%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC069+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 : n006.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 08:56:44 AM UTC 2026
% Result : Theorem 38.45s 6.91s
% Output : CNFRefutation 38.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 15 unt; 0 def)
% Number of atoms : 214 ( 86 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 242 ( 88 ~; 88 |; 49 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 18 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('theBenchmark.p',ax28) ).
fof(ax83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('theBenchmark.p',ax83) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Z] :
( ssList(Z)
=> ( ~ segmentP(W,Z)
| ~ segmentP(X,Z)
| ~ neq(Z,nil) ) ) )
| ( nil = U
& nil = V )
| ( nil = X
& nil != W )
| ? [Y] :
( segmentP(U,Y)
& segmentP(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)
=> ( ( neq(X,nil)
& ! [Z] :
( ssList(Z)
=> ( ~ segmentP(W,Z)
| ~ segmentP(X,Z)
| ~ neq(Z,nil) ) ) )
| ( nil = U
& nil = V )
| ( nil = X
& nil != W )
| ? [Y] :
( segmentP(U,Y)
& segmentP(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] :
( ( ~ neq(X,nil)
| ? [Z] :
( segmentP(W,Z)
& segmentP(X,Z)
& neq(Z,nil)
& ssList(Z) ) )
& ( nil != U
| nil != V )
& ( nil != X
| nil = W )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(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,
( ( ~ neq(sK2,nil)
| ( segmentP(sK0,sK1)
& segmentP(sK2,sK1)
& neq(sK1,nil)
& ssList(sK1) ) )
& ( nil != sK4
| nil != sK3 )
& ( nil != sK2
| nil = sK0 )
& ! [Y] :
( ~ segmentP(sK4,Y)
| ~ segmentP(sK3,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK0 = sK4
& sK2 = sK3
& ssList(sK2)
& ssList(sK0)
& ssList(sK3)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK3,sK0,sK2,sK1]),skolemize(U,sK4),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK2),skolemize(Z,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 != sK4
| nil != sK3 )
& ( nil != sK2
| nil = sK0 )
& ! [VAR_0] :
( ~ segmentP(sK4,VAR_0)
| ~ segmentP(sK3,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) )
& sK0 = sK4
& sK2 = sK3
& ssList(sK2)
& ssList(sK0)
& ssList(sK3)
& ssList(sK4) ),
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_191,negated_conjecture,
( ~ neq(sK2,nil)
| segmentP(sK2,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_194,negated_conjecture,
( nil != sK4
| nil != sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_26696,negated_conjecture,
( nil != sK4
| sK3 != nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_195,negated_conjecture,
( sK4 != nil
| sK3 != nil ),
inference(copy,[status(thm)],[c_26696]) ).
cnf(c_196,negated_conjecture,
( nil != sK2
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_26697,negated_conjecture,
( nil != sK2
| sK0 = nil ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_197,negated_conjecture,
( sK2 != nil
| sK0 = nil ),
inference(copy,[status(thm)],[c_26697]) ).
cnf(c_198,negated_conjecture,
( ~ segmentP(sK4,A)
| ~ segmentP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
sK0 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
ssList(sK0),
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_204,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_220,plain,
( nil = B
| app(A,B) != nil
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax83]) ).
cnf(c_286,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax28]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_300,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_302,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_1645,plain,
( ~ neq(sK3,nil)
| segmentP(sK0,sK1) ),
inference(paramod,[status(thm)],[c_200,c_190]) ).
cnf(c_1646,plain,
( ~ neq(sK3,nil)
| segmentP(sK2,sK1) ),
inference(paramod,[status(thm)],[c_200,c_191]) ).
cnf(c_1647,plain,
( ~ neq(sK3,nil)
| neq(sK1,nil) ),
inference(paramod,[status(thm)],[c_200,c_192]) ).
cnf(c_1648,plain,
( ~ neq(sK3,nil)
| ssList(sK1) ),
inference(paramod,[status(thm)],[c_200,c_193]) ).
cnf(c_1649,plain,
( sK3 != nil
| sK0 = nil ),
inference(paramod,[status(thm)],[c_200,c_197]) ).
cnf(c_26698,negated_conjecture,
( nil = sK4
| app(A,sK4) != nil
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_220,c_204]) ).
cnf(c_1690,negated_conjecture,
( sK4 = nil
| app(A,sK4) != nil
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_26698]) ).
cnf(c_1804,plain,
app(nil,sK0) = sK0,
inference(resolve,[status(thm)],[c_286,c_202]) ).
cnf(c_26699,negated_conjecture,
( A = sK3
| neq(sK3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_302,c_203]) ).
cnf(c_1860,negated_conjecture,
( sK3 = A
| neq(sK3,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_26699]) ).
cnf(c_5632,plain,
( sK4 = nil
| app(nil,sK4) != nil ),
inference(resolve,[status(thm)],[c_1690,c_300]) ).
cnf(c_5638,plain,
( sK3 = nil
| neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_1860,c_300]) ).
cnf(c_5662,plain,
( ssList(sK1)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_5638,c_1648]) ).
cnf(c_5663,plain,
( neq(sK1,nil)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_5638,c_1647]) ).
cnf(c_5664,plain,
( segmentP(sK2,sK1)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_5638,c_1646]) ).
cnf(c_5665,plain,
( segmentP(sK0,sK1)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_5638,c_1645]) ).
cnf(c_5835,plain,
( ~ segmentP(sK4,sK1)
| ~ segmentP(sK3,sK1)
| ~ ssList(sK1)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_5663,c_198]) ).
cnf(c_5852,plain,
( segmentP(sK3,sK1)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_200,c_5664]) ).
cnf(c_5900,plain,
( segmentP(sK4,sK1)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_199,c_5665]) ).
cnf(c_15854,plain,
app(nil,sK4) = sK0,
inference(paramod,[status(thm)],[c_199,c_1804]) ).
cnf(c_26700,plain,
( sK3 = nil
| ~ segmentP(sK4,sK1)
| ~ ssList(sK1)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_5835,c_5852]) ).
cnf(c_25746,plain,
( ~ segmentP(sK4,sK1)
| ~ ssList(sK1)
| sK3 = nil ),
inference(copy,[status(thm)],[c_26700]) ).
cnf(c_26701,plain,
( sK3 = nil
| ~ ssList(sK1)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_25746,c_5900]) ).
cnf(c_25748,plain,
( ~ ssList(sK1)
| sK3 = nil ),
inference(copy,[status(thm)],[c_26701]) ).
cnf(c_26702,plain,
( sK3 = nil
| sK3 = nil ),
inference(resolve,[status(thm)],[c_25748,c_5662]) ).
cnf(c_25750,plain,
sK3 = nil,
inference(copy,[status(thm)],[c_26702]) ).
cnf(c_25773,plain,
sK0 = nil,
inference(resolve,[status(thm)],[c_25750,c_1649]) ).
cnf(c_25774,negated_conjecture,
sK4 != nil,
inference(resolve,[status(thm)],[c_25750,c_195]) ).
cnf(c_26194,negated_conjecture,
app(nil,sK4) != nil,
inference(resolve,[status(thm)],[c_25774,c_5632]) ).
cnf(c_26703,plain,
sK0 != nil,
inference(paramod,[status(thm)],[c_15854,c_26194]) ).
cnf(c_26695,plain,
$false,
inference(resolve,[status(thm)],[c_25773,c_26703]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC069+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 12:10:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1216183 was started by sandbox on n006,
% 0.11/0.37 % Sat Sep 26 12:10:25 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 38.45/6.91
% 38.45/6.91 % given #500 (I,wt=49): 698 -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(366,a,f)].
% 38.45/6.91
% 38.45/6.91 % given #1000 (I,wt=67): 1223 -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(718,d,e)].
% 38.45/6.91
% 38.45/6.91 % given #1500 (T,wt=11): 1793 frontsegP(nil,c6) | c6 != nil. [resolve(259,a,201,a),flip(b)].
% 38.45/6.91
% 38.45/6.91 % given #2000 (A,wt=25): 1825 c6 = nil | cons(f43(c6),f42(c6)) = c6. [resolve(294,a,201,a),flip(a)].
% 38.45/6.91
% 38.45/6.91 % given #2500 (F,wt=24): 13549 cons(c2,f5(c3,c3)) != f5(c3,c3). [resolve(5016,a,2050,a)].
% 38.45/6.91
% 38.45/6.91 % given #3000 (W,wt=16): 2550 -ssList(A) | ssList(cons(c1,A)). [resolve(339,a,301,b)].
% 38.45/6.91
% 38.45/6.91 % SZS status Theorem for theBenchmark
% 38.45/6.91
% 38.45/6.91 % Proof 1 at 5.34 (+ 1.11) seconds.
% 38.45/6.91 % Length of proof is 47.
% 38.45/6.91 % Level of proof is 11.
% 38.45/6.91 % Maximum clause weight is 22.000.
% 38.45/6.91 % Given clauses 3135.
% 38.45/6.91
% 38.45/6.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------