frontsegP(B,A)
| ~ frontsegP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax41]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_307,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_5077,negated_conjecture,
( neq(sK0,nil)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_207,c_197]) ).
cnf(c_556,negated_conjecture,
( neq(sK2,nil)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_206,c_5077]) ).
cnf(c_5078,negated_conjecture,
( frontsegP(sK1,sK0)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_207,c_195]) ).
cnf(c_5079,negated_conjecture,
( frontsegP(sK3,sK0)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_207,c_5078]) ).
cnf(c_557,negated_conjecture,
( frontsegP(sK3,sK2)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_206,c_5079]) ).
cnf(c_5080,negated_conjecture,
( neq(sK0,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_206,c_193]) ).
cnf(c_558,negated_conjecture,
( neq(sK2,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_206,c_5080]) ).
cnf(c_5081,negated_conjecture,
( frontsegP(sK1,sK0)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_206,c_191]) ).
cnf(c_5082,negated_conjecture,
( frontsegP(sK3,sK0)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_207,c_5081]) ).
cnf(c_559,negated_conjecture,
( frontsegP(sK3,sK2)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_206,c_5082]) ).
cnf(c_1729,plain,
frontsegP(sK2,nil),
inference(resolve,[status(thm)],[c_268,c_211]) ).
cnf(c_1731,plain,
frontsegP(sK2,sK2),
inference(resolve,[status(thm)],[c_273,c_211]) ).
cnf(c_1753,plain,
frontsegP(nil,nil),
inference(resolve,[status(thm)],[c_307,c_273]) ).
cnf(c_5083,negated_conjecture,
( ~ frontsegP(sK2,sK2)
| ~ frontsegP(sK3,sK2)
| ~ ssList(sK2)
| sK3 = nil
| sK3 = nil ),
inference(resolve,[status(thm)],[c_556,c_203]) ).
cnf(c_5084,negated_conjecture,
( ~ frontsegP(sK2,sK2)
| ~ frontsegP(sK3,sK2)
| ~ ssList(sK2)
| sK3 = nil ),
inference(copy,[status(thm)],[c_5083]) ).
cnf(c_5085,negated_conjecture,
( ~ frontsegP(sK2,sK2)
| ~ frontsegP(sK3,sK2)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_211,c_5084]) ).
cnf(c_4149,negated_conjecture,
( ~ frontsegP(sK3,sK2)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_1731,c_5085]) ).
cnf(c_4157,plain,
( neq(sK3,nil)
| neq(sK2,nil) ),
inference(resolve,[status(thm)],[c_558,c_201]) ).
cnf(c_5086,negated_conjecture,
( sK3 = sK2
| ~ frontsegP(sK2,sK3)
| ~ ssList(sK3)
| ~ ssList(sK2)
| sK2 = nil ),
inference(resolve,[status(thm)],[c_559,c_274]) ).
cnf(c_5087,negated_conjecture,
( sK3 = sK2
| ~ frontsegP(sK2,sK3)
| ~ ssList(sK3)
| sK2 = nil ),
inference(resolve,[status(thm)],[c_211,c_5086]) ).
cnf(c_4163,negated_conjecture,
( sK3 = sK2
| ~ frontsegP(sK2,sK3)
| sK2 = nil ),
inference(resolve,[status(thm)],[c_209,c_5087]) ).
cnf(c_5088,negated_conjecture,
( sK3 = nil
| sK3 = nil ),
inference(resolve,[status(thm)],[c_4149,c_557]) ).
cnf(c_5066,negated_conjecture,
sK3 = nil,
inference(copy,[status(thm)],[c_5088]) ).
cnf(c_5089,negated_conjecture,
( sK3 = sK2
| ~ frontsegP(sK2,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_5066,c_4163]) ).
cnf(c_5090,negated_conjecture,
( nil = sK2
| ~ frontsegP(sK2,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_5066,c_5089]) ).
cnf(c_5091,negated_conjecture,
( sK2 = nil
| ~ frontsegP(sK2,nil)
| sK2 = nil ),
inference(copy,[status(thm)],[c_5090]) ).
cnf(c_5092,negated_conjecture,
( ~ frontsegP(sK2,nil)
| sK2 = nil ),
inference(copy,[status(thm)],[c_5091]) ).
cnf(c_5071,negated_conjecture,
sK2 = nil,
inference(resolve,[status(thm)],[c_1729,c_5092]) ).
cnf(c_5093,plain,
( neq(sK3,nil)
| neq(nil,nil) ),
inference(paramod,[status(thm)],[c_5071,c_4157]) ).
cnf(c_5094,plain,
( neq(nil,nil)
| neq(nil,nil) ),
inference(paramod,[status(thm)],[c_5066,c_5093]) ).
cnf(c_5072,plain,
neq(nil,nil),
inference(copy,[status(thm)],[c_5094]) ).
cnf(c_5095,negated_conjecture,
( ~ frontsegP(sK2,A)
| ~ frontsegP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil != nil ),
inference(paramod,[status(thm)],[c_5071,c_199]) ).
cnf(c_5096,negated_conjecture,
( ~ frontsegP(sK2,A)
| ~ frontsegP(nil,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil != nil ),
inference(paramod,[status(thm)],[c_5066,c_5095]) ).
cnf(c_5097,negated_conjecture,
( ~ frontsegP(nil,A)
| ~ frontsegP(nil,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil != nil ),
inference(paramod,[status(thm)],[c_5071,c_5096]) ).
cnf(c_5098,negated_conjecture,
( ~ frontsegP(nil,A)
| ~ frontsegP(nil,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_5097]) ).
cnf(c_5074,negated_conjecture,
( ~ frontsegP(nil,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_5098]) ).
cnf(c_5099,negated_conjecture,
( ~ frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_5072,c_5074]) ).
cnf(c_5100,negated_conjecture,
~ frontsegP(nil,nil),
inference(resolve,[status(thm)],[c_307,c_5099]) ).
cnf(c_5076,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1753,c_5100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC017+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 12:04:37 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 1244138 was started by sandbox on n019,
% 0.08/0.34 % Sat Sep 26 12:04:37 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 20.14/5.55
% 20.14/5.55 % given #500 (I,wt=44): 710 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(B,D)),cons(B,E)) != A | ssList(f35(A)). [factor(373,b,c),xx(g)].
% 20.14/5.55
% 20.14/5.55 % given #1000 (I,wt=60): 1235 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,A)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(730,b,c),xx(f)].
% 20.14/5.55
% 20.14/5.55 % SZS status Theorem for theBenchmark
% 20.14/5.55
% 20.14/5.55 % Proof 1 at 2.31 (+ 0.23) seconds.
% 20.14/5.55 % Length of proof is 43.
% 20.14/5.55 % Level of proof is 8.
% 20.14/5.55 % Maximum clause weight is 19.000.
% 20.14/5.55 % Given clauses 1447.
% 20.14/5.55
% 20.14/5.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------