%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC206+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 : n018.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 08:57:09 AM UTC 2026
% Result : Theorem 36.87s 5.15s
% Output : CNFRefutation 36.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 17 unt; 0 def)
% Number of atoms : 158 ( 38 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 178 ( 64 ~; 56 |; 41 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 29 ( 0 sgn 15 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
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(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Y] :
( ssList(Y)
=> ( ~ segmentP(W,Y)
| ~ segmentP(X,Y)
| ~ neq(Y,nil) ) ) )
| ( nil = X
& nil != W )
| neq(U,nil)
| ~ 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)
=> ( ( neq(X,nil)
& ! [Y] :
( ssList(Y)
=> ( ~ segmentP(W,Y)
| ~ segmentP(X,Y)
| ~ neq(Y,nil) ) ) )
| ( nil = X
& nil != W )
| neq(U,nil)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( segmentP(W,Y)
& segmentP(X,Y)
& neq(Y,nil)
& ssList(Y) ) )
& ( nil != X
| nil = W )
& ~ neq(U,nil)
& 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,
( ( ~ neq(sK2,nil)
| ( segmentP(sK0,sK1)
& segmentP(sK2,sK1)
& neq(sK1,nil)
& ssList(sK1) ) )
& ( nil != sK2
| nil = sK0 )
& ~ neq(sK3,nil)
& neq(sK4,nil)
& sK0 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK0)
& ssList(sK4)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK0,sK2,sK1]),skolemize(U,sK3),skolemize(V,sK4),skolemize(W,sK0),skolemize(X,sK2),skolemize(Y,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK2,nil)
| segmentP(sK0,sK1) )
& ( ~ neq(sK2,nil)
| segmentP(sK2,sK1) )
& ( ~ neq(sK2,nil)
| neq(sK1,nil) )
& ( ~ neq(sK2,nil)
| ssList(sK1) )
& ( nil != sK2
| nil = sK0 )
& ~ neq(sK3,nil)
& neq(sK4,nil)
& sK0 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK0)
& ssList(sK4)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK2,nil)
| segmentP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK2,nil)
| neq(sK1,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( ~ neq(sK2,nil)
| ssList(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
~ neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
neq(sK4,nil),
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,
sK2 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_246,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax57]) ).
cnf(c_249,plain,
( B = A
| ~ segmentP(B,A)
| ~ segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax54]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_299,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_301,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_302,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_5947,plain,
( ~ neq(sK4,nil)
| segmentP(sK0,sK1) ),
inference(paramod,[status(thm)],[c_199,c_190]) ).
cnf(c_1644,negated_conjecture,
segmentP(sK0,sK1),
inference(resolve,[status(thm)],[c_197,c_5947]) ).
cnf(c_5948,plain,
( ~ neq(sK4,nil)
| neq(sK1,nil) ),
inference(paramod,[status(thm)],[c_199,c_192]) ).
cnf(c_1646,negated_conjecture,
neq(sK1,nil),
inference(resolve,[status(thm)],[c_197,c_5948]) ).
cnf(c_5949,plain,
( ~ neq(sK4,nil)
| ssList(sK1) ),
inference(paramod,[status(thm)],[c_199,c_193]) ).
cnf(c_1647,negated_conjecture,
ssList(sK1),
inference(resolve,[status(thm)],[c_197,c_5949]) ).
cnf(c_5950,negated_conjecture,
( A = sK3
| neq(sK3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_301,c_203]) ).
cnf(c_1858,negated_conjecture,
( sK3 = A
| neq(sK3,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_5950]) ).
cnf(c_4892,plain,
segmentP(sK3,sK1),
inference(paramod,[status(thm)],[c_198,c_1644]) ).
cnf(c_5951,plain,
( nil != sK1
| ~ ssList(nil)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_1646,c_302]) ).
cnf(c_5952,plain,
( sK1 != nil
| ~ ssList(nil)
| ~ ssList(sK1) ),
inference(copy,[status(thm)],[c_5951]) ).
cnf(c_5953,plain,
( sK1 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_1647,c_5952]) ).
cnf(c_4911,plain,
sK1 != nil,
inference(resolve,[status(thm)],[c_299,c_5953]) ).
cnf(c_4995,plain,
segmentP(sK1,nil),
inference(resolve,[status(thm)],[c_1647,c_246]) ).
cnf(c_5954,plain,
( sK1 = nil
| ~ segmentP(nil,sK1)
| ~ ssList(sK1)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_4995,c_249]) ).
cnf(c_5955,plain,
( sK1 = nil
| ~ segmentP(nil,sK1)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_299,c_5954]) ).
cnf(c_5956,plain,
( sK1 = nil
| ~ segmentP(nil,sK1) ),
inference(resolve,[status(thm)],[c_1647,c_5955]) ).
cnf(c_5642,plain,
~ segmentP(nil,sK1),
inference(resolve,[status(thm)],[c_4911,c_5956]) ).
cnf(c_5957,plain,
( sK3 = nil
| neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_1858,c_299]) ).
cnf(c_5917,negated_conjecture,
sK3 = nil,
inference(resolve,[status(thm)],[c_196,c_5957]) ).
cnf(c_5958,plain,
segmentP(nil,sK1),
inference(paramod,[status(thm)],[c_5917,c_4892]) ).
cnf(c_5946,plain,
$false,
inference(resolve,[status(thm)],[c_5642,c_5958]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC206+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 12:33:21 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 448646 was started by sandbox2 on n018,
% 0.16/0.43 % Sat Sep 26 12:33:21 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.47
% 0.16/0.47 % From the command line: assign(max_seconds, 300).
% 36.87/5.15
% 36.87/5.15 % given #500 (I,wt=49): 697 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,A)) != A | C != B | ssList(f35(A)). [factor(365,a,f)].
% 36.87/5.15
% 36.87/5.15 % given #1000 (I,wt=67): 1222 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,A)),cons(C,D)) != A | C != B | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(717,d,e)].
% 36.87/5.15
% 36.87/5.15 % given #1500 (T,wt=11): 1768 segmentP(nil,c6) | c6 != nil. [resolve(244,a,200,a),flip(b)].
% 36.87/5.15
% 36.87/5.15 % SZS status Theorem for theBenchmark
% 36.87/5.15
% 36.87/5.15 % Proof 1 at 4.29 (+ 0.35) seconds.
% 36.87/5.15 % Length of proof is 27.
% 36.87/5.15 % Level of proof is 5.
% 36.87/5.15 % Maximum clause weight is 18.000.
% 36.87/5.15 % Given clauses 1579.
% 36.87/5.15
% 36.87/5.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------