%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC049+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 08:56:40 AM UTC 2026
% Result : Theorem 16.23s 2.80s
% Output : CNFRefutation 16.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 91 ( 23 unt; 0 def)
% Number of atoms : 289 ( 81 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 320 ( 122 ~; 129 |; 44 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 53 ( 0 sgn 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax47,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( rearsegP(V,W)
& rearsegP(U,V) )
=> rearsegP(U,W) ) ) ) ),
file('theBenchmark.p',ax47) ).
fof(ax49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('theBenchmark.p',ax49) ).
fof(ax51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('theBenchmark.p',ax51) ).
fof(ax52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('theBenchmark.p',ax52) ).
fof(ax54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('theBenchmark.p',ax54) ).
fof(ax57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('theBenchmark.p',ax57) ).
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)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = U
& nil = V )
| ( nil = X
& nil != W )
| ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| 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)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = U
& nil = V )
| ( nil = X
& nil != W )
| ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( rearsegP(X,W)
& neq(W,nil) )
| ~ neq(X,nil) )
& ( nil != U
| nil != V )
& ( nil != X
| nil = W )
& ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ 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,
( ( ( rearsegP(sK0,sK1)
& neq(sK1,nil) )
| ~ neq(sK0,nil) )
& ( nil != sK3
| nil != sK2 )
& ( nil != sK0
| nil = sK1 )
& ! [Y] :
( ~ rearsegP(sK3,Y)
| ~ rearsegP(sK2,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK1 = sK3
& sK0 = sK2
& ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK1,sK0]),skolemize(U,sK3),skolemize(V,sK2),skolemize(W,sK1),skolemize(X,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( rearsegP(sK0,sK1)
| ~ neq(sK0,nil) )
& ( neq(sK1,nil)
| ~ neq(sK0,nil) )
& ( nil != sK3
| nil != sK2 )
& ( nil != sK0
| nil = sK1 )
& ! [VAR_0] :
( ~ rearsegP(sK3,VAR_0)
| ~ rearsegP(sK2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) )
& sK1 = sK3
& sK0 = sK2
& ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( rearsegP(sK0,sK1)
| ~ neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( neq(sK1,nil)
| ~ neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( nil != sK3
| nil != sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6427,negated_conjecture,
( nil != sK3
| sK2 != nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_193,negated_conjecture,
( sK3 != nil
| sK2 != nil ),
inference(copy,[status(thm)],[c_6427]) ).
cnf(c_194,negated_conjecture,
( nil != sK0
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6428,negated_conjecture,
( nil != sK0
| sK1 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_195,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_6428]) ).
cnf(c_196,negated_conjecture,
( ~ rearsegP(sK3,A)
| ~ rearsegP(sK2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_243,plain,
( nil != A
| segmentP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_245,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax57]) ).
cnf(c_248,plain,
( B = A
| ~ segmentP(B,A)
| ~ segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax54]) ).
cnf(c_250,plain,
( nil != A
| rearsegP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax52]) ).
cnf(c_252,plain,
( rearsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax51]) ).
cnf(c_254,plain,
( rearsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax49]) ).
cnf(c_256,plain,
( rearsegP(A,C)
| ~ rearsegP(B,C)
| ~ rearsegP(A,B)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax47]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_298,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_300,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_301,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_6429,negated_conjecture,
( nil != sK0
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_243,c_199]) ).
cnf(c_1762,negated_conjecture,
( sK0 != nil
| segmentP(nil,sK0) ),
inference(copy,[status(thm)],[c_6429]) ).
cnf(c_1764,plain,
segmentP(sK2,nil),
inference(resolve,[status(thm)],[c_245,c_201]) ).
cnf(c_6430,negated_conjecture,
( nil != sK1
| rearsegP(nil,sK1) ),
inference(resolve,[status(thm)],[c_250,c_200]) ).
cnf(c_1773,negated_conjecture,
( sK1 != nil
| rearsegP(nil,sK1) ),
inference(copy,[status(thm)],[c_6430]) ).
cnf(c_1778,plain,
rearsegP(sK0,nil),
inference(resolve,[status(thm)],[c_252,c_199]) ).
cnf(c_1779,plain,
rearsegP(sK3,sK3),
inference(resolve,[status(thm)],[c_254,c_202]) ).
cnf(c_1781,plain,
rearsegP(sK1,sK1),
inference(resolve,[status(thm)],[c_254,c_200]) ).
cnf(c_6431,plain,
( A = nil
| neq(nil,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_300,c_298]) ).
cnf(c_1851,plain,
( nil = A
| neq(nil,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6431]) ).
cnf(c_6432,negated_conjecture,
( A = sK3
| neq(sK3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_300,c_202]) ).
cnf(c_1852,negated_conjecture,
( sK3 = A
| neq(sK3,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6432]) ).
cnf(c_6433,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_300,c_199]) ).
cnf(c_1855,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6433]) ).
cnf(c_6434,plain,
( sK2 = nil
| ~ segmentP(nil,sK2)
| ~ ssList(sK2)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_1764,c_248]) ).
cnf(c_6435,plain,
( sK2 = nil
| ~ segmentP(nil,sK2)
| ~ ssList(sK2) ),
inference(resolve,[status(thm)],[c_298,c_6434]) ).
cnf(c_4900,negated_conjecture,
( sK2 = nil
| ~ segmentP(nil,sK2) ),
inference(resolve,[status(thm)],[c_201,c_6435]) ).
cnf(c_5024,plain,
rearsegP(sK3,sK1),
inference(paramod,[status(thm)],[c_197,c_1781]) ).
cnf(c_6436,negated_conjecture,
( nil = sK0
| neq(nil,sK0) ),
inference(resolve,[status(thm)],[c_1851,c_199]) ).
cnf(c_5573,negated_conjecture,
( sK0 = nil
| neq(nil,sK0) ),
inference(copy,[status(thm)],[c_6436]) ).
cnf(c_5587,plain,
( sK1 = nil
| neq(nil,sK0) ),
inference(resolve,[status(thm)],[c_5573,c_195]) ).
cnf(c_5755,plain,
( rearsegP(nil,sK1)
| neq(nil,sK0) ),
inference(resolve,[status(thm)],[c_5587,c_1773]) ).
cnf(c_6437,plain,
( sK0 != nil
| ~ ssList(sK0)
| ~ ssList(nil)
| rearsegP(nil,sK1) ),
inference(resolve,[status(thm)],[c_5755,c_301]) ).
cnf(c_6438,plain,
( sK0 != nil
| ~ ssList(sK0)
| rearsegP(nil,sK1) ),
inference(resolve,[status(thm)],[c_298,c_6437]) ).
cnf(c_5771,negated_conjecture,
( sK0 != nil
| rearsegP(nil,sK1) ),
inference(resolve,[status(thm)],[c_199,c_6438]) ).
cnf(c_5820,plain,
( sK3 = nil
| neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_1852,c_298]) ).
cnf(c_6439,negated_conjecture,
( ~ rearsegP(sK3,sK3)
| ~ rearsegP(sK2,sK3)
| ~ ssList(sK3)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_5820,c_196]) ).
cnf(c_6440,negated_conjecture,
( ~ rearsegP(sK3,sK3)
| ~ rearsegP(sK2,sK3)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_202,c_6439]) ).
cnf(c_5823,negated_conjecture,
( ~ rearsegP(sK2,sK3)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_1779,c_6440]) ).
cnf(c_6060,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_1855,c_298]) ).
cnf(c_6064,plain,
( neq(sK1,nil)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_6060,c_191]) ).
cnf(c_6065,plain,
( rearsegP(sK0,sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_6060,c_190]) ).
cnf(c_6096,plain,
( segmentP(nil,sK0)
| neq(sK1,nil) ),
inference(resolve,[status(thm)],[c_6064,c_1762]) ).
cnf(c_6101,plain,
( rearsegP(nil,sK1)
| rearsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_6065,c_5771]) ).
cnf(c_6441,negated_conjecture,
( ~ rearsegP(sK3,sK1)
| ~ rearsegP(sK2,sK1)
| ~ ssList(sK1)
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_6096,c_196]) ).
cnf(c_6442,negated_conjecture,
( ~ rearsegP(sK3,sK1)
| ~ rearsegP(sK2,sK1)
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_200,c_6441]) ).
cnf(c_6226,negated_conjecture,
( ~ rearsegP(sK2,sK1)
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_5024,c_6442]) ).
cnf(c_6443,plain,
( rearsegP(A,sK1)
| ~ rearsegP(A,nil)
| ~ ssList(sK1)
| ~ ssList(nil)
| ~ ssList(A)
| rearsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_6101,c_256]) ).
cnf(c_6444,plain,
( rearsegP(A,sK1)
| ~ rearsegP(A,nil)
| ~ ssList(sK1)
| ~ ssList(A)
| rearsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_298,c_6443]) ).
cnf(c_6295,negated_conjecture,
( rearsegP(A,sK1)
| ~ rearsegP(A,nil)
| ~ ssList(A)
| rearsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_200,c_6444]) ).
cnf(c_6445,plain,
( ~ rearsegP(sK0,nil)
| ~ ssList(sK0)
| rearsegP(sK0,sK1) ),
inference(factor,[status(thm)],[c_6295]) ).
cnf(c_6446,negated_conjecture,
( ~ rearsegP(sK0,nil)
| rearsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_199,c_6445]) ).
cnf(c_6299,negated_conjecture,
rearsegP(sK0,sK1),
inference(resolve,[status(thm)],[c_1778,c_6446]) ).
cnf(c_6308,plain,
rearsegP(sK0,sK3),
inference(paramod,[status(thm)],[c_197,c_6299]) ).
cnf(c_6309,plain,
rearsegP(sK2,sK1),
inference(paramod,[status(thm)],[c_198,c_6299]) ).
cnf(c_6310,negated_conjecture,
segmentP(nil,sK0),
inference(resolve,[status(thm)],[c_6309,c_6226]) ).
cnf(c_6346,plain,
rearsegP(sK2,sK3),
inference(paramod,[status(thm)],[c_198,c_6308]) ).
cnf(c_6352,negated_conjecture,
sK3 = nil,
inference(resolve,[status(thm)],[c_6346,c_5823]) ).
cnf(c_6362,negated_conjecture,
sK2 != nil,
inference(resolve,[status(thm)],[c_6352,c_193]) ).
cnf(c_6380,negated_conjecture,
~ segmentP(nil,sK2),
inference(resolve,[status(thm)],[c_6362,c_4900]) ).
cnf(c_6447,plain,
segmentP(nil,sK2),
inference(paramod,[status(thm)],[c_198,c_6310]) ).
cnf(c_6426,plain,
$false,
inference(resolve,[status(thm)],[c_6380,c_6447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC049+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n019.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 12:08:03 UTC 2026
% 0.18/0.42 % CPUTime :
% 0.18/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.42 % Process 1250980 was started by sandbox on n019,
% 0.18/0.42 % Sat Sep 26 12:08:03 2026
% 0.18/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 16.23/2.80
% 16.23/2.80 % given #500 (I,wt=47): 698 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,D)),cons(C,E)) != A | C != B | ssList(f35(A)). [factor(364,d,e)].
% 16.23/2.80
% 16.23/2.80 % given #1000 (I,wt=63): 1223 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,D)),cons(C,A)) != A | C != B | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(717,d,e)].
% 16.23/2.80
% 16.23/2.80 % given #1500 (T,wt=11): 4900 -segmentP(nil,c4) | c4 = nil. [resolve(1764,a,248,d),unit_del(a,298),unit_del(b,201)].
% 16.23/2.80
% 16.23/2.80 % SZS status Theorem for theBenchmark
% 16.23/2.80
% 16.23/2.80 % Proof 1 at 2.10 (+ 0.20) seconds.
% 16.23/2.80 % Length of proof is 65.
% 16.23/2.80 % Level of proof is 15.
% 16.23/2.80 % Maximum clause weight is 20.000.
% 16.23/2.80 % Given clauses 1723.
% 16.23/2.80
% 16.23/2.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------