%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC051+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 : n020.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 18.53s 2.85s
% Output : CNFRefutation 18.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 81 ( 19 unt; 0 def)
% Number of atoms : 265 ( 61 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 296 ( 112 ~; 117 |; 42 &)
% ( 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 : 51 ( 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 = X
& nil != W )
| ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| 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 = X
& nil != W )
| ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| 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 != X
| nil = W )
& ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil)
& 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 != sK0
| nil = sK1 )
& ! [Y] :
( ~ rearsegP(sK3,Y)
| ~ rearsegP(sK2,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK2,nil)
& 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 != sK0
| nil = sK1 )
& ! [VAR_0] :
( ~ rearsegP(sK3,VAR_0)
| ~ rearsegP(sK2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) )
& neq(sK2,nil)
& 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 != sK0
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6246,negated_conjecture,
( nil != sK0
| sK1 = nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_193,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_6246]) ).
cnf(c_194,negated_conjecture,
( ~ rearsegP(sK3,A)
| ~ rearsegP(sK2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
neq(sK2,nil),
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,
sK0 = sK2,
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_200,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_242,plain,
( nil != A
| segmentP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_244,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax57]) ).
cnf(c_247,plain,
( B = A
| ~ segmentP(B,A)
| ~ segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax54]) ).
cnf(c_249,plain,
( nil != A
| rearsegP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax52]) ).
cnf(c_251,plain,
( rearsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax51]) ).
cnf(c_253,plain,
( rearsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax49]) ).
cnf(c_255,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_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_6247,negated_conjecture,
( nil != sK0
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_242,c_198]) ).
cnf(c_1762,negated_conjecture,
( sK0 != nil
| segmentP(nil,sK0) ),
inference(copy,[status(thm)],[c_6247]) ).
cnf(c_1764,plain,
segmentP(sK2,nil),
inference(resolve,[status(thm)],[c_244,c_200]) ).
cnf(c_6248,negated_conjecture,
( nil != sK1
| rearsegP(nil,sK1) ),
inference(resolve,[status(thm)],[c_249,c_199]) ).
cnf(c_1773,negated_conjecture,
( sK1 != nil
| rearsegP(nil,sK1) ),
inference(copy,[status(thm)],[c_6248]) ).
cnf(c_1778,plain,
rearsegP(sK0,nil),
inference(resolve,[status(thm)],[c_251,c_198]) ).
cnf(c_1781,plain,
rearsegP(sK1,sK1),
inference(resolve,[status(thm)],[c_253,c_199]) ).
cnf(c_6249,plain,
( A = nil
| neq(nil,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_299,c_297]) ).
cnf(c_1852,plain,
( nil = A
| neq(nil,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6249]) ).
cnf(c_6250,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_299,c_198]) ).
cnf(c_1856,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6250]) ).
cnf(c_6251,negated_conjecture,
( nil != sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolve,[status(thm)],[c_300,c_195]) ).
cnf(c_6252,negated_conjecture,
( sK2 != nil
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(copy,[status(thm)],[c_6251]) ).
cnf(c_6253,negated_conjecture,
( sK2 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_200,c_6252]) ).
cnf(c_1862,negated_conjecture,
sK2 != nil,
inference(resolve,[status(thm)],[c_297,c_6253]) ).
cnf(c_6254,plain,
( sK2 = nil
| ~ segmentP(nil,sK2)
| ~ ssList(sK2)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_1764,c_247]) ).
cnf(c_6255,plain,
( sK2 = nil
| ~ segmentP(nil,sK2)
| ~ ssList(sK2) ),
inference(resolve,[status(thm)],[c_297,c_6254]) ).
cnf(c_6256,negated_conjecture,
( sK2 = nil
| ~ segmentP(nil,sK2) ),
inference(resolve,[status(thm)],[c_200,c_6255]) ).
cnf(c_4915,negated_conjecture,
~ segmentP(nil,sK2),
inference(resolve,[status(thm)],[c_1862,c_6256]) ).
cnf(c_5038,plain,
rearsegP(sK3,sK1),
inference(paramod,[status(thm)],[c_196,c_1781]) ).
cnf(c_6257,negated_conjecture,
( nil = sK0
| neq(nil,sK0) ),
inference(resolve,[status(thm)],[c_1852,c_198]) ).
cnf(c_5571,negated_conjecture,
( sK0 = nil
| neq(nil,sK0) ),
inference(copy,[status(thm)],[c_6257]) ).
cnf(c_5581,plain,
( sK1 = nil
| neq(nil,sK0) ),
inference(resolve,[status(thm)],[c_5571,c_193]) ).
cnf(c_5714,plain,
( rearsegP(nil,sK1)
| neq(nil,sK0) ),
inference(resolve,[status(thm)],[c_5581,c_1773]) ).
cnf(c_6258,plain,
( sK0 != nil
| ~ ssList(sK0)
| ~ ssList(nil)
| rearsegP(nil,sK1) ),
inference(resolve,[status(thm)],[c_5714,c_300]) ).
cnf(c_6259,plain,
( sK0 != nil
| ~ ssList(sK0)
| rearsegP(nil,sK1) ),
inference(resolve,[status(thm)],[c_297,c_6258]) ).
cnf(c_5728,negated_conjecture,
( sK0 != nil
| rearsegP(nil,sK1) ),
inference(resolve,[status(thm)],[c_198,c_6259]) ).
cnf(c_5917,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_1856,c_297]) ).
cnf(c_5936,plain,
( neq(sK1,nil)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_5917,c_191]) ).
cnf(c_5937,plain,
( rearsegP(sK0,sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_5917,c_190]) ).
cnf(c_5947,plain,
( segmentP(nil,sK0)
| neq(sK1,nil) ),
inference(resolve,[status(thm)],[c_5936,c_1762]) ).
cnf(c_5952,plain,
( rearsegP(nil,sK1)
| rearsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_5937,c_5728]) ).
cnf(c_6260,negated_conjecture,
( ~ rearsegP(sK3,sK1)
| ~ rearsegP(sK2,sK1)
| ~ ssList(sK1)
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_5947,c_194]) ).
cnf(c_6261,negated_conjecture,
( ~ rearsegP(sK3,sK1)
| ~ rearsegP(sK2,sK1)
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_199,c_6260]) ).
cnf(c_6096,negated_conjecture,
( ~ rearsegP(sK2,sK1)
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_5038,c_6261]) ).
cnf(c_6262,plain,
( rearsegP(A,sK1)
| ~ rearsegP(A,nil)
| ~ ssList(sK1)
| ~ ssList(nil)
| ~ ssList(A)
| rearsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_5952,c_255]) ).
cnf(c_6263,plain,
( rearsegP(A,sK1)
| ~ rearsegP(A,nil)
| ~ ssList(sK1)
| ~ ssList(A)
| rearsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_297,c_6262]) ).
cnf(c_6161,negated_conjecture,
( rearsegP(A,sK1)
| ~ rearsegP(A,nil)
| ~ ssList(A)
| rearsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_199,c_6263]) ).
cnf(c_6264,plain,
( ~ rearsegP(sK0,nil)
| ~ ssList(sK0)
| rearsegP(sK0,sK1) ),
inference(factor,[status(thm)],[c_6161]) ).
cnf(c_6265,negated_conjecture,
( ~ rearsegP(sK0,nil)
| rearsegP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_198,c_6264]) ).
cnf(c_6165,negated_conjecture,
rearsegP(sK0,sK1),
inference(resolve,[status(thm)],[c_1778,c_6265]) ).
cnf(c_6175,plain,
rearsegP(sK2,sK1),
inference(paramod,[status(thm)],[c_197,c_6165]) ).
cnf(c_6176,negated_conjecture,
segmentP(nil,sK0),
inference(resolve,[status(thm)],[c_6175,c_6096]) ).
cnf(c_6266,plain,
segmentP(nil,sK2),
inference(paramod,[status(thm)],[c_197,c_6176]) ).
cnf(c_6245,plain,
$false,
inference(resolve,[status(thm)],[c_4915,c_6266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC051+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n020.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 12:09:04 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 1501441 was started by sandbox2 on n020,
% 0.15/0.43 % Sat Sep 26 12:09:04 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.47
% 0.15/0.47 % From the command line: assign(max_seconds, 300).
% 18.53/2.85
% 18.53/2.85 % given #500 (I,wt=47): 697 -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(363,d,e)].
% 18.53/2.85
% 18.53/2.85 % given #1000 (I,wt=63): 1222 -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(716,d,e)].
% 18.53/2.85
% 18.53/2.85 % given #1500 (T,wt=11): 5004 -rearsegP(nil,c5) | c5 = nil. [resolve(1777,a,254,d),unit_del(a,297),unit_del(b,199)].
% 18.53/2.85
% 18.53/2.85 % SZS status Theorem for theBenchmark
% 18.53/2.85
% 18.53/2.85 % Proof 1 at 2.13 (+ 0.22) seconds.
% 18.53/2.85 % Length of proof is 55.
% 18.53/2.85 % Level of proof is 12.
% 18.53/2.85 % Maximum clause weight is 20.000.
% 18.53/2.85 % Given clauses 1659.
% 18.53/2.85
% 18.53/2.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------