%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC116+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 : n012.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 08:56:53 AM UTC 2026
% Result : Theorem 11.65s 1.86s
% Output : CNFRefutation 11.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 81 ( 20 unt; 0 def)
% Number of atoms : 257 ( 82 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 284 ( 108 ~; 115 |; 40 &)
% ( 2 <=>; 19 =>; 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 : 41 ( 0 sgn 17 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(V,W)
& segmentP(U,V) )
=> segmentP(U,W) ) ) ) ),
file('theBenchmark.p',ax53) ).
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)
=> ( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( segmentP(V,U)
& neq(U,nil) )
| ( nil = U
& nil = V )
| ( nil = X
& nil != 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)
=> ( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( segmentP(V,U)
& neq(U,nil) )
| ( nil = U
& nil = V )
| ( nil = X
& nil != W )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( segmentP(X,W)
& neq(W,nil) )
| ~ neq(X,nil) )
& ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& ( nil != U
| nil != V )
& ( nil != X
| nil = W )
& 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,
( ( ( segmentP(sK0,sK1)
& neq(sK1,nil) )
| ~ neq(sK0,nil) )
& ( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) )
& ( nil != sK2
| nil != sK3 )
& ( nil != sK0
| nil = sK1 )
& sK1 = sK2
& sK0 = sK3
& ssList(sK0)
& ssList(sK1)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK1,sK0]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK1),skolemize(X,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( segmentP(sK0,sK1)
| ~ neq(sK0,nil) )
& ( neq(sK1,nil)
| ~ neq(sK0,nil) )
& ( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) )
& ( nil != sK2
| nil != sK3 )
& ( nil != sK0
| nil = sK1 )
& sK1 = sK2
& sK0 = sK3
& ssList(sK0)
& ssList(sK1)
& ssList(sK3)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( segmentP(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,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( nil != sK2
| nil != sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6516,negated_conjecture,
( nil != sK2
| sK3 != nil ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_194,negated_conjecture,
( sK2 != nil
| sK3 != nil ),
inference(copy,[status(thm)],[c_6516]) ).
cnf(c_195,negated_conjecture,
( nil != sK0
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6517,negated_conjecture,
( nil != sK0
| sK1 = nil ),
inference(copy,[status(thm)],[c_195]) ).
cnf(c_196,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_6517]) ).
cnf(c_197,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
sK0 = sK3,
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(sK3),
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_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_249,plain,
( segmentP(A,C)
| ~ segmentP(B,C)
| ~ segmentP(A,B)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax53]) ).
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_6518,negated_conjecture,
( nil != sK1
| segmentP(nil,sK1) ),
inference(resolve,[status(thm)],[c_243,c_200]) ).
cnf(c_1761,negated_conjecture,
( sK1 != nil
| segmentP(nil,sK1) ),
inference(copy,[status(thm)],[c_6518]) ).
cnf(c_6519,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_6519]) ).
cnf(c_1764,plain,
segmentP(sK3,nil),
inference(resolve,[status(thm)],[c_245,c_201]) ).
cnf(c_1766,plain,
segmentP(sK0,nil),
inference(resolve,[status(thm)],[c_245,c_199]) ).
cnf(c_6520,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_6520]) ).
cnf(c_6521,negated_conjecture,
( A = sK2
| neq(sK2,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_300,c_202]) ).
cnf(c_1852,negated_conjecture,
( sK2 = A
| neq(sK2,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_6521]) ).
cnf(c_6522,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_6522]) ).
cnf(c_6523,plain,
( sK3 = nil
| ~ segmentP(nil,sK3)
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_1764,c_248]) ).
cnf(c_6524,plain,
( sK3 = nil
| ~ segmentP(nil,sK3)
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_298,c_6523]) ).
cnf(c_4900,negated_conjecture,
( sK3 = nil
| ~ segmentP(nil,sK3) ),
inference(resolve,[status(thm)],[c_201,c_6524]) ).
cnf(c_6525,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_6525]) ).
cnf(c_5587,plain,
( sK1 = nil
| neq(nil,sK0) ),
inference(resolve,[status(thm)],[c_5573,c_196]) ).
cnf(c_5756,plain,
( segmentP(nil,sK1)
| neq(nil,sK0) ),
inference(resolve,[status(thm)],[c_5587,c_1761]) ).
cnf(c_6526,plain,
( sK0 != nil
| ~ ssList(sK0)
| ~ ssList(nil)
| segmentP(nil,sK1) ),
inference(resolve,[status(thm)],[c_5756,c_301]) ).
cnf(c_6527,plain,
( sK0 != nil
| ~ ssList(sK0)
| segmentP(nil,sK1) ),
inference(resolve,[status(thm)],[c_298,c_6526]) ).
cnf(c_5780,negated_conjecture,
( sK0 != nil
| segmentP(nil,sK1) ),
inference(resolve,[status(thm)],[c_199,c_6527]) ).
cnf(c_5820,plain,
( sK2 = nil
| neq(sK2,nil) ),
inference(resolve,[status(thm)],[c_1852,c_298]) ).
cnf(c_5823,plain,
( ~ segmentP(sK3,sK2)
| sK2 = nil ),
inference(resolve,[status(thm)],[c_5820,c_192]) ).
cnf(c_6033,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_1855,c_298]) ).
cnf(c_6036,plain,
( neq(sK1,nil)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_6033,c_191]) ).
cnf(c_6037,plain,
( segmentP(sK0,sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_6033,c_190]) ).
cnf(c_6047,plain,
( segmentP(nil,sK0)
| neq(sK1,nil) ),
inference(resolve,[status(thm)],[c_6036,c_1762]) ).
cnf(c_6050,plain,
( segmentP(nil,sK1)
| segmentP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_6037,c_5780]) ).
cnf(c_6528,plain,
( nil != sK1
| ~ ssList(nil)
| ~ ssList(sK1)
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_6047,c_301]) ).
cnf(c_6529,plain,
( sK1 != nil
| ~ ssList(nil)
| ~ ssList(sK1)
| segmentP(nil,sK0) ),
inference(copy,[status(thm)],[c_6528]) ).
cnf(c_6530,negated_conjecture,
( sK1 != nil
| ~ ssList(nil)
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_200,c_6529]) ).
cnf(c_6194,negated_conjecture,
( sK1 != nil
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_298,c_6530]) ).
cnf(c_6531,plain,
( segmentP(A,sK1)
| ~ segmentP(A,nil)
| ~ ssList(sK1)
| ~ ssList(nil)
| ~ ssList(A)
| segmentP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_6050,c_249]) ).
cnf(c_6532,plain,
( segmentP(A,sK1)
| ~ segmentP(A,nil)
| ~ ssList(sK1)
| ~ ssList(A)
| segmentP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_298,c_6531]) ).
cnf(c_6239,negated_conjecture,
( segmentP(A,sK1)
| ~ segmentP(A,nil)
| ~ ssList(A)
| segmentP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_200,c_6532]) ).
cnf(c_6533,plain,
( ~ segmentP(sK0,nil)
| ~ ssList(sK0)
| segmentP(sK0,sK1) ),
inference(factor,[status(thm)],[c_6239]) ).
cnf(c_6534,negated_conjecture,
( ~ segmentP(sK0,nil)
| segmentP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_199,c_6533]) ).
cnf(c_6243,negated_conjecture,
segmentP(sK0,sK1),
inference(resolve,[status(thm)],[c_1766,c_6534]) ).
cnf(c_6267,plain,
segmentP(sK0,sK2),
inference(paramod,[status(thm)],[c_197,c_6243]) ).
cnf(c_6285,plain,
segmentP(sK3,sK2),
inference(paramod,[status(thm)],[c_198,c_6267]) ).
cnf(c_6291,plain,
sK2 = nil,
inference(resolve,[status(thm)],[c_6285,c_5823]) ).
cnf(c_6302,negated_conjecture,
sK3 != nil,
inference(resolve,[status(thm)],[c_6291,c_194]) ).
cnf(c_6349,negated_conjecture,
~ segmentP(nil,sK3),
inference(resolve,[status(thm)],[c_6302,c_4900]) ).
cnf(c_6410,plain,
sK1 = nil,
inference(paramod,[status(thm)],[c_6291,c_197]) ).
cnf(c_6440,negated_conjecture,
segmentP(nil,sK0),
inference(resolve,[status(thm)],[c_6410,c_6194]) ).
cnf(c_6535,plain,
segmentP(nil,sK3),
inference(paramod,[status(thm)],[c_198,c_6440]) ).
cnf(c_6515,plain,
$false,
inference(resolve,[status(thm)],[c_6349,c_6535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC116+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.32 % Computer : n012.cluster.edu
% 0.07/0.32 % Model : x86_64 x86_64
% 0.07/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.32 % Memory : 8046.5625MB
% 0.07/0.32 % OS : Linux 6.8.0-71-generic
% 0.07/0.32 % CPULimit : 300
% 0.07/0.32 % WCLimit : 300
% 0.07/0.32 % DateTime : Sat Sep 26 12:16:49 UTC 2026
% 0.07/0.32 % CPUTime :
% 0.07/0.32 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.32 % Process 559254 was started by sandbox on n012,
% 0.07/0.32 % Sat Sep 26 12:16:49 2026
% 0.07/0.32 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.34
% 0.10/0.34 % From the command line: assign(max_seconds, 300).
% 11.65/1.86
% 11.65/1.86 % 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)].
% 11.65/1.86
% 11.65/1.86 % 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)].
% 11.65/1.86
% 11.65/1.86 % given #1500 (T,wt=11): 4900 -segmentP(nil,c4) | c4 = nil. [resolve(1764,a,248,d),unit_del(a,298),unit_del(b,201)].
% 11.65/1.86
% 11.65/1.86 % SZS status Theorem for theBenchmark
% 11.65/1.86
% 11.65/1.86 % Proof 1 at 1.38 (+ 0.13) seconds.
% 11.65/1.86 % Length of proof is 56.
% 11.65/1.86 % Level of proof is 15.
% 11.65/1.86 % Maximum clause weight is 20.000.
% 11.65/1.86 % Given clauses 1722.
% 11.65/1.86
% 11.65/1.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------