%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC076+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 : 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 08:56:45 AM UTC 2026
% Result : Theorem 34.10s 15.32s
% Output : CNFRefutation 34.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 20 unt; 0 def)
% Number of atoms : 237 ( 92 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 295 ( 110 ~; 96 |; 70 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 38 !; 22 ?)
% 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(ax55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('theBenchmark.p',ax55) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = W
& ssList(X7) )
& app(cons(X5,nil),X6) = X1
& ssList(X6) )
& ssItem(X5) )
| ? [X2] :
( ? [X3] :
( ? [X4] :
( app(cons(X2,nil),X4) = W
& ssList(X4) )
& app(X3,cons(X2,nil)) = Z
& ssList(X3) )
& ssItem(X2) )
| ~ equalelemsP(W)
| app(app(Z,W),X1) != X ) ) )
| ? [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)
=> ( ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = W
& ssList(X7) )
& app(cons(X5,nil),X6) = X1
& ssList(X6) )
& ssItem(X5) )
| ? [X2] :
( ? [X3] :
( ? [X4] :
( app(cons(X2,nil),X4) = W
& ssList(X4) )
& app(X3,cons(X2,nil)) = Z
& ssList(X3) )
& ssItem(X2) )
| ~ equalelemsP(W)
| app(app(Z,W),X1) != X ) ) )
| ? [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] :
( ( nil != U
| nil != V )
& ( nil != W
| nil = X )
& ? [Z] :
( ? [X1] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != W
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X1
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X2] :
( ! [X3] :
( ! [X4] :
( app(cons(X2,nil),X4) != W
| ~ ssList(X4) )
| app(X3,cons(X2,nil)) != Z
| ~ ssList(X3) )
| ~ ssItem(X2) )
& equalelemsP(W)
& app(app(Z,W),X1) = X
& ssList(X1) )
& ssList(Z) )
& ! [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,
( ( nil != sK1
| nil != sK0 )
& ( nil != sK3
| nil = sK2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK3
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK5
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X2] :
( ! [X3] :
( ! [X4] :
( app(cons(X2,nil),X4) != sK3
| ~ ssList(X4) )
| app(X3,cons(X2,nil)) != sK4
| ~ ssList(X3) )
| ~ ssItem(X2) )
& equalelemsP(sK3)
& app(app(sK4,sK3),sK5) = sK2
& ssList(sK5)
& ssList(sK4)
& ! [Y] :
( ~ segmentP(sK1,Y)
| ~ segmentP(sK0,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK3 = sK1
& sK2 = sK0
& ssList(sK2)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK3,sK2,sK4,sK5]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK3),skolemize(X,sK2),skolemize(Z,sK4),skolemize(X1,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( nil != sK1
| nil != sK0 )
& ( nil != sK3
| nil = sK2 )
& ! [VAR_0,VAR_1,VAR_2] :
( app(VAR_2,cons(VAR_0,nil)) != sK3
| ~ ssList(VAR_2)
| app(cons(VAR_0,nil),VAR_1) != sK5
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( app(cons(VAR_0,nil),VAR_2) != sK3
| ~ ssList(VAR_2)
| app(VAR_1,cons(VAR_0,nil)) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& equalelemsP(sK3)
& app(app(sK4,sK3),sK5) = sK2
& ssList(sK5)
& ssList(sK4)
& ! [VAR_0] :
( ~ segmentP(sK1,VAR_0)
| ~ segmentP(sK0,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) )
& sK3 = sK1
& sK2 = sK0
& ssList(sK2)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( nil != sK1
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_15980,negated_conjecture,
( nil != sK1
| sK0 != nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_193,negated_conjecture,
( sK1 != nil
| sK0 != nil ),
inference(copy,[status(thm)],[c_15980]) ).
cnf(c_194,negated_conjecture,
( nil != sK3
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_15981,negated_conjecture,
( nil != sK3
| sK2 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_195,negated_conjecture,
( sK3 != nil
| sK2 = nil ),
inference(copy,[status(thm)],[c_15981]) ).
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,
( ~ segmentP(sK1,A)
| ~ segmentP(sK0,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
sK3 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
sK2 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_204,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_203,c_204]) ).
cnf(c_206,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_202,c_206]) ).
cnf(c_252,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax55]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_303,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_305,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_323,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_15982,negated_conjecture,
app(app(sK4,sK1),sK5) = sK2,
inference(paramod,[status(thm)],[c_202,c_198]) ).
cnf(c_557,negated_conjecture,
app(app(sK4,sK1),sK5) = sK0,
inference(paramod,[status(thm)],[c_203,c_15982]) ).
cnf(c_15983,negated_conjecture,
( sK3 != nil
| sK0 = nil ),
inference(paramod,[status(thm)],[c_203,c_195]) ).
cnf(c_560,negated_conjecture,
( sK1 != nil
| sK0 = nil ),
inference(paramod,[status(thm)],[c_202,c_15983]) ).
cnf(c_4343,plain,
( ~ segmentP(sK1,sK1)
| ~ segmentP(sK0,sK1)
| ~ neq(sK1,nil) ),
inference(resolve,[status(thm)],[c_207,c_201]) ).
cnf(c_5421,plain,
segmentP(sK1,sK1),
inference(resolve,[status(thm)],[c_252,c_207]) ).
cnf(c_5425,plain,
( ~ segmentP(sK0,sK1)
| ~ neq(sK1,nil) ),
inference(resolve,[status(thm)],[c_5421,c_4343]) ).
cnf(c_15984,negated_conjecture,
( A = sK1
| neq(sK1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_305,c_207]) ).
cnf(c_6476,negated_conjecture,
( sK1 = A
| neq(sK1,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_15984]) ).
cnf(c_15985,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK0,sK1)
| ~ ssList(sK1)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_557,c_323]) ).
cnf(c_15986,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK0,sK1)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_205,c_15985]) ).
cnf(c_15987,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_207,c_15986]) ).
cnf(c_15988,negated_conjecture,
( ~ ssList(sK5)
| segmentP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_200,c_15987]) ).
cnf(c_12542,negated_conjecture,
segmentP(sK0,sK1),
inference(resolve,[status(thm)],[c_199,c_15988]) ).
cnf(c_12543,plain,
~ neq(sK1,nil),
inference(resolve,[status(thm)],[c_12542,c_5425]) ).
cnf(c_15989,plain,
( sK1 = nil
| neq(sK1,nil) ),
inference(resolve,[status(thm)],[c_6476,c_303]) ).
cnf(c_15933,plain,
sK1 = nil,
inference(resolve,[status(thm)],[c_12543,c_15989]) ).
cnf(c_15990,negated_conjecture,
( nil != nil
| sK0 = nil ),
inference(paramod,[status(thm)],[c_15933,c_560]) ).
cnf(c_15971,negated_conjecture,
sK0 = nil,
inference(copy,[status(thm)],[c_15990]) ).
cnf(c_15991,negated_conjecture,
( sK1 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_15971,c_193]) ).
cnf(c_15992,negated_conjecture,
( nil != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_15933,c_15991]) ).
cnf(c_15993,negated_conjecture,
nil != nil,
inference(copy,[status(thm)],[c_15992]) ).
cnf(c_15979,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_15993]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC076+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n009.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Sat Sep 26 12:11:42 UTC 2026
% 0.08/10.38 % CPUTime :
% 0.08/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.38 % Process 63009 was started by sandbox2 on n009,
% 0.08/10.38 % Sat Sep 26 12:11:42 2026
% 0.08/10.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/10.40
% 0.13/10.40 % From the command line: assign(max_seconds, 300).
% 34.10/15.32
% 34.10/15.32 % given #500 (I,wt=49): 706 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,D)),cons(C,E)) != A | C != B | ssItem(f34(A)). [factor(367,d,e)].
% 34.10/15.32
% 34.10/15.32 % given #1000 (I,wt=64): 1237 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,A)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(732,b,c),xx(f)].
% 34.10/15.32
% 34.10/15.32 % SZS status Theorem for theBenchmark
% 34.10/15.32
% 34.10/15.32 % Proof 1 at 4.39 (+ 0.48) seconds.
% 34.10/15.32 % Length of proof is 33.
% 34.10/15.32 % Level of proof is 8.
% 34.10/15.32 % Maximum clause weight is 35.000.
% 34.10/15.32 % Given clauses 1486.
% 34.10/15.32
% 34.10/15.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------