%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC118+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 : n009.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 100.92s 29.43s
% Output : CNFRefutation 100.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 235 ( 92 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 296 ( 108 ~; 96 |; 74 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 40 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('theBenchmark.p',ax7) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( segmentP(V,U)
& neq(U,nil) )
| ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| 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(V,U)
& neq(U,nil) )
| ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& ( nil != U
| nil != V )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ leq(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& 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,
( ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) )
& ( nil != sK0
| nil != sK1 )
& ( nil != sK3
| nil = sK2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != sK3
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != sK5
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ leq(X1,X3)
| app(cons(X3,nil),X4) != sK3
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != sK4
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(sK3)
& app(app(sK4,sK3),sK5) = sK2
& ssList(sK5)
& ssList(sK4)
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2,sK4,sK5]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK4),skolemize(Z,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) )
& ( nil != sK0
| nil != sK1 )
& ( nil != sK3
| nil = sK2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ leq(VAR_2,VAR_0)
| app(VAR_3,cons(VAR_2,nil)) != sK3
| ~ ssList(VAR_3)
| ~ ssItem(VAR_2)
| app(cons(VAR_0,nil),VAR_1) != sK5
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ leq(VAR_0,VAR_2)
| app(cons(VAR_2,nil),VAR_3) != sK3
| ~ ssList(VAR_3)
| ~ ssItem(VAR_2)
| app(VAR_1,cons(VAR_0,nil)) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& totalorderedP(sK3)
& app(app(sK4,sK3),sK5) = sK2
& ssList(sK5)
& ssList(sK4)
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( nil != sK0
| nil != sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3016,negated_conjecture,
( nil != sK0
| sK1 != nil ),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_192,negated_conjecture,
( sK0 != nil
| sK1 != nil ),
inference(copy,[status(thm)],[c_3016]) ).
cnf(c_193,negated_conjecture,
( nil != sK3
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3017,negated_conjecture,
( nil != sK3
| sK2 = nil ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_194,negated_conjecture,
( sK3 != nil
| sK2 = nil ),
inference(copy,[status(thm)],[c_3017]) ).
cnf(c_198,negated_conjecture,
app(app(sK4,sK3),sK5) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
ssList(sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_204,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_202,c_203]) ).
cnf(c_205,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_206,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_201,c_205]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_302,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_304,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_322,plain,
( app(app(C,B),D) != A
| ~ ssList(D)
| ~ ssList(C)
| segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax7]) ).
cnf(c_3018,negated_conjecture,
app(app(sK4,sK0),sK5) = sK2,
inference(paramod,[status(thm)],[c_201,c_198]) ).
cnf(c_555,negated_conjecture,
app(app(sK4,sK0),sK5) = sK1,
inference(paramod,[status(thm)],[c_202,c_3018]) ).
cnf(c_3019,negated_conjecture,
( sK3 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_202,c_194]) ).
cnf(c_559,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_201,c_3019]) ).
cnf(c_3020,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_304,c_206]) ).
cnf(c_2152,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_3020]) ).
cnf(c_3021,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0)
| ~ ssList(sK0)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_555,c_322]) ).
cnf(c_3022,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_204,c_3021]) ).
cnf(c_3023,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_206,c_3022]) ).
cnf(c_3024,negated_conjecture,
( ~ ssList(sK5)
| segmentP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_200,c_3023]) ).
cnf(c_2526,negated_conjecture,
segmentP(sK1,sK0),
inference(resolve,[status(thm)],[c_199,c_3024]) ).
cnf(c_2527,negated_conjecture,
~ neq(sK0,nil),
inference(resolve,[status(thm)],[c_2526,c_190]) ).
cnf(c_3025,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_2152,c_302]) ).
cnf(c_3009,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_2527,c_3025]) ).
cnf(c_3026,negated_conjecture,
( nil != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_3009,c_559]) ).
cnf(c_3012,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_3026]) ).
cnf(c_3027,negated_conjecture,
( sK0 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_3012,c_192]) ).
cnf(c_3028,negated_conjecture,
( nil != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_3009,c_3027]) ).
cnf(c_3029,negated_conjecture,
nil != nil,
inference(copy,[status(thm)],[c_3028]) ).
cnf(c_3015,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_3029]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC118+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.34 % Computer : n009.cluster.edu
% 0.05/0.34 % Model : x86_64 x86_64
% 0.05/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.34 % Memory : 8046.5625MB
% 0.05/0.34 % OS : Linux 6.8.0-71-generic
% 0.05/0.34 % CPULimit : 300
% 0.05/0.34 % WCLimit : 300
% 0.05/0.34 % DateTime : Sat Sep 26 12:17:29 UTC 2026
% 0.05/0.34 % CPUTime :
% 0.05/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.35 % Process 85086 was started by sandbox on n009,
% 0.05/0.35 % Sat Sep 26 12:17:29 2026
% 0.05/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/0.37
% 0.05/0.37 % From the command line: assign(max_seconds, 300).
% 100.92/29.43
% 100.92/29.43 % given #500 (I,wt=49): 697 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,D)),cons(C,E)) != A | C != B | ssItem(f33(A)). [factor(364,d,e)].
% 100.92/29.43
% 100.92/29.43 % given #1000 (I,wt=47): 1217 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(A,cons(B,A)),cons(C,D)) != A | C != B | ssList(f37(A)). [factor(721,a,d)].
% 100.92/29.43
% 100.92/29.43 % given #1500 (T,wt=11): 1881 -frontsegP(nil,c8) | c8 = nil. [resolve(262,a,199,a),flip(b)].
% 100.92/29.43
% 100.92/29.43 % SZS status Theorem for theBenchmark
% 100.92/29.43
% 100.92/29.43 % Proof 1 at 1.74 (+ 0.32) seconds.
% 100.92/29.43 % Length of proof is 28.
% 100.92/29.43 % Level of proof is 7.
% 100.92/29.43 % Maximum clause weight is 35.000.
% 100.92/29.43 % Given clauses 1512.
% 100.92/29.43
% 100.92/29.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------