%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC398+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 : n014.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 08:57:42 AM UTC 2026
% Result : Theorem 35.42s 5.70s
% Output : CNFRefutation 35.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 128 ( 40 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 150 ( 45 ~; 40 |; 49 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 24 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('theBenchmark.p',ax36) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = W
& nil != X )
| ! [X3] :
( ssItem(X3)
=> ( memberP(V,X3)
| ~ memberP(U,X3) ) )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(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)
=> ( ( nil = W
& nil != X )
| ! [X3] :
( ssItem(X3)
=> ( memberP(V,X3)
| ~ memberP(U,X3) ) )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != X ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_258,plain,
( ~ memberP(B,A)
| memberP(app(B,C),A)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax36]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ? [X3] :
( ~ memberP(V,X3)
& memberP(U,X3)
& ssItem(X3) )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(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,
( ( nil != sK3
| nil = sK1 )
& ~ memberP(sK2,sK5)
& memberP(sK0,sK5)
& ssItem(sK5)
& ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != sK3
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != sK4
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(sK3)
& app(sK3,sK4) = sK1
& ssList(sK4)
& sK3 = sK0
& sK1 = sK2
& ssList(sK1)
& ssList(sK3)
& ssList(sK2)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK3,sK1,sK4,sK5]),skolemize(U,sK0),skolemize(V,sK2),skolemize(W,sK3),skolemize(X,sK1),skolemize(Y,sK4),skolemize(X3,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( nil != sK3
| nil = sK1 )
& ~ memberP(sK2,sK5)
& memberP(sK0,sK5)
& ssItem(sK5)
& ! [VAR_0,VAR_1,VAR_2] :
( app(VAR_2,cons(VAR_0,nil)) != sK3
| ~ ssList(VAR_2)
| app(cons(VAR_0,nil),VAR_1) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& equalelemsP(sK3)
& app(sK3,sK4) = sK1
& ssList(sK4)
& sK3 = sK0
& sK1 = sK2
& ssList(sK1)
& ssList(sK3)
& ssList(sK2)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_329,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_335,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
app(sK3,sK4) = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3742,negated_conjecture,
app(sK0,sK4) = sK1,
inference(paramod,[status(thm)],[c_334,c_336]) ).
cnf(c_337,negated_conjecture,
app(sK0,sK4) = sK2,
inference(paramod,[status(thm)],[c_333,c_3742]) ).
cnf(c_340,negated_conjecture,
ssItem(sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_341,negated_conjecture,
memberP(sK0,sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_342,negated_conjecture,
~ memberP(sK2,sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3743,negated_conjecture,
( ~ memberP(A,sK5)
| memberP(app(A,B),sK5)
| ~ ssList(B)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_258,c_340]) ).
cnf(c_3744,negated_conjecture,
( ~ memberP(sK0,sK5)
| memberP(app(sK0,A),sK5)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_3743,c_329]) ).
cnf(c_3745,negated_conjecture,
( ~ memberP(sK0,sK5)
| memberP(app(sK0,sK4),sK5) ),
inference(resolve,[status(thm)],[c_3744,c_335]) ).
cnf(c_3746,negated_conjecture,
memberP(app(sK0,sK4),sK5),
inference(resolve,[status(thm)],[c_3745,c_341]) ).
cnf(c_3747,negated_conjecture,
memberP(sK2,sK5),
inference(paramod,[status(thm)],[c_337,c_3746]) ).
cnf(c_3741,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_342,c_3747]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC398+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 12:58:02 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3209981 was started by sandbox2 on n014,
% 0.10/0.38 % Sat Sep 26 12:58:02 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.41
% 0.14/0.41 % From the command line: assign(max_seconds, 300).
% 35.42/5.70
% 35.42/5.70 % SZS status Theorem for theBenchmark
% 35.42/5.70
% 35.42/5.70 % Proof 1 at 4.60 (+ 0.14) seconds.
% 35.42/5.70 % Length of proof is 13.
% 35.42/5.70 % Level of proof is 3.
% 35.42/5.70 % Maximum clause weight is 24.000.
% 35.42/5.70 % Given clauses 165.
% 35.42/5.70
% 35.42/5.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------