%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC100+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 : n016.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 08:56:49 AM UTC 2026
% Result : Theorem 95.93s 18.50s
% Output : CNFRefutation 95.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 18 unt; 0 def)
% Number of atoms : 241 ( 101 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 284 ( 104 ~; 100 |; 59 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 30 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('theBenchmark.p',ax42) ).
fof(ax43,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
file('theBenchmark.p',ax43) ).
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)
=> ( ( ( ( frontsegP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != 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)
=> ( ( ( ( frontsegP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ( ~ frontsegP(V,U)
| ~ neq(U,nil) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ lt(X2,Z)
| app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(W)
& app(W,Y) = X
& 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,
( ( ( ( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( nil != sK3
| nil = sK2 )
& ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ lt(X2,Z)
| app(X3,cons(X2,nil)) != sK3
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != sK4
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(sK3)
& app(sK3,sK4) = sK2
& 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]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil)
| nil != sK0 )
& ( neq(sK1,nil)
| nil != sK0 )
& ( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& ( nil != sK3
| nil = sK2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ lt(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) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& strictorderedP(sK3)
& app(sK3,sK4) = sK2
& 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,
( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil)
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil)
| sK0 != nil ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_192,negated_conjecture,
( neq(sK1,nil)
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( neq(sK1,nil)
| sK0 != nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_194,negated_conjecture,
( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil)
| sK1 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_198,negated_conjecture,
( nil != sK3
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_55984,negated_conjecture,
( nil != sK3
| sK2 = nil ),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_199,negated_conjecture,
( sK3 != nil
| sK2 = nil ),
inference(copy,[status(thm)],[c_55984]) ).
cnf(c_202,negated_conjecture,
app(sK3,sK4) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_204,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_208,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_209,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_204,c_208]) ).
cnf(c_224,plain,
( nil = A
| app(A,B) != nil
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax83]) ).
cnf(c_270,plain,
( frontsegP(app(A,C),B)
| ~ frontsegP(A,B)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax43]) ).
cnf(c_271,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax42]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_305,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_307,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_55985,negated_conjecture,
app(sK0,sK4) = sK2,
inference(paramod,[status(thm)],[c_204,c_202]) ).
cnf(c_555,negated_conjecture,
app(sK0,sK4) = sK1,
inference(paramod,[status(thm)],[c_205,c_55985]) ).
cnf(c_55986,negated_conjecture,
( sK3 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_205,c_199]) ).
cnf(c_558,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_204,c_55986]) ).
cnf(c_585,plain,
( frontsegP(app(A,B),A)
| ~ frontsegP(A,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_270]) ).
cnf(c_55987,negated_conjecture,
( nil = sK0
| app(sK0,A) != nil
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_224,c_209]) ).
cnf(c_1676,negated_conjecture,
( sK0 = nil
| app(sK0,A) != nil
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_55987]) ).
cnf(c_1766,plain,
frontsegP(sK0,sK0),
inference(resolve,[status(thm)],[c_271,c_209]) ).
cnf(c_55988,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_307,c_209]) ).
cnf(c_1818,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_55988]) ).
cnf(c_55989,plain,
( frontsegP(app(sK0,A),sK0)
| ~ ssList(A)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_1766,c_585]) ).
cnf(c_4923,negated_conjecture,
( frontsegP(app(sK0,A),sK0)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_209,c_55989]) ).
cnf(c_55990,negated_conjecture,
( sK0 = nil
| app(sK0,sK4) != nil ),
inference(resolve,[status(thm)],[c_1676,c_203]) ).
cnf(c_9816,negated_conjecture,
( sK0 = nil
| sK1 != nil ),
inference(paramod,[status(thm)],[c_555,c_55990]) ).
cnf(c_28137,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_1818,c_305]) ).
cnf(c_47113,plain,
( ~ frontsegP(sK1,sK0)
| sK1 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_28137,c_195]) ).
cnf(c_55991,negated_conjecture,
frontsegP(app(sK0,sK4),sK0),
inference(resolve,[status(thm)],[c_4923,c_203]) ).
cnf(c_55821,negated_conjecture,
frontsegP(sK1,sK0),
inference(paramod,[status(thm)],[c_555,c_55991]) ).
cnf(c_55822,plain,
( sK1 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_55821,c_47113]) ).
cnf(c_55824,negated_conjecture,
( ~ neq(sK0,nil)
| sK0 != nil ),
inference(resolve,[status(thm)],[c_55821,c_191]) ).
cnf(c_55992,plain,
( sK0 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_55822,c_9816]) ).
cnf(c_55942,plain,
sK0 = nil,
inference(copy,[status(thm)],[c_55992]) ).
cnf(c_55993,negated_conjecture,
( ~ neq(sK0,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_55942,c_55824]) ).
cnf(c_55994,negated_conjecture,
( ~ neq(nil,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_55942,c_55993]) ).
cnf(c_55943,negated_conjecture,
~ neq(nil,nil),
inference(copy,[status(thm)],[c_55994]) ).
cnf(c_55995,negated_conjecture,
( nil != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_55942,c_558]) ).
cnf(c_55979,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_55995]) ).
cnf(c_55996,negated_conjecture,
( neq(sK1,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_55942,c_193]) ).
cnf(c_55997,negated_conjecture,
( neq(nil,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_55979,c_55996]) ).
cnf(c_55998,negated_conjecture,
neq(nil,nil),
inference(copy,[status(thm)],[c_55997]) ).
cnf(c_55983,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_55943,c_55998]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC100+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n016.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 12:20:05 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 848457 was started by sandbox2 on n016,
% 0.10/5.38 % Sat Sep 26 12:20:05 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.40
% 0.14/5.40 % From the command line: assign(max_seconds, 300).
% 95.93/18.50
% 95.93/18.50 % given #500 (I,wt=27): 707 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,A)),cons(C,E)) != A | C != B | ssList(f35(A)). [factor(371,a,e)].
% 95.93/18.50
% 95.93/18.50 % given #1000 (I,wt=35): 1232 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,A)),cons(B,D)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(728,b,c),xx(f)].
% 95.93/18.50
% 95.93/18.50 % given #1500 (T,wt=4): 4921 ssList(f4(c3,c3)). [resolve(1766,a,628,b),unit_del(a,209)].
% 95.93/18.50
% 95.93/18.50 % given #2000 (F,wt=7): 15365 app(cons(c2,c7),c4) != nil. [resolve(14880,a,1680,a),flip(b),unit_del(b,4838)].
% 95.93/18.50
% 95.93/18.50 % given #2500 (T,wt=6): 13255 ssList(app(c7,f5(c7,c7))). [resolve(1774,a,4889,a)].
% 95.93/18.50
% 95.93/18.50 % given #3000 (F,wt=9): 24921 app(cons(c2,c7),f7(c7,nil)) != nil. [resolve(15437,a,4820,a)].
% 95.93/18.50
% 95.93/18.50 % SZS status Theorem for theBenchmark
% 95.93/18.50
% 95.93/18.50 % Proof 1 at 10.35 (+ 2.67) seconds.
% 95.93/18.50 % Length of proof is 41.
% 95.93/18.50 % Level of proof is 9.
% 95.93/18.50 % Maximum clause weight is 14.000.
% 95.93/18.50 % Given clauses 3400.
% 95.93/18.50
% 95.93/18.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------