%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC068+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 : n008.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 08:56:43 AM UTC 2026
% Result : Theorem 53.33s 8.16s
% Output : CNFRefutation 53.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 168 ( 69 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 187 ( 74 ~; 67 |; 25 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 20 !; 6 ?)
% 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(ax55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('theBenchmark.p',ax55) ).
fof(ax56,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
file('theBenchmark.p',ax56) ).
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)
=> ( ( nil = U
& nil = V )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X
| app(X,X) != W ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = U
& nil = V )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X
| app(X,X) != W ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != U
| nil != V )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& W = U
& X = V
& app(X,X) = W
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ( nil != sK1
| nil != sK0 )
& ! [Y] :
( ~ segmentP(sK1,Y)
| ~ segmentP(sK0,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK2 = sK1
& sK3 = sK0
& app(sK3,sK3) = sK2
& ssList(sK3)
& ssList(sK2)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2,sK3]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK2),skolemize(X,sK3)],[nnf_87]) ).
cnf(c_190,negated_conjecture,
( nil != sK1
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_5136,negated_conjecture,
( nil != sK1
| sK0 != nil ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_191,negated_conjecture,
( sK1 != nil
| sK0 != nil ),
inference(copy,[status(thm)],[c_5136]) ).
cnf(c_192,negated_conjecture,
( ~ segmentP(sK1,A)
| ~ segmentP(sK0,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
app(sK3,sK3) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_5137,negated_conjecture,
app(sK0,sK3) = sK2,
inference(paramod,[status(thm)],[c_194,c_195]) ).
cnf(c_5138,negated_conjecture,
app(sK0,sK0) = sK2,
inference(paramod,[status(thm)],[c_194,c_5137]) ).
cnf(c_196,negated_conjecture,
app(sK0,sK0) = sK1,
inference(paramod,[status(thm)],[c_193,c_5138]) ).
cnf(c_197,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_194,c_197]) ).
cnf(c_214,plain,
( nil != A
| nil != B
| app(A,B) = nil
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax83]) ).
cnf(c_244,plain,
( segmentP(app(app(C,A),D),B)
| ~ segmentP(A,B)
| ~ ssList(D)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax56]) ).
cnf(c_245,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax55]) ).
cnf(c_282,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax28]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_296,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_298,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_5139,plain,
( nil != A
| nil != A
| app(A,A) = nil
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_214]) ).
cnf(c_549,plain,
( nil != A
| app(A,A) = nil
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_5139]) ).
cnf(c_558,plain,
( segmentP(app(app(B,A),C),A)
| ~ segmentP(A,A)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_244]) ).
cnf(c_1038,plain,
( segmentP(app(app(B,A),A),A)
| ~ segmentP(A,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_558]) ).
cnf(c_1725,plain,
segmentP(sK0,sK0),
inference(resolve,[status(thm)],[c_245,c_198]) ).
cnf(c_1740,plain,
app(nil,sK0) = sK0,
inference(resolve,[status(thm)],[c_282,c_198]) ).
cnf(c_5140,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_298,c_198]) ).
cnf(c_5141,negated_conjecture,
( nil = sK0
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_5140,c_296]) ).
cnf(c_1797,negated_conjecture,
( sK0 = nil
| neq(sK0,nil) ),
inference(copy,[status(thm)],[c_5141]) ).
cnf(c_5142,negated_conjecture,
( nil != sK0
| app(sK0,sK0) = nil ),
inference(resolve,[status(thm)],[c_549,c_198]) ).
cnf(c_5143,negated_conjecture,
( nil != sK0
| sK1 = nil ),
inference(paramod,[status(thm)],[c_196,c_5142]) ).
cnf(c_4087,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_5143]) ).
cnf(c_5144,negated_conjecture,
( segmentP(app(app(A,sK0),sK0),sK0)
| ~ segmentP(sK0,sK0)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_1038,c_198]) ).
cnf(c_5145,negated_conjecture,
( segmentP(app(app(nil,sK0),sK0),sK0)
| ~ segmentP(sK0,sK0) ),
inference(resolve,[status(thm)],[c_5144,c_296]) ).
cnf(c_5146,negated_conjecture,
segmentP(app(app(nil,sK0),sK0),sK0),
inference(resolve,[status(thm)],[c_5145,c_1725]) ).
cnf(c_5147,negated_conjecture,
segmentP(app(sK0,sK0),sK0),
inference(paramod,[status(thm)],[c_1740,c_5146]) ).
cnf(c_4751,negated_conjecture,
segmentP(sK1,sK0),
inference(paramod,[status(thm)],[c_196,c_5147]) ).
cnf(c_5148,negated_conjecture,
( ~ segmentP(sK1,sK0)
| ~ segmentP(sK0,sK0)
| ~ ssList(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_1797,c_192]) ).
cnf(c_5149,negated_conjecture,
( ~ segmentP(sK1,sK0)
| ~ segmentP(sK0,sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_198,c_5148]) ).
cnf(c_5150,negated_conjecture,
( ~ segmentP(sK1,sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_1725,c_5149]) ).
cnf(c_5127,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_4751,c_5150]) ).
cnf(c_5151,negated_conjecture,
( nil != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_5127,c_4087]) ).
cnf(c_5132,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_5151]) ).
cnf(c_5152,negated_conjecture,
( sK1 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_5127,c_191]) ).
cnf(c_5153,negated_conjecture,
( nil != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_5132,c_5152]) ).
cnf(c_5154,negated_conjecture,
nil != nil,
inference(copy,[status(thm)],[c_5153]) ).
cnf(c_5135,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_5154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC068+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 12:11:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3612927 was started by sandbox2 on n008,
% 0.08/0.36 % Sat Sep 26 12:11:24 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 53.33/8.16
% 53.33/8.16 % given #500 (I,wt=52): 700 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,A)),cons(C,E)) != A | C != B | ssList(f36(A)). [factor(364,a,e)].
% 53.33/8.16
% 53.33/8.16 % given #1000 (I,wt=73): 1225 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,D)),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)].
% 53.33/8.16
% 53.33/8.16 % SZS status Theorem for theBenchmark
% 53.33/8.16
% 53.33/8.16 % Proof 1 at 7.26 (+ 0.25) seconds.
% 53.33/8.16 % Length of proof is 32.
% 53.33/8.16 % Level of proof is 7.
% 53.33/8.16 % Maximum clause weight is 38.000.
% 53.33/8.16 % Given clauses 1434.
% 53.33/8.16
% 53.33/8.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------